From e47c6ae1846da7f6d47361569dfc056435071aa6 Mon Sep 17 00:00:00 2001 From: Robitzsch Date: Mon, 9 Sep 2024 16:18:10 +0200 Subject: [PATCH] 4.3-4 --- DESCRIPTION | 4 +- R/RcppExports.R | 2 +- R/tam.jml.R | 14 +- R/tam.mml.2pl.R | 2 +- R/tam_jml_version1.R | 41 +- R/tam_jml_wle.R | 22 +- R/tam_mml_2pl_mstep_slope.R | 16 +- README.md | 4 +- docs/404.html | 119 +- docs/authors.html | 142 +- docs/index.html | 94 +- docs/pkgdown.css | 87 +- docs/pkgdown.js | 4 +- docs/pkgdown.yml | 8 +- docs/reference/DescribeBy.html | 139 +- docs/reference/IRT.WrightMap.html | 519 ++- docs/reference/IRT.cv.html | 141 +- docs/reference/IRT.data.tam.html | 201 +- docs/reference/IRT.drawPV.html | 187 +- docs/reference/IRT.expectedCounts.tam.html | 207 +- docs/reference/IRT.factor.scores.tam.html | 222 +- docs/reference/IRT.frequencies.tam.html | 208 +- docs/reference/IRT.informationCurves.html | 384 +- docs/reference/IRT.irfprob.tam.html | 191 +- docs/reference/IRT.itemfit.html | 283 +- docs/reference/IRT.likelihood.tam.html | 239 +- docs/reference/IRT.linearCFA.html | 195 +- docs/reference/IRT.residuals.html | 267 +- docs/reference/IRT.simulate.html | 392 +- docs/reference/IRT.threshold.html | 342 +- docs/reference/IRT.truescore.html | 270 +- docs/reference/IRTLikelihood.cfa.html | 299 +- docs/reference/IRTLikelihood.ctt.html | 244 +- docs/reference/Scale.html | 139 +- docs/reference/TAM-defunct.html | 136 +- docs/reference/TAM-package.html | 142 +- docs/reference/TAM-utilities.html | 665 ++-- docs/reference/WLErel.html | 205 +- docs/reference/anova.tam.html | 295 +- docs/reference/cfa.extract.itempars.html | 298 +- docs/reference/data.cqc.html | 598 ++- docs/reference/data.ctest.html | 175 +- docs/reference/data.examples.html | 278 +- docs/reference/data.fims.Aus.Jpn.html | 286 +- docs/reference/data.geiser.html | 462 +-- docs/reference/data.gpcm.html | 144 +- docs/reference/data.janssen.html | 271 +- docs/reference/data.mc.html | 135 +- docs/reference/data.numeracy.html | 286 +- docs/reference/data.sim.mfr.html | 273 +- docs/reference/data.sim.rasch.html | 236 +- docs/reference/data.timssAusTwn.html | 328 +- docs/reference/designMatrices.html | 333 +- docs/reference/doparse.html | 320 +- docs/reference/index.html | 406 +- docs/reference/lavaanify.IRT.html | 594 ++- docs/reference/msq.itemfit.html | 462 +-- docs/reference/plot.tam.html | 397 +- docs/reference/plotDevianceTAM.html | 190 +- docs/reference/predict.html | 183 +- docs/reference/tam.ctt.html | 433 +- docs/reference/tam.fa.html | 384 +- docs/reference/tam.fit.html | 575 ++- docs/reference/tam.jml.html | 613 ++- docs/reference/tam.latreg.html | 343 +- docs/reference/tam.linking.html | 762 ++-- docs/reference/tam.mml.3pl.html | 653 ++- docs/reference/tam.mml.html | 4191 ++++++++++---------- docs/reference/tam.modelfit.html | 494 +-- docs/reference/tam.np.html | 564 ++- docs/reference/tam.personfit.html | 173 +- docs/reference/tam.pv.html | 1187 +++--- docs/reference/tam.se.html | 300 +- docs/reference/tam.threshold.html | 311 +- docs/reference/tam.wle.html | 759 ++-- docs/reference/tam_NA_pattern.html | 186 +- docs/reference/tam_downcode.html | 197 +- docs/reference/tam_irf_3pl.html | 210 +- docs/reference/tamaan.html | 1070 +++-- docs/reference/tamaanify.html | 615 ++- docs/reference/tampv2datalist.html | 188 +- docs/reference/weighted_Stats.html | 231 +- docs/sitemap.xml | 216 + inst/NEWS | 9 +- man/IRT.residuals.Rd | 7 +- man/IRT.threshold.Rd | 9 +- man/tam.jml.Rd | 40 +- man/tam.wle.Rd | 5 +- src/RcppExports.cpp | 2 +- src/init.c | 2 +- 90 files changed, 11810 insertions(+), 16645 deletions(-) create mode 100644 docs/sitemap.xml diff --git a/DESCRIPTION b/DESCRIPTION index 7d24546..e144082 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -1,8 +1,8 @@ Package: TAM Type: Package Title: Test Analysis Modules -Version: 4.3-2 -Date: 2024-02-20 00:16:18 +Version: 4.3-4 +Date: 2024-09-09 14:17:19 Author: Alexander Robitzsch [aut,cre] (), Thomas Kiefer [aut], diff --git a/R/RcppExports.R b/R/RcppExports.R index ef6beb1..149f5ef 100644 --- a/R/RcppExports.R +++ b/R/RcppExports.R @@ -1,5 +1,5 @@ ## File Name: RcppExports.R -## File Version: 4.003002 +## File Version: 4.003004 # Generated by using Rcpp::compileAttributes() -> do not edit by hand # Generator token: 10BE3573-1514-4C36-9D1C-5A225CD40393 diff --git a/R/tam.jml.R b/R/tam.jml.R index 8030eb8..0adc7a3 100644 --- a/R/tam.jml.R +++ b/R/tam.jml.R @@ -1,11 +1,11 @@ ## File Name: tam.jml.R -## File Version: 9.367 +## File Version: 9.373 tam.jml <- function( resp, group=NULL, adj=.3, disattenuate=FALSE, - bias=TRUE, xsi.fixed=NULL, xsi.inits=NULL, theta.fixed=NULL, + bias=TRUE, xsi.fixed=NULL, xsi.inits=NULL, theta.fixed=NULL, A=NULL, B=NULL, Q=NULL, ndim=1, - pweights=NULL, constraint="cases", + pweights=NULL, constraint="cases", theta_proc=NULL, verbose=TRUE, control=list(), version=3 ) { CALL <- match.call() @@ -23,13 +23,19 @@ tam.jml <- function( resp, group=NULL, adj=.3, disattenuate=FALSE, } } + #*** theta_proc + if (!is.null(theta_proc)){ + version <- 1 + } + #**** version=1 if (version==1){ constraint <- "cases" res <- tam_jml_version1( resp=resp, group=group, adj=adj, disattenuate=disattenuate, bias=bias, xsi.fixed=xsi.fixed, xsi.inits=xsi.inits, A=A, B=B, Q=Q, ndim=ndim, - theta.fixed=theta.fixed, pweights=pweights, control=control ) + theta.fixed=theta.fixed, pweights=pweights, control=control, + theta_proc=theta_proc) } #**** version=2 if (version>=2){ diff --git a/R/tam.mml.2pl.R b/R/tam.mml.2pl.R index cfcc6c7..9298453 100644 --- a/R/tam.mml.2pl.R +++ b/R/tam.mml.2pl.R @@ -1,5 +1,5 @@ ## File Name: tam.mml.2pl.R -## File Version: 9.589 +## File Version: 9.593 tam.mml.2pl <- function( resp, Y=NULL, group=NULL, irtmodel="2PL", formulaY=NULL, dataY=NULL, diff --git a/R/tam_jml_version1.R b/R/tam_jml_version1.R index dcb9f28..65f2b00 100644 --- a/R/tam_jml_version1.R +++ b/R/tam_jml_version1.R @@ -1,11 +1,11 @@ ## File Name: tam_jml_version1.R -## File Version: 9.358 +## File Version: 9.369 tam_jml_version1 <- function( resp, group=NULL, adj=.3, disattenuate=FALSE, bias=TRUE, xsi.fixed=NULL, xsi.inits=NULL, theta.fixed=NULL, A=NULL, B=NULL, Q=NULL, ndim=1, - pweights=NULL, control=list() ) + pweights=NULL, theta_proc=NULL, control=list() ) { @@ -23,10 +23,11 @@ tam_jml_version1 <- function( resp, group=NULL, adj=.3, disattenuate=FALSE, Lcon <- length(con) con1a <- con1 <- con ; names(con1) <- NULL - for (cc in 1:Lcon ){ + for (cc in 1L:Lcon ){ assign( names(con)[cc], con1[[cc]], envir=e1 ) } + resp <- add.colnames.resp(resp) # maximum no. of categories per item. @@ -70,8 +71,8 @@ tam_jml_version1 <- function( resp, group=NULL, adj=.3, disattenuate=FALSE, } else { xsi <- rep(0,np) } if ( ! is.null( xsi.fixed ) ){ xsi[ xsi.fixed[,1] ] <- xsi.fixed[,2] - est.xsi.index <- setdiff( 1:np, xsi.fixed[,1] ) - } else { est.xsi.index <- 1:np } + est.xsi.index <- setdiff( 1L:np, xsi.fixed[,1] ) + } else { est.xsi.index <- 1L:np } # group indicators for variance matrix @@ -79,27 +80,27 @@ tam_jml_version1 <- function( resp, group=NULL, adj=.3, disattenuate=FALSE, groups <- sort(unique(group)) G <- length(groups) # user must label groups from 1, ..., G - if ( length( setdiff( 1:G, groups) ) > 0 ){ + if ( length( setdiff( 1L:G, groups) ) > 0 ){ stop("Label groups from 1, ...,G\n") } } else { G <- 1 } # define response indicator matrix for missings resp.ind <- 1 - is.na(resp) - resp.ind.list <- list( 1:nitems ) - for (i in 1:nitems){ resp.ind.list[[i]] <- which( resp.ind[,i]==1) } + resp.ind.list <- list( 1L:nitems ) + for (i in 1L:nitems){ resp.ind.list[[i]] <- which( resp.ind[,i]==1) } resp[ is.na(resp) ] <- 0 # set all missings to zero # Create an index linking items and parameters indexIP <- colSums(aperm(A, c(2,1,3)) !=0, na.rm=TRUE) # define list of elements for item parameters - indexIP.list <- list( 1:np ) - for ( kk in 1:np ){ + indexIP.list <- list( 1L:np ) + for ( kk in 1L:np ){ indexIP.list[[kk]] <- which( indexIP[,kk] > 0 ) } - col.index <- rep( 1:nitems, each=maxK ) + col.index <- rep( 1L:nitems, each=maxK ) cResp <- resp[, col.index ]*resp.ind[, col.index ] # This line does not take missings into account cResp <- 1 * t( t(cResp)==rep(0:(maxK-1), nitems) ) @@ -154,7 +155,7 @@ tam_jml_version1 <- function( resp, group=NULL, adj=.3, disattenuate=FALSE, deviance <- 0 deviance.history <- matrix( 0, nrow=maxiter, ncol=2) colnames(deviance.history) <- c("iter", "deviance") - deviance.history[,1] <- 1:maxiter + deviance.history[,1] <- 1L:maxiter iter <- 0 meanChangeWLE <- maxChangeWLE <- maxChangeP <- 999 # item parameter change @@ -178,7 +179,7 @@ tam_jml_version1 <- function( resp, group=NULL, adj=.3, disattenuate=FALSE, #-- update theta (ability estimates) jmlAbility <- tam_jml_wle( tamobj, resp, resp.ind, A, B, nstud, nitems, maxK, convM, PersonScores, theta, xsi, Msteps, WLE=FALSE, - theta.fixed=theta.fixed) + theta.fixed=theta.fixed, theta_proc=theta_proc) theta <- jmlAbility$theta if (is.null(xsi.fixed)){ @@ -187,6 +188,7 @@ tam_jml_version1 <- function( resp, group=NULL, adj=.3, disattenuate=FALSE, meanChangeWLE <- jmlAbility$meanChangeWLE errorMLE <- jmlAbility$errorWLE + #update xsi, item parameters jmlxsi <- tam_jml_version1_calc_xsi( resp, resp.ind, A, B, nstud, nitems, maxK, convM, ItemScore, theta, xsi, Msteps, pweightsM, @@ -197,12 +199,12 @@ tam_jml_version1 <- function( resp, group=NULL, adj=.3, disattenuate=FALSE, #Deviance #Calculate Axsi. Only need to do this once for ability estimates. - for (i in 1:nitems) { - for (k in 1:maxK){ + for (i in 1L:nitems) { + for (k in 1L:maxK){ AXsi[i,k] <- ( A[i,k,] %*% xsi ) } } - res <- tam_mml_calc_prob(iIndex=1:nitems, A, AXsi, + res <- tam_mml_calc_prob(iIndex=1L:nitems, A, AXsi, B, xsi, theta, nstud, maxK, recalc=FALSE ) rprobs <- res[["rprobs"]] crprobs <- t( matrix( aperm( rprobs, c(2,1,3) ), nrow=dim(rprobs)[3], byrow=TRUE ) ) @@ -223,13 +225,14 @@ tam_jml_version1 <- function( resp, group=NULL, adj=.3, disattenuate=FALSE, #@ARb 2012-08-27 # stop loop (break) if there is no change in deviation if ( abs( deviance-olddeviance) < 1E-10 ){ break } + }# end of all convergence #After convergence, compute final WLE (WLE set to TRUE) jmlWLE <- tam_jml_wle( tamobj, resp, resp.ind, A, B, nstud, nitems, maxK, convM, PersonScores, theta, xsi, Msteps, WLE=TRUE, - theta.fixed=theta.fixed ) + theta.fixed=theta.fixed, theta_proc=theta_proc ) thetaWLE <- jmlWLE$theta[,1] @@ -254,7 +257,7 @@ tam_jml_version1 <- function( resp, group=NULL, adj=.3, disattenuate=FALSE, # collect item statistics item <- data.frame( "xsi.label"=dimnames(A)[[3]], - "xsi.index"=1:( length(xsi) ), "xsi"=xsi, + "xsi.index"=1L:( length(xsi) ), "xsi"=xsi, "se.xsi"=errorP ) @@ -271,7 +274,7 @@ tam_jml_version1 <- function( resp, group=NULL, adj=.3, disattenuate=FALSE, } # Output list - deviance.history <- deviance.history[ 1:iter, ] + deviance.history <- deviance.history[ 1L:iter, ] res <- list( "item"=item, "xsi"=xsi, "errorP"=errorP, "theta"=theta[,1], "errorWLE"=errorWLE, "WLE"=thetaWLE, "WLEreliability"=WLEreliability, diff --git a/R/tam_jml_wle.R b/R/tam_jml_wle.R index 6b8d1cf..5c60147 100644 --- a/R/tam_jml_wle.R +++ b/R/tam_jml_wle.R @@ -1,12 +1,12 @@ ## File Name: tam_jml_wle.R -## File Version: 9.324 +## File Version: 9.330 #-- WLE in JML estimation tam_jml_wle <- function ( tamobj, resp, resp.ind, A, B, nstud, nitems, maxK, convM, PersonScores, theta, xsi, Msteps, WLE=FALSE, theta.fixed=NULL, progress=FALSE, output.prob=TRUE, damp=0, - version=2) + version=2, theta_proc=NULL) { AXsi <- matrix(0, nrow=nitems, ncol=maxK) @@ -21,8 +21,8 @@ tam_jml_wle <- function ( tamobj, resp, resp.ind, A, B, nstud, nitems, maxK, con B_Cube <- array(0,dim=nstud) #Calculate Axsi. Only need to do this once for ability estimates. - for (i in 1:nitems) { - for (k in 1:maxK){ + for (i in 1L:nitems) { + for (k in 1L:maxK){ AXsi[i,k] <- ( A[i,k,] %*% xsi ) } } @@ -52,7 +52,7 @@ a0 <- Sys.time() while (!convergeWLE & ( iterWLE <=Msteps ) ){ if (version==2){ - resWLE <- tam_mml_calc_prob(iIndex=1:nitems, A=A, AXsi=AXsi, + resWLE <- tam_mml_calc_prob(iIndex=1L:nitems, A=A, AXsi=AXsi, B=B, xsi=xsi, theta=theta, nnodes=nstud, maxK=maxK, recalc=FALSE ) rprobsWLE <- resWLE$rprobs rprobsWLE[ is.na(rprobsWLE) ] <- 0 @@ -66,7 +66,7 @@ a0 <- Sys.time() if (version==2){ B_bari <- B1[,1] * rprobsWLE[, 1, ] BB_bari <- BB[,1] * rprobsWLE[, 1, ] - for (kk in 2:maxK){ + for (kk in 2L:maxK){ B_bari <- B_bari + B1[,kk]*rprobsWLE[,kk,] BB_bari <- BB_bari + BB[,kk] * rprobsWLE[, kk, ] } @@ -80,7 +80,7 @@ a0 <- Sys.time() BB_bari <- res$BB_bari } - # B_bari.OLD <- sapply(1:nitems, function(i) colSums(B1[i,] * rprobsWLE[i,,], na.rm=TRUE)) * resp.ind + # B_bari.OLD <- sapply(1L:nitems, function(i) colSums(B1[i,] * rprobsWLE[i,,], na.rm=TRUE)) * resp.ind # B1 [ nitems, maxK ] # rprobsWLE [ nitems, maxK, nstud ] # resp.ind [ nstud, nitems ] @@ -96,7 +96,7 @@ a0 <- Sys.time() if (WLE) { BBB_bari <- BBB[,1] * rprobsWLE[, 1, ] - for (kk in 2:maxK){ + for (kk in 2L:maxK){ BBB_bari <- BBB_bari + BBB[,kk] * rprobsWLE[, kk, ] } BBB_bari <- t(BBB_bari) * resp.ind @@ -134,6 +134,11 @@ a0 <- Sys.time() } cat("\n") + + if (!is.null(theta_proc)){ + theta <- theta_proc(theta=theta) + } + meanChangeWLE <- mean(theta - thetaOld) #standard errors of theta estimates errorWLE <- sqrt(err_inv) @@ -141,6 +146,7 @@ a0 <- Sys.time() errorWLE[ theta.fixed[,1] ] <- 0 } + res <- list( "theta"=theta, "errorWLE"=errorWLE, "meanChangeWLE"=meanChangeWLE) return (res) } diff --git a/R/tam_mml_2pl_mstep_slope.R b/R/tam_mml_2pl_mstep_slope.R index ef3e2d2..753f45c 100644 --- a/R/tam_mml_2pl_mstep_slope.R +++ b/R/tam_mml_2pl_mstep_slope.R @@ -1,5 +1,5 @@ ## File Name: tam_mml_2pl_mstep_slope.R -## File Version: 9.579 +## File Version: 9.584 tam_mml_2pl_mstep_slope <- function (B_orig, B, B_obs, B.fixed, max.increment, nitems, A, @@ -13,8 +13,8 @@ tam_mml_2pl_mstep_slope <- function (B_orig, B, B_obs, B.fixed, max.increment, n xtemp <- matrix(0, nrow=1, ncol=1) converge <- FALSE Biter <- 1 - mK <- 1:maxK - items.temp <- 1:nitems + mK <- 1L:maxK + items.temp <- 1L:nitems items.conv <- NULL items.conv1 <- c(-1) increments_msteps <- rep(NA,Msteps) @@ -51,7 +51,7 @@ tam_mml_2pl_mstep_slope <- function (B_orig, B, B_obs, B.fixed, max.increment, n LIT <- length(items.temp) ###### D I M E N S I O N S ###### - for (dd in 1:ndim){ + for (dd in 1L:ndim){ if ( irtmodel %in% c("GPCM","GPCM.design","GPCM.groups") ){ xtemp <- matrix(0, nrow=LIT, ncol=TP ) } @@ -131,7 +131,7 @@ tam_mml_2pl_mstep_slope <- function (B_orig, B, B_obs, B.fixed, max.increment, n increment <- tam_outer( increment.temp, mK-1) d1 <- tam_outer( 1 / abs( deriv.temp ), mK-1 ) LL <- ncol(d1) - for (ll in 1:LL){ + for (ll in 1L:LL){ m1 <- sqrt( diag( E %*% d1[,ll] %*% t( d1[,ll] ) %*% t(E) ) ) if (Biter==1){ se.B[,ll,dd] <- m1 @@ -139,9 +139,9 @@ tam_mml_2pl_mstep_slope <- function (B_orig, B, B_obs, B.fixed, max.increment, n } nB <- dim(B) B_ind <- 1 * ( B_orig !=0 ) - for (dd in 1:nB[3]){ + for (dd in 1L:nB[3]){ EB <- E %*% basispar[,dd] - for (cc in 1:(nB[2]-1)){ + for (cc in 1L:(nB[2]-1)){ B[,cc+1,dd] <- cc * EB * B_ind[,cc+1,dd] } } @@ -189,7 +189,7 @@ tam_mml_2pl_mstep_slope <- function (B_orig, B, B_obs, B.fixed, max.increment, n if ( irtmodel=="2PL" ){ items.temp <- which( apply( old_increment, 1, FUN=function(ll){ ! ( max(abs(ll)) < convM ) } ) ) - items.conv <- setdiff( 1:nitems, items.temp ) + items.conv <- setdiff( 1L:nitems, items.temp ) if ( length(items.conv) > 0 ){ items.conv1 <- items.conv } diff --git a/README.md b/README.md index a696d24..725d163 100644 --- a/README.md +++ b/README.md @@ -21,9 +21,9 @@ The CRAN version can be installed from within R using: utils::install.packages("TAM") ``` -#### GitHub version `TAM` 4.3-2 (2024-02-20) +#### GitHub version `TAM` 4.3-4 (2024-09-09) -[![](https://img.shields.io/badge/github%20version-4.3--2-orange.svg)](https://github.com/alexanderrobitzsch/TAM)   +[![](https://img.shields.io/badge/github%20version-4.3--4-orange.svg)](https://github.com/alexanderrobitzsch/TAM)   The version hosted [here](https://github.com/alexanderrobitzsch/TAM) is the development version of `TAM`. The GitHub version can be installed using `devtools` as diff --git a/docs/404.html b/docs/404.html index f77bc79..0d2ab99 100644 --- a/docs/404.html +++ b/docs/404.html @@ -1,66 +1,27 @@ - - - - + + + + - Page not found (404) • TAM - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + - - - - -
-
- + +
+ + + - - -
+

Page not found (404)

@@ -115,31 +70,31 @@

Page not found (404)

+
-
-
-

Developed by Alexander Robitzsch.

+
+

+

Developed by Alexander Robitzsch.

-

Site built with pkgdown 1.5.1.

+

+

Site built with pkgdown 2.0.7.

-
+
+ + - - diff --git a/docs/authors.html b/docs/authors.html index 7909b4c..3f2618b 100644 --- a/docs/authors.html +++ b/docs/authors.html @@ -1,66 +1,12 @@ - - - - - - - -Citation and Authors • TAM - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Authors and Citation • TAM - - + + - - -
-
- -
- -
+
-
-

Citation

- Source: inst/CITATION +
+
+

Authors

+
+ + +
  • +

    Alexander Robitzsch. Maintainer. +

    +
    • +
+
+
+

Citation

+ Source: inst/CITATION
+
+ -

Robitzsch, A., Kiefer, T., & Wu, M. (2023). TAM: Test Analysis Modules. R package version 4.2-2. https://CRAN.R-project.org/package=TAM

- 
@Manual{TAM_4.2-2,
+    
Robitzsch, A., Kiefer, T., & Wu, M. (2024). TAM: Test Analysis Modules. R package version 4.3-4. https://CRAN.R-project.org/package=TAM

+    
@Manual{TAM_4.3-4,
   title = {TAM: Test Analysis Modules},
   author = {Alexander Robitzsch and Thomas Kiefer and Margaret Wu},
-  year = {2023},
-  note = {R package version 4.2-2},
+  year = {2024},
+  note = {R package version 4.3-4},
   url = {https://CRAN.R-project.org/package=TAM},
 }

 
-    

-      
Authors

-    

-
-    
    
-      
  • 
-        
    Alexander Robitzsch. Maintainer. 
-        
    
-      
    • 
-    

-
-
-
-

Developed by Alexander Robitzsch.

+
+

Developed by Alexander Robitzsch.

-

Site built with pkgdown 1.5.1.

+

Site built with pkgdown 2.0.7.

-
-
+
- - + + diff --git a/docs/index.html b/docs/index.html index 33810ec..2c8d271 100644 --- a/docs/index.html +++ b/docs/index.html @@ -31,6 +31,8 @@ + +
-
-

-TAM

-
-

-Test Analysis Modules

-

If you use TAM and have suggestions for improvement or have found bugs, please email me at

-. Please always provide a minimal dataset, necessary to demonstrate the problem, a minimal runnable code necessary to reproduce the issue, which can be run on the given dataset, and all necessary information on the used librarys, the R version, and the OS it is run on, perhaps a sessionInfo(). -
-
-

-Manual

-

The manual may be found here https://alexanderrobitzsch.github.io/TAM/

+
+

TAM +

+
+

Test Analysis Modules +

+

If you use TAM and have suggestions for improvement or have found bugs, please email me at . Please always provide a minimal dataset, necessary to demonstrate the problem, a minimal runnable code necessary to reproduce the issue, which can be run on the given dataset, and all necessary information on the used librarys, the R version, and the OS it is run on, perhaps a sessionInfo().

-
-

-CRAN version

+
+

CRAN version +

-

The official version of TAM is hosted on CRAN and may be found here. The CRAN version can be installed from within R using:

-
utils::install.packages("TAM")
+

The official version of TAM is hosted on CRAN and may be found here. The CRAN version can be installed from within R using:

+
+utils::install.packages("TAM")
-
-

-GitHub version

-

The version hosted here is the development version of TAM. The GitHub version can be installed using devtools as:

-
devtools::install_github("alexanderrobitzsch/TAM")
+
+

GitHub version +

+

The version hosted here is the development version of TAM. The GitHub version can be installed using devtools as

+
+devtools::install_github("alexanderrobitzsch/TAM")
+

or alternatively use

+
+utils::install.packages('TAM', repos = c('https://alexanderrobitzsch.r-universe.dev', 'https://cloud.r-project.org'))
-

Developed by Alexander Robitzsch.

+

+

Developed by Alexander Robitzsch.

-

Site built with pkgdown 1.5.1.

+

+

Site built with pkgdown 2.0.7.

@@ -163,5 +159,7 @@

Developers

+ + diff --git a/docs/pkgdown.css b/docs/pkgdown.css index c01e592..80ea5b8 100644 --- a/docs/pkgdown.css +++ b/docs/pkgdown.css @@ -56,8 +56,10 @@ img.icon { float: right; } -img { +/* Ensure in-page images don't run outside their container */ +.contents img { max-width: 100%; + height: auto; } /* Fix bug in bootstrap (only seen in firefox) */ @@ -78,11 +80,10 @@ dd { /* Section anchors ---------------------------------*/ a.anchor { - margin-left: -30px; - display:inline-block; - width: 30px; - height: 30px; - visibility: hidden; + display: none; + margin-left: 5px; + width: 20px; + height: 20px; background-image: url(./link.svg); background-repeat: no-repeat; @@ -90,17 +91,15 @@ a.anchor { background-position: center center; } -.hasAnchor:hover a.anchor { - visibility: visible; -} - -@media (max-width: 767px) { - .hasAnchor:hover a.anchor { - visibility: hidden; - } +h1:hover .anchor, +h2:hover .anchor, +h3:hover .anchor, +h4:hover .anchor, +h5:hover .anchor, +h6:hover .anchor { + display: inline-block; } - /* Fixes for fixed navbar --------------------------*/ .contents h1, .contents h2, .contents h3, .contents h4 { @@ -244,14 +243,14 @@ nav[data-toggle='toc'] .nav .nav > .active:focus > a { .ref-index th {font-weight: normal;} -.ref-index td {vertical-align: top;} +.ref-index td {vertical-align: top; min-width: 100px} .ref-index .icon {width: 40px;} .ref-index .alias {width: 40%;} .ref-index-icons .alias {width: calc(40% - 40px);} .ref-index .title {width: 60%;} .ref-arguments th {text-align: right; padding-right: 10px;} -.ref-arguments th, .ref-arguments td {vertical-align: top;} +.ref-arguments th, .ref-arguments td {vertical-align: top; min-width: 100px} .ref-arguments .name {width: 20%;} .ref-arguments .desc {width: 80%;} @@ -264,31 +263,26 @@ table { /* Syntax highlighting ---------------------------------------------------- */ -pre { - word-wrap: normal; - word-break: normal; - border: 1px solid #eee; -} - -pre, code { +pre, code, pre code { background-color: #f8f8f8; color: #333; } +pre, pre code { + white-space: pre-wrap; + word-break: break-all; + overflow-wrap: break-word; +} -pre code { - overflow: auto; - word-wrap: normal; - white-space: pre; +pre { + border: 1px solid #eee; } -pre .img { +pre .img, pre .r-plt { margin: 5px 0; } -pre .img img { +pre .img img, pre .r-plt img { background-color: #fff; - display: block; - height: auto; } code a, pre a { @@ -305,9 +299,8 @@ a.sourceLine:hover { .kw {color: #264D66;} /* keyword */ .co {color: #888888;} /* comment */ -.message { color: black; font-weight: bolder;} -.error { color: orange; font-weight: bolder;} -.warning { color: #6A0366; font-weight: bolder;} +.error {font-weight: bolder;} +.warning {font-weight: bolder;} /* Clipboard --------------------------*/ @@ -365,3 +358,27 @@ mark { content: ""; } } + +/* Section anchors --------------------------------- + Added in pandoc 2.11: https://github.com/jgm/pandoc-templates/commit/9904bf71 +*/ + +div.csl-bib-body { } +div.csl-entry { + clear: both; +} +.hanging-indent div.csl-entry { + margin-left:2em; + text-indent:-2em; +} +div.csl-left-margin { + min-width:2em; + float:left; +} +div.csl-right-inline { + margin-left:2em; + padding-left:1em; +} +div.csl-indent { + margin-left: 2em; +} diff --git a/docs/pkgdown.js b/docs/pkgdown.js index 7e7048f..6f0eee4 100644 --- a/docs/pkgdown.js +++ b/docs/pkgdown.js @@ -80,7 +80,7 @@ $(document).ready(function() { var copyButton = ""; - $(".examples, div.sourceCode").addClass("hasCopyButton"); + $("div.sourceCode").addClass("hasCopyButton"); // Insert copy buttons: $(copyButton).prependTo(".hasCopyButton"); @@ -91,7 +91,7 @@ // Initialize clipboard: var clipboardBtnCopies = new ClipboardJS('[data-clipboard-copy]', { text: function(trigger) { - return trigger.parentNode.textContent; + return trigger.parentNode.textContent.replace(/\n#>[^\n]*/g, ""); } }); diff --git a/docs/pkgdown.yml b/docs/pkgdown.yml index 4330535..6d22707 100644 --- a/docs/pkgdown.yml +++ b/docs/pkgdown.yml @@ -1,6 +1,6 @@ -pandoc: 1.13.1 -pkgdown: 1.5.1 +pandoc: 3.1.1 +pkgdown: 2.0.7 pkgdown_sha: ~ -articles: [] -last_built: 2023-01-25T12:12Z +articles: {} +last_built: 2024-09-09T12:29Z diff --git a/docs/reference/DescribeBy.html b/docs/reference/DescribeBy.html index 7f0ba87..accd3a3 100644 --- a/docs/reference/DescribeBy.html +++ b/docs/reference/DescribeBy.html @@ -1,67 +1,12 @@ - - - - - - - -S3 Method for Descriptive Statistics of Objects — DescribeBy • TAM - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -S3 Method for Descriptive Statistics of Objects — DescribeBy • TAM - - - - + + -
-
- -
- -
+

S3 Method for Descriptive Statistics of Objects

@@ -117,50 +49,45 @@

S3 Method for Descriptive Statistics of Objects

S3 method for descriptive statistics of objects

- 
DescribeBy(object, ...)
+
+ 
DescribeBy(object, ...)
+
-

Arguments

- - - - - - - - - - -
object

An object

...

Further arguments to be passed

+
+

Arguments

+
object
+

An object

-

See also

+
...
+

Further arguments to be passed

-

psych::describe

+
+
+

See also

+

psych::describe

+
+
-
-
-

Developed by Alexander Robitzsch.

+
+

Developed by Alexander Robitzsch.

-

Site built with pkgdown 1.5.1.

+

Site built with pkgdown 2.0.7.

-
-
+
- - + + diff --git a/docs/reference/IRT.WrightMap.html b/docs/reference/IRT.WrightMap.html index 92921a2..d661e9b 100644 --- a/docs/reference/IRT.WrightMap.html +++ b/docs/reference/IRT.WrightMap.html @@ -1,71 +1,16 @@ - - - - - - - -Wright Map for Item Response Models by Using the <span class="pkg">WrightMap</span> Package — IRT.WrightMap • TAM - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -WrightMap Package — IRT.WrightMap" /> -Wright Map for Item Response Models by Using the WrightMap Package — IRT.WrightMap • TAM - - - - - - - - - - - - - + + -
-
- -
- -
+

Wright Map for Item Response Models by Using the WrightMap Package

@@ -119,245 +51,250 @@

Wright Map for Item Response Models by Using the WrightMap

This function creates a Wright map and works as a wrapper to the -wrightMap function in +wrightMap function in the WrightMap package. The arguments thetas and thresholds are automatically generated from fitted objects in TAM.

- 
# S3 method for tam.mml
-IRT.WrightMap(object, prob.lvl=.5, type="PV", ...)
+    

+    
# S3 method for tam.mml
+IRT.WrightMap(object, prob.lvl=.5, type="PV", ...)
+
+# S3 method for tamaan
+IRT.WrightMap(object, prob.lvl=.5, type="PV", ...)

+    

+
+    

+    
Arguments

+    
object

+
Object of class tam.mml or class tamaan

 
-# S3 method for tamaan
-IRT.WrightMap(object, prob.lvl=.5, type="PV", ...)
+
prob.lvl
+

Requested probability level of thresholds.

-

Arguments

- - - - - - - - - - - - - - - - - - -
object

Object of class tam.mml or class tamaan

prob.lvl

Requested probability level of thresholds.

type

Type of person parameter estimate. "PV" (plausible values), +

type
+

Type of person parameter estimate. "PV" (plausible values), "WLE" (weighted likelihood estimates) and -"Pop" (population trait distribution) can be specified.

...

Further arguments to be passed in the -wrightMap (WrightMap) function. -See Examples.

+"Pop" (population trait distribution) can be specified.

-

Details

+
...
+

Further arguments to be passed in the +wrightMap (WrightMap) function. +See Examples.

+

+
+

Details

A Wright map is only created for models with an assumed normal distribution. -Hence, not for all models of the tamaan functions +Hence, not for all models of the tamaan functions Wright maps are created.

-

Value

- -

A Wright map generated by the WrightMap package.

-

See also

+
+
+

Value

+ -

See the WrightMap::wrightMap function in +

A Wright map generated by the WrightMap package.

+
+
+

Author

+

The IRT.WrightMap function is based on the +WrightMap::wrightMap function +in the WrightMap package.

+
+
+

See also

+

See the WrightMap::wrightMap function in the WrightMap package.

+
-

Examples

- 
if (FALSE) {
-library(WrightMap)
-
-#############################################################################
-# EXAMPLE 1: Unidimensional models dichotomous data
-#############################################################################
-
-data(data.sim.rasch)
-str(data.sim.rasch)
-dat <- data.sim.rasch
-
-# fit Rasch model
-mod1 <- TAM::tam.mml(resp=dat)
-# Wright map
-IRT.WrightMap( mod1 )
-# some customized plots
-IRT.WrightMap( mod1, show.thr.lab=FALSE, label.items=c(1:40), label.items.rows=3)
-
-IRT.WrightMap( mod1,  show.thr.sym=FALSE, thr.lab.text=paste0("I",1:ncol(dat)),
-     label.items="", label.items.ticks=FALSE)
-
-#--- direct specification with wrightMap function
-theta <- TAM::tam.wle(mod1)$theta
-thr <- TAM::tam.threshold(mod1)
-
-# default wrightMap plots
-WrightMap::wrightMap( theta, thr, label.items.srt=90)
-WrightMap::wrightMap( theta, t(thr), label.items=c("items") )
-
-# stack all items below each other
-thr.lab.text <- matrix( "", 1, ncol(dat) )
-thr.lab.text[1,] <- colnames(dat)
-WrightMap::wrightMap( theta, t(thr), label.items=c("items"),
-       thr.lab.text=thr.lab.text, show.thr.sym=FALSE )
-
-#############################################################################
-# EXAMPLE 2: Unidimensional model polytomous data
-#############################################################################
-
-data( data.Students, package="CDM")
-dat <- data.Students
-
-# fit generalized partial credit model using the tamaan function
-tammodel <- "
-LAVAAN MODEL:
-  SC=~ sc1__sc4
-  SC ~~ 1*SC
-    "
-mod1 <- TAM::tamaan( tammodel, dat )
-# create item level colors
-library(RColorBrewer)
-ncat <- 3               # number of category parameters
-I <- ncol(mod1$resp)    # number of items
-itemlevelcolors <- matrix(rep( RColorBrewer::brewer.pal(ncat, "Set1"), I),
-        byrow=TRUE, ncol=ncat)
-# Wright map
-IRT.WrightMap(mod1, prob.lvl=.625, thr.sym.col.fg=itemlevelcolors,
-     thr.sym.col.bg=itemlevelcolors, label.items=colnames( mod1$resp) )
-
-#############################################################################
-# EXAMPLE 3: Multidimensional item response model
-#############################################################################
-
-data( data.read, package="sirt")
-dat <- data.read
-
-# fit three-dimensional Rasch model
-Q <- matrix( 0, nrow=12, ncol=3 )
-Q[1:4,1] <- Q[5:8,2] <- Q[9:12,3] <- 1
-mod1 <- TAM::tam.mml( dat, Q=Q, control=list(maxiter=20, snodes=1000)  )
-summary(mod1)
-# define matrix with colors for thresholds
-c1 <- matrix( c( rep(1,4), rep(2,4), rep(4,4)), ncol=1 )
-# create Wright map using WLE
-IRT.WrightMap( mod1, prob.lvl=.65, type="WLE", thr.lab.col=c1, thr.sym.col.fg=c1,
-        thr.sym.col.bg=c1, label.items=colnames(dat) )
-# Wright map using PV (the default)
-IRT.WrightMap( mod1, prob.lvl=.65, type="PV" )
-# Wright map using population distribution
-IRT.WrightMap( mod1, prob.lvl=.65, type="Pop" )
-
-#############################################################################
-# EXAMPLE 4: Wright map for a multi-faceted Rasch model
-#############################################################################
-
-# This example is copied from
-# http://wrightmap.org/post/107431190622/wrightmap-multifaceted-models
-
-library(WrightMap)
-data(data.ex10)
-dat <- data.ex10
-
-#--- fit multi-faceted Rasch model
-facets <- dat[, "rater", drop=FALSE]  # define facet (rater)
-pid <- dat$pid  # define person identifier (a person occurs multiple times)
-resp <- dat[, -c(1:2)]  # item response data
-formulaA <- ~item * rater  # formula
-mod <- TAM::tam.mml.mfr(resp=resp, facets=facets, formulaA=formulaA, pid=dat$pid)
-
-# person parameters
-persons.mod <- TAM::tam.wle(mod)
-theta <- persons.mod$theta
-# thresholds
-thr <- TAM::tam.threshold(mod)
-item.labs <- c("I0001", "I0002", "I0003", "I0004", "I0005")
-rater.labs <- c("rater1", "rater2", "rater3")
-
-#--- Plot 1: Item specific
-thr1 <- matrix(thr, nrow=5, byrow=TRUE)
-WrightMap::wrightMap(theta, thr1, label.items=item.labs,
-   thr.lab.text=rep(rater.labs, each=5))
-
-#--- Plot 2: Rater specific
-thr2 <- matrix(thr, nrow=3)
-WrightMap::wrightMap(theta, thr2, label.items=rater.labs,
-   thr.lab.text=rep(item.labs,  each=3), axis.items="Raters")
-
-#--- Plot 3a: item, rater and item*rater parameters
-pars <- mod$xsi.facets$xsi
-facet <- mod$xsi.facets$facet
-
-item.par <- pars[facet=="item"]
-rater.par <- pars[facet=="rater"]
-item_rat <- pars[facet=="item:rater"]
-
-len <- length(item_rat)
-item.long <- c(item.par, rep(NA, len - length(item.par)))
-rater.long <- c(rater.par, rep(NA, len - length(rater.par)))
-ir.labs <- mod$xsi.facets$parameter[facet=="item:rater"]
-
-WrightMap::wrightMap(theta, rbind(item.long, rater.long, item_rat),
-    label.items=c("Items",  "Raters", "Item*Raters"),
-    thr.lab.text=rbind(item.labs, rater.labs, ir.labs), axis.items="")
-
-#--- Plot 3b: item, rater and item*rater (separated by raters) parameters
-
-# parameters item*rater
-ir_rater <- matrix(item_rat, nrow=3, byrow=TRUE)
-# define matrix of thresholds
-thr <- rbind(item.par, c(rater.par, NA, NA), ir_rater)
-# matrix with threshold labels
-thr.lab.text <- rbind(item.labs, rater.labs,
-           matrix(item.labs, nrow=3, ncol=5, byrow=TRUE))
-
-WrightMap::wrightMap(theta, thresholds=thr,
-      label.items=c("Items", "Raters", "Item*Raters (R1)",
-                           "Item*Raters (R2)", "Item*Raters (R3)"),
-      axis.items="", thr.lab.text=thr.lab.text )
-
-#--- Plot 3c: item, rater and item*rater (separated by items) parameters
-
-# thresholds
-ir_item <- matrix(item_rat, nrow=5)
-thr <- rbind(item.par, c(rater.par, NA, NA), cbind(ir_item, NA, NA))
-# labels
-label.items <- c("Items", "Raters", "Item*Raters\n (I1)", "Item*Raters \n(I2)",
-     "Item*Raters \n(I3)", "Item*Raters \n (I4)", "Item*Raters \n(I5)")
-thr.lab.text <- rbind(item.labs,
-          matrix(c(rater.labs, NA, NA), nrow=6, ncol=5, byrow=TRUE))
-
-WrightMap::wrightMap(theta, thr,  label.items=label.items,
-      axis.items="", thr.lab.text=thr.lab.text  )
-}
+
+

Examples

+ 
if (FALSE) {
+library(WrightMap)
+
+#############################################################################
+# EXAMPLE 1: Unidimensional models dichotomous data
+#############################################################################
+
+data(data.sim.rasch)
+str(data.sim.rasch)
+dat <- data.sim.rasch
+
+# fit Rasch model
+mod1 <- TAM::tam.mml(resp=dat)
+# Wright map
+IRT.WrightMap( mod1 )
+# some customized plots
+IRT.WrightMap( mod1, show.thr.lab=FALSE, label.items=c(1:40), label.items.rows=3)
+
+IRT.WrightMap( mod1,  show.thr.sym=FALSE, thr.lab.text=paste0("I",1:ncol(dat)),
+     label.items="", label.items.ticks=FALSE)
+
+#--- direct specification with wrightMap function
+theta <- TAM::tam.wle(mod1)$theta
+thr <- TAM::tam.threshold(mod1)
+
+# default wrightMap plots
+WrightMap::wrightMap( theta, thr, label.items.srt=90)
+WrightMap::wrightMap( theta, t(thr), label.items=c("items") )
+
+# stack all items below each other
+thr.lab.text <- matrix( "", 1, ncol(dat) )
+thr.lab.text[1,] <- colnames(dat)
+WrightMap::wrightMap( theta, t(thr), label.items=c("items"),
+       thr.lab.text=thr.lab.text, show.thr.sym=FALSE )
+
+#############################################################################
+# EXAMPLE 2: Unidimensional model polytomous data
+#############################################################################
+
+data( data.Students, package="CDM")
+dat <- data.Students
+
+# fit generalized partial credit model using the tamaan function
+tammodel <- "
+LAVAAN MODEL:
+  SC=~ sc1__sc4
+  SC ~~ 1*SC
+    "
+mod1 <- TAM::tamaan( tammodel, dat )
+# create item level colors
+library(RColorBrewer)
+ncat <- 3               # number of category parameters
+I <- ncol(mod1$resp)    # number of items
+itemlevelcolors <- matrix(rep( RColorBrewer::brewer.pal(ncat, "Set1"), I),
+        byrow=TRUE, ncol=ncat)
+# Wright map
+IRT.WrightMap(mod1, prob.lvl=.625, thr.sym.col.fg=itemlevelcolors,
+     thr.sym.col.bg=itemlevelcolors, label.items=colnames( mod1$resp) )
+
+#############################################################################
+# EXAMPLE 3: Multidimensional item response model
+#############################################################################
+
+data( data.read, package="sirt")
+dat <- data.read
+
+# fit three-dimensional Rasch model
+Q <- matrix( 0, nrow=12, ncol=3 )
+Q[1:4,1] <- Q[5:8,2] <- Q[9:12,3] <- 1
+mod1 <- TAM::tam.mml( dat, Q=Q, control=list(maxiter=20, snodes=1000)  )
+summary(mod1)
+# define matrix with colors for thresholds
+c1 <- matrix( c( rep(1,4), rep(2,4), rep(4,4)), ncol=1 )
+# create Wright map using WLE
+IRT.WrightMap( mod1, prob.lvl=.65, type="WLE", thr.lab.col=c1, thr.sym.col.fg=c1,
+        thr.sym.col.bg=c1, label.items=colnames(dat) )
+# Wright map using PV (the default)
+IRT.WrightMap( mod1, prob.lvl=.65, type="PV" )
+# Wright map using population distribution
+IRT.WrightMap( mod1, prob.lvl=.65, type="Pop" )
+
+#############################################################################
+# EXAMPLE 4: Wright map for a multi-faceted Rasch model
+#############################################################################
+
+# This example is copied from
+# http://wrightmap.org/post/107431190622/wrightmap-multifaceted-models
+
+library(WrightMap)
+data(data.ex10)
+dat <- data.ex10
+
+#--- fit multi-faceted Rasch model
+facets <- dat[, "rater", drop=FALSE]  # define facet (rater)
+pid <- dat$pid  # define person identifier (a person occurs multiple times)
+resp <- dat[, -c(1:2)]  # item response data
+formulaA <- ~item * rater  # formula
+mod <- TAM::tam.mml.mfr(resp=resp, facets=facets, formulaA=formulaA, pid=dat$pid)
+
+# person parameters
+persons.mod <- TAM::tam.wle(mod)
+theta <- persons.mod$theta
+# thresholds
+thr <- TAM::tam.threshold(mod)
+item.labs <- c("I0001", "I0002", "I0003", "I0004", "I0005")
+rater.labs <- c("rater1", "rater2", "rater3")
+
+#--- Plot 1: Item specific
+thr1 <- matrix(thr, nrow=5, byrow=TRUE)
+WrightMap::wrightMap(theta, thr1, label.items=item.labs,
+   thr.lab.text=rep(rater.labs, each=5))
+
+#--- Plot 2: Rater specific
+thr2 <- matrix(thr, nrow=3)
+WrightMap::wrightMap(theta, thr2, label.items=rater.labs,
+   thr.lab.text=rep(item.labs,  each=3), axis.items="Raters")
+
+#--- Plot 3a: item, rater and item*rater parameters
+pars <- mod$xsi.facets$xsi
+facet <- mod$xsi.facets$facet
+
+item.par <- pars[facet=="item"]
+rater.par <- pars[facet=="rater"]
+item_rat <- pars[facet=="item:rater"]
+
+len <- length(item_rat)
+item.long <- c(item.par, rep(NA, len - length(item.par)))
+rater.long <- c(rater.par, rep(NA, len - length(rater.par)))
+ir.labs <- mod$xsi.facets$parameter[facet=="item:rater"]
+
+WrightMap::wrightMap(theta, rbind(item.long, rater.long, item_rat),
+    label.items=c("Items",  "Raters", "Item*Raters"),
+    thr.lab.text=rbind(item.labs, rater.labs, ir.labs), axis.items="")
+
+#--- Plot 3b: item, rater and item*rater (separated by raters) parameters
+
+# parameters item*rater
+ir_rater <- matrix(item_rat, nrow=3, byrow=TRUE)
+# define matrix of thresholds
+thr <- rbind(item.par, c(rater.par, NA, NA), ir_rater)
+# matrix with threshold labels
+thr.lab.text <- rbind(item.labs, rater.labs,
+           matrix(item.labs, nrow=3, ncol=5, byrow=TRUE))
+
+WrightMap::wrightMap(theta, thresholds=thr,
+      label.items=c("Items", "Raters", "Item*Raters (R1)",
+                           "Item*Raters (R2)", "Item*Raters (R3)"),
+      axis.items="", thr.lab.text=thr.lab.text )
+
+#--- Plot 3c: item, rater and item*rater (separated by items) parameters
+
+# thresholds
+ir_item <- matrix(item_rat, nrow=5)
+thr <- rbind(item.par, c(rater.par, NA, NA), cbind(ir_item, NA, NA))
+# labels
+label.items <- c("Items", "Raters", "Item*Raters\n (I1)", "Item*Raters \n(I2)",
+     "Item*Raters \n(I3)", "Item*Raters \n (I4)", "Item*Raters \n(I5)")
+thr.lab.text <- rbind(item.labs,
+          matrix(c(rater.labs, NA, NA), nrow=6, ncol=5, byrow=TRUE))
+
+WrightMap::wrightMap(theta, thr,  label.items=label.items,
+      axis.items="", thr.lab.text=thr.lab.text  )
+}
+
+
-
-
-

Developed by Alexander Robitzsch.

+
+

Developed by Alexander Robitzsch.

-

Site built with pkgdown 1.5.1.

+

Site built with pkgdown 2.0.7.

-
-
+
- - + + diff --git a/docs/reference/IRT.cv.html b/docs/reference/IRT.cv.html index 2ea87f4..843f0c5 100644 --- a/docs/reference/IRT.cv.html +++ b/docs/reference/IRT.cv.html @@ -1,67 +1,12 @@ - - - - - - - -Cross-Validation of a Fitted IRT Model — IRT.cv • TAM - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Cross-Validation of a Fitted IRT Model — IRT.cv • TAM - - - - + + -
-
- -
- -
+

Cross-Validation of a Fitted IRT Model

@@ -117,50 +49,47 @@

Cross-Validation of a Fitted IRT Model

This S3 method performs a cross-validation of a fitted item response model.

- 
IRT.cv(object, ...)
+
+ 
IRT.cv(object, ...)
+
+ +
+

Arguments

+
object
+

Object

-

Arguments

- - - - - - - - - - -
object

Object

...

Further arguments to be passed

+
...
+

Further arguments to be passed

-

Value

+
+
+

Value

+ -

Numeric value: the cross-validated deviance value

+

Numeric value: the cross-validated deviance value

+
+
-
-
-

Developed by Alexander Robitzsch.

+
+

Developed by Alexander Robitzsch.

-

Site built with pkgdown 1.5.1.

+

Site built with pkgdown 2.0.7.

-
-
+
- - + + diff --git a/docs/reference/IRT.data.tam.html b/docs/reference/IRT.data.tam.html index be47255..0bc4292 100644 --- a/docs/reference/IRT.data.tam.html +++ b/docs/reference/IRT.data.tam.html @@ -1,69 +1,14 @@ - - - - - - - -Extracting Item Response Dataset — IRT.data.tam • TAM - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Extracting Item Response Dataset — IRT.data.tam • TAM - - - - - - - - - - - - - + + -
-
- -
- -
+

Extracting Item Response Dataset

@@ -117,77 +49,76 @@

Extracting Item Response Dataset

Extracts the used data set for models -fitted in TAM. See CDM::IRT.data +fitted in TAM. See CDM::IRT.data for more details.

- 
# S3 method for tam.mml
-IRT.data(object, ...)
-
-# S3 method for tam.mml.3pl
-IRT.data(object, ...)
-
-# S3 method for tamaan
-IRT.data(object, ...)
- -

Arguments

- - - - - - - - - - -
object

Object of class tam, tam.mml, -tam.mml.3pl or tamaan.

...

Further arguments to be passed

- -

Value

- -

A dataset with item responses

- -

Examples

- 
if (FALSE) {
-#############################################################################
-# EXAMPLE 1: Dichotomous data data.sim.rasch
-#############################################################################
-
-data(data.sim.rasch)
-dat <- data.sim.rasch
-
-# estimate model
-mod1 <- TAM::tam.mml(dat)
-# extract dataset (and weights and group if available)
-dmod1 <- IRT.data(mod1)
-str(dmod1)
-}
+
+ 
# S3 method for tam.mml
+IRT.data(object, ...)
+
+# S3 method for tam.mml.3pl
+IRT.data(object, ...)
+
+# S3 method for tamaan
+IRT.data(object, ...)
+
+ +
+

Arguments

+
object
+

Object of class tam, tam.mml, +tam.mml.3pl or tamaan.

+ +
...
+

Further arguments to be passed

+ +
+
+

Value

+ + +

A dataset with item responses

+
+ +
+

Examples

+ 
if (FALSE) {
+#############################################################################
+# EXAMPLE 1: Dichotomous data data.sim.rasch
+#############################################################################
+
+data(data.sim.rasch)
+dat <- data.sim.rasch
+
+# estimate model
+mod1 <- TAM::tam.mml(dat)
+# extract dataset (and weights and group if available)
+dmod1 <- IRT.data(mod1)
+str(dmod1)
+}
+
+
-
-
-

Developed by Alexander Robitzsch.

+
+

Developed by Alexander Robitzsch.

-

Site built with pkgdown 1.5.1.

+

Site built with pkgdown 2.0.7.

-
-
+
- - + + diff --git a/docs/reference/IRT.drawPV.html b/docs/reference/IRT.drawPV.html index 35ebd08..454fc6b 100644 --- a/docs/reference/IRT.drawPV.html +++ b/docs/reference/IRT.drawPV.html @@ -1,70 +1,15 @@ - - - - - - - -Function for Drawing Plausible Values — IRT.drawPV • TAM - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Function for Drawing Plausible Values — IRT.drawPV • TAM - - - - - - - - - - - - - + + -
-
- -
- -
+

Function for Drawing Plausible Values

@@ -119,70 +51,69 @@

Function for Drawing Plausible Values

This function draws plausible values of a continuous latent variable based on a fitted object for which the -CDM::IRT.posterior method +CDM::IRT.posterior method is defined.

- 
IRT.drawPV(object,NPV=5)
- -

Arguments

- - - - - - - - - - -
object

Object for which the method CDM::IRT.posterior - does exist.

NPV

Number of plausible values to be drawn.

- -

Value

- -

Matrix with plausible values

- -

Examples

- 
if (FALSE) {
-#############################################################################
-# EXAMPLE 1: Plausible value imputation for Rasch model in sirt
-#############################################################################
-
-library(sirt)
-data(data.read, package="sirt")
-dat <- data.read
-
-# fit Rasch model
-mod <- rasch.mml2(dat)
-# draw 10 plausible values
-pv1 <- TAM::IRT.drawPV(mod, NPV=10)
-}
+
+ 
IRT.drawPV(object,NPV=5)
+
+ +
+

Arguments

+
object
+

Object for which the method CDM::IRT.posterior + does exist.

+ +
NPV
+

Number of plausible values to be drawn.

+ +
+
+

Value

+ + +

Matrix with plausible values

+
+ +
+

Examples

+ 
if (FALSE) {
+#############################################################################
+# EXAMPLE 1: Plausible value imputation for Rasch model in sirt
+#############################################################################
+
+library(sirt)
+data(data.read, package="sirt")
+dat <- data.read
+
+# fit Rasch model
+mod <- rasch.mml2(dat)
+# draw 10 plausible values
+pv1 <- TAM::IRT.drawPV(mod, NPV=10)
+}
+
+
-
-
-

Developed by Alexander Robitzsch.

+
+

Developed by Alexander Robitzsch.

-

Site built with pkgdown 1.5.1.

+

Site built with pkgdown 2.0.7.

-
-
+
- - + + diff --git a/docs/reference/IRT.expectedCounts.tam.html b/docs/reference/IRT.expectedCounts.tam.html index c02df25..a88194b 100644 --- a/docs/reference/IRT.expectedCounts.tam.html +++ b/docs/reference/IRT.expectedCounts.tam.html @@ -1,69 +1,14 @@ - - - - - - - -Extracting Expected Counts — IRT.expectedCounts • TAM - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Extracting Expected Counts — IRT.expectedCounts • TAM - - - - - - - - - - - - - + + -
-
- -
- -
+

Extracting Expected Counts

@@ -117,80 +49,79 @@

Extracting Expected Counts

Extracts expected counts for models -fitted in TAM. See CDM::IRT.expectedCounts +fitted in TAM. See CDM::IRT.expectedCounts for more details.

- 
# S3 method for tam
-IRT.expectedCounts(object, ...)
-
-# S3 method for tam.mml
-IRT.expectedCounts(object, ...)
-
-# S3 method for tam.mml.3pl
-IRT.expectedCounts(object, ...)
-
-# S3 method for tamaan
-IRT.expectedCounts(object, ...)
-
-# S3 method for tam.np
-IRT.expectedCounts(object, ...)
- -

Arguments

- - - - - - - - - - -
object

Object of class tam, tam.mml, -tam.mml.3pl, tam.np or tamaan.

...

Further arguments to be passed

- -

Value

- -

See CDM::IRT.expectedCounts.

- -

Examples

- 
if (FALSE) {
-#############################################################################
-# EXAMPLE 1: Dichotomous data data.sim.rasch - extract expected counts
-#############################################################################
-
-data(data.sim.rasch)
-# 1PL estimation
-mod1 <- TAM::tam.mml(resp=data.sim.rasch)
-# extract expected counts
-IRT.expectedCounts(mod1)
-}
+
+ 
# S3 method for tam
+IRT.expectedCounts(object, ...)
+
+# S3 method for tam.mml
+IRT.expectedCounts(object, ...)
+
+# S3 method for tam.mml.3pl
+IRT.expectedCounts(object, ...)
+
+# S3 method for tamaan
+IRT.expectedCounts(object, ...)
+
+# S3 method for tam.np
+IRT.expectedCounts(object, ...)
+
+ +
+

Arguments

+
object
+

Object of class tam, tam.mml, +tam.mml.3pl, tam.np or tamaan.

+ +
...
+

Further arguments to be passed

+ +
+
+

Value

+ + +

See CDM::IRT.expectedCounts.

+
+ +
+

Examples

+ 
if (FALSE) {
+#############################################################################
+# EXAMPLE 1: Dichotomous data data.sim.rasch - extract expected counts
+#############################################################################
+
+data(data.sim.rasch)
+# 1PL estimation
+mod1 <- TAM::tam.mml(resp=data.sim.rasch)
+# extract expected counts
+IRT.expectedCounts(mod1)
+}
+
+
-
-
-

Developed by Alexander Robitzsch.

+
+

Developed by Alexander Robitzsch.

-

Site built with pkgdown 1.5.1.

+

Site built with pkgdown 2.0.7.

-
-
+
- - + + diff --git a/docs/reference/IRT.factor.scores.tam.html b/docs/reference/IRT.factor.scores.tam.html index 5d7257a..f16e73a 100644 --- a/docs/reference/IRT.factor.scores.tam.html +++ b/docs/reference/IRT.factor.scores.tam.html @@ -1,69 +1,14 @@ - - - - - - - -Extracting Factor Scores in <span class="pkg">TAM</span> — IRT.factor.scores • TAM - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -TAM — IRT.factor.scores" /> -Extracting Factor Scores in TAM — IRT.factor.scores • TAM - - - - - - - - - - - - - + + -
-
- -
- -
+

Extracting Factor Scores in TAM

@@ -117,90 +49,88 @@

Extracting Factor Scores in TAM

Extracts factor scores for models -fitted in TAM. See CDM::IRT.factor.scores +fitted in TAM. See CDM::IRT.factor.scores for more details.

- 
# S3 method for tam
-IRT.factor.scores(object, type="EAP", ...)
-
-# S3 method for tam.mml
-IRT.factor.scores(object, type="EAP", ...)
-
-# S3 method for tam.mml.3pl
-IRT.factor.scores(object, type="EAP", ...)
-
-# S3 method for tamaan
-IRT.factor.scores(object, type="EAP", ...)
- -

Arguments

- - - - - - - - - - - - - - -
object

Object of class tam, tam.mml, -tam.mml.3pl or tamaan.

type

Type of factor score to be used. type="EAP" can be used +

+ 
# S3 method for tam
+IRT.factor.scores(object, type="EAP", ...)
+
+# S3 method for tam.mml
+IRT.factor.scores(object, type="EAP", ...)
+
+# S3 method for tam.mml.3pl
+IRT.factor.scores(object, type="EAP", ...)
+
+# S3 method for tamaan
+IRT.factor.scores(object, type="EAP", ...)
+
+ +
+

Arguments

+
object
+

Object of class tam, tam.mml, +tam.mml.3pl or tamaan.

+ +
type
+

Type of factor score to be used. type="EAP" can be used for all classes in TAM while type="WLE" and type="MLE" can only be used for objects of class - tam.mml. Further arguments to the - used function tam.wle can be specified - with ....

...

Further arguments to be passed

- -

Value

- -

See CDM::IRT.factor.scores.

- -

Examples

- 
if (FALSE) {
-#############################################################################
-# EXAMPLE 1: data.sim.rasch - Different factor scores in Rasch model
-#############################################################################
-
-data(data.sim.rasch)
-# 1PL estimation
-mod1 <- TAM::tam.mml(resp=data.sim.rasch)
-# EAP
-pmod1 <- IRT.factor.scores( mod1 )
-# WLE
-pmod1 <- IRT.factor.scores( mod1, type="WLE" )
-# MLE
-pmod1 <- IRT.factor.scores( mod1, type="MLE" )
-}
+ tam.mml. Further arguments to the + used function tam.wle can be specified + with ....

+ +
...
+

Further arguments to be passed

+ +
+
+

Value

+ + +

See CDM::IRT.factor.scores.

+
+ +
+

Examples

+ 
if (FALSE) {
+#############################################################################
+# EXAMPLE 1: data.sim.rasch - Different factor scores in Rasch model
+#############################################################################
+
+data(data.sim.rasch)
+# 1PL estimation
+mod1 <- TAM::tam.mml(resp=data.sim.rasch)
+# EAP
+pmod1 <- IRT.factor.scores( mod1 )
+# WLE
+pmod1 <- IRT.factor.scores( mod1, type="WLE" )
+# MLE
+pmod1 <- IRT.factor.scores( mod1, type="MLE" )
+}
+
+
-
-
-

Developed by Alexander Robitzsch.

+
+

Developed by Alexander Robitzsch.

-

Site built with pkgdown 1.5.1.

+

Site built with pkgdown 2.0.7.

-
-
+
- - + + diff --git a/docs/reference/IRT.frequencies.tam.html b/docs/reference/IRT.frequencies.tam.html index ae9d86b..bc42a06 100644 --- a/docs/reference/IRT.frequencies.tam.html +++ b/docs/reference/IRT.frequencies.tam.html @@ -1,69 +1,14 @@ - - - - - - - -Observed and Expected Frequencies for Univariate and Bivariate Distributions — IRT.frequencies.tam • TAM - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Observed and Expected Frequencies for Univariate and Bivariate Distributions — IRT.frequencies.tam • TAM - - - - - - - - - - - - - + + -
-
- -
- -
+

Observed and Expected Frequencies for Univariate and Bivariate Distributions

@@ -117,80 +49,80 @@

Observed and Expected Frequencies for Univariate and Bivariate Distributions

Computes observed and expected frequencies for univariate and bivariate distributions -for models fitted in TAM. See CDM::IRT.frequencies +for models fitted in TAM. See CDM::IRT.frequencies for more details.

- 
# S3 method for tam.mml
-IRT.frequencies(object, ...)
-
-# S3 method for tam.mml.3pl
-IRT.frequencies(object, ...)
-
-# S3 method for tamaan
-IRT.frequencies(object, ...)
- -

Arguments

- - - - - - - - - - -
object

Object of class tam, tam.mml, -tam.mml.3pl or tamaan.

...

Further arguments to be passed

- -

Value

- -

See CDM::IRT.frequencies.

-

See also

- -

CDM::IRT.frequencies

- -

Examples

- 
if (FALSE) {
-#############################################################################
-# EXAMPLE 1: Dichotomous data data.sim.rasch
-#############################################################################
-
-data(data.sim.rasch)
-dat <- data.sim.rasch
-
-# estimate model
-mod1 <- TAM::tam.mml(dat)
-# compute observed and expected frequencies
-fmod1 <- IRT.frequencies(mod1)
-str(fmod1)
-}
+
+ 
# S3 method for tam.mml
+IRT.frequencies(object, ...)
+
+# S3 method for tam.mml.3pl
+IRT.frequencies(object, ...)
+
+# S3 method for tamaan
+IRT.frequencies(object, ...)
+
+ +
+

Arguments

+
object
+

Object of class tam, tam.mml, +tam.mml.3pl or tamaan.

+ +
...
+

Further arguments to be passed

+ +
+
+

Value

+ + +

See CDM::IRT.frequencies.

+
+
+

See also

+

CDM::IRT.frequencies

+
+ +
+

Examples

+ 
if (FALSE) {
+#############################################################################
+# EXAMPLE 1: Dichotomous data data.sim.rasch
+#############################################################################
+
+data(data.sim.rasch)
+dat <- data.sim.rasch
+
+# estimate model
+mod1 <- TAM::tam.mml(dat)
+# compute observed and expected frequencies
+fmod1 <- IRT.frequencies(mod1)
+str(fmod1)
+}
+
+
-
-
-

Developed by Alexander Robitzsch.

+
+

Developed by Alexander Robitzsch.

-

Site built with pkgdown 1.5.1.

+

Site built with pkgdown 2.0.7.

-
-
+
- - + + diff --git a/docs/reference/IRT.informationCurves.html b/docs/reference/IRT.informationCurves.html index ed0afc4..8f57f7f 100644 --- a/docs/reference/IRT.informationCurves.html +++ b/docs/reference/IRT.informationCurves.html @@ -1,67 +1,12 @@ - - - - - - - -Item and Test Information Curve — IRT.informationCurves • TAM - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Item and Test Information Curve — IRT.informationCurves • TAM - - - - + + -
-
- -
- -
+

Item and Test Information Curve

@@ -117,180 +49,184 @@

Item and Test Information Curve

An S3 method which computes item and test information curves, see Muraki (1993).

- 
IRT.informationCurves(object, ...)
+    

+    
IRT.informationCurves(object, ...)
+
+# S3 method for tam.mml
+IRT.informationCurves( object, h=.0001, iIndex=NULL,
+          theta=NULL, ... )
+
+# S3 method for tam.mml.2pl
+IRT.informationCurves( object, h=.0001, iIndex=NULL,
+          theta=NULL, ... )
+
+# S3 method for tam.mml.mfr
+IRT.informationCurves( object, h=.0001, iIndex=NULL,
+          theta=NULL, ... )
+
+# S3 method for tam.mml.3pl
+IRT.informationCurves( object, h=.0001, iIndex=NULL,
+          theta=NULL, ... )
+
+# S3 method for IRT.informationCurves
+plot(x, curve_type="test", ...)

+    

 
-# S3 method for tam.mml
-IRT.informationCurves( object, h=.0001, iIndex=NULL,
-          theta=NULL, ... )
+    

+    
Arguments

+    
object

+
Object of class tam.mml, tam.mml.2pl, tam.mml.mfr
+or tam.mml.3pl.

 
-# S3 method for tam.mml.2pl
-IRT.informationCurves( object, h=.0001, iIndex=NULL,
-          theta=NULL, ... )
+  
...

+
Further arguments to be passed

 
-# S3 method for tam.mml.mfr
-IRT.informationCurves( object, h=.0001, iIndex=NULL,
-          theta=NULL, ... )
+
h

+
Numerical differentiation parameter

 
-# S3 method for tam.mml.3pl
-IRT.informationCurves( object, h=.0001, iIndex=NULL,
-          theta=NULL, ... )
+
iIndex

+
Indices of items for which test information should be computed.
+The default is to use all items.

 
-# S3 method for IRT.informationCurves
-plot(x, curve_type="test", ...)
+
theta
+

Optional vector of \(\theta\) for which information curves +should be computed.

-

Arguments

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
object

Object of class tam.mml, tam.mml.2pl, tam.mml.mfr -or tam.mml.3pl.

...

Further arguments to be passed

h

Numerical differentiation parameter

iIndex

Indices of items for which test information should be computed. -The default is to use all items.

theta

Optional vector of \(\theta\) for which information curves -should be computed.

curve_type

Type of information to be plotted. It can be "test" +

curve_type
+

Type of information to be plotted. It can be "test" for the test information curve and "se" for the -standard error curve.

x

Object of class tam.mml, tam.mml.2pl, tam.mml.mfr -or tam.mml.3pl.

- -

Value

- -

List with following entries

-
se_curve

Standard error curves

-
test_info_curve

Test information curve

-
info_curves_item

Item information curves

-
info_curves_categories

Item-category information curves

-
theta

Used \(\theta\) grid

- -

References

- -

Muraki, E. (1993). Information functions of the generalized partial credit -model. Applied Psychological Measurement, 17(4), 351-363. -doi: 10.1177/014662169301700403

- -

Examples

- 
if (FALSE) {
-#############################################################################
-# EXAMPLE 1: Dichotomous data | data.read
-#############################################################################
-
-data(data.read, package="sirt")
-dat <- data.read
+standard error curve.

 
-# fit 2PL model
-mod1 <- TAM::tam.mml.2pl( dat )
-summary(mod1)
+  
x

+
Object of class tam.mml, tam.mml.2pl, tam.mml.mfr
+or tam.mml.3pl.

 
-# compute information curves at grid seq(-5,5,length=100)
-imod1 <- TAM::IRT.informationCurves( mod1, theta=seq(-5,5,len=100)  )
-str(imod1)
-# plot test information
-plot( imod1 )
-# plot standard error curve
-plot( imod1, curve_type="se", xlim=c(-3,2) )
-# cutomized plot
-plot( imod1, curve_type="se", xlim=c(-3,2), ylim=c(0,2), lwd=2, lty=3)
-
-#############################################################################
-# EXAMPLE 2: Mixed dichotomous and polytomous data
-#############################################################################
+
+
+

Value

+ -data(data.timssAusTwn.scored, package="TAM") -dat <- data.timssAusTwn.scored -# select item response data -items <- grep( "M0", colnames(dat), value=TRUE ) -resp <- dat[, items ] +

List with following entries

+
se_curve
+

Standard error curves

-#*** Model 1: Partial credit model -mod1 <- TAM::tam.mml( resp ) -summary(mod1) -# information curves -imod1 <- TAM::IRT.informationCurves( mod1, theta=seq(-3,3,len=20) ) +
test_info_curve
+

Test information curve

-#*** Model 2: Generalized partial credit model -mod2 <- TAM::tam.mml.2pl( resp, irtmodel="GPCM") -summary(mod2) -imod2 <- TAM::IRT.informationCurves( mod2 ) +
info_curves_item
+

Item information curves

-#*** Model 3: Mixed 3PL and generalized partial credit model -psych::describe(resp) -maxK <- apply( resp, 2, max, na.rm=TRUE ) -I <- ncol(resp) -# specify guessing parameters, including a prior distribution -est.guess <- 1:I -est.guess[ maxK > 1 ] <- 0 -guess <- .2*(est.guess >0) -guess.prior <- matrix( 0, nrow=I, ncol=2 ) -guess.prior[ est.guess > 0, 1] <- 5 -guess.prior[ est.guess > 0, 2] <- 17 +
info_curves_categories
+

Item-category information curves

-# fit model -mod3 <- TAM::tam.mml.3pl( resp, gammaslope.des="2PL", est.guess=est.guess, guess=guess, - guess.prior=guess.prior, - control=list( maxiter=100, Msteps=10, fac.oldxsi=0.1, - nodes=seq(-8,8,len=41) ), est.variance=FALSE ) -summary(mod3) +
theta
+

Used \(\theta\) grid

-# information curves -imod3 <- TAM::IRT.informationCurves( mod3 ) -imod3 +
+
+

References

+

Muraki, E. (1993). Information functions of the generalized partial credit +model. Applied Psychological Measurement, 17(4), 351-363. +doi:10.1177/014662169301700403

+
-#*** estimate model in mirt package -library(mirt) -itemtype <- rep("gpcm", I) -itemtype[ maxK==1] <- "3PL" -mod3b <- mirt::mirt(resp, 1, itemtype=itemtype, verbose=TRUE ) -print(mod3b) -} +
+

Examples

+ 
if (FALSE) {
+#############################################################################
+# EXAMPLE 1: Dichotomous data | data.read
+#############################################################################
+
+data(data.read, package="sirt")
+dat <- data.read
+
+# fit 2PL model
+mod1 <- TAM::tam.mml.2pl( dat )
+summary(mod1)
+
+# compute information curves at grid seq(-5,5,length=100)
+imod1 <- TAM::IRT.informationCurves( mod1, theta=seq(-5,5,len=100)  )
+str(imod1)
+# plot test information
+plot( imod1 )
+# plot standard error curve
+plot( imod1, curve_type="se", xlim=c(-3,2) )
+# cutomized plot
+plot( imod1, curve_type="se", xlim=c(-3,2), ylim=c(0,2), lwd=2, lty=3)
+
+#############################################################################
+# EXAMPLE 2: Mixed dichotomous and polytomous data
+#############################################################################
+
+data(data.timssAusTwn.scored, package="TAM")
+dat <- data.timssAusTwn.scored
+# select item response data
+items <- grep( "M0", colnames(dat), value=TRUE )
+resp <- dat[, items ]
+
+#*** Model 1: Partial credit model
+mod1 <- TAM::tam.mml( resp )
+summary(mod1)
+# information curves
+imod1 <- TAM::IRT.informationCurves( mod1, theta=seq(-3,3,len=20)  )
+
+#*** Model 2: Generalized partial credit model
+mod2 <- TAM::tam.mml.2pl( resp, irtmodel="GPCM")
+summary(mod2)
+imod2 <- TAM::IRT.informationCurves( mod2 )
+
+#*** Model 3: Mixed 3PL and generalized partial credit model
+psych::describe(resp)
+maxK <- apply( resp, 2, max, na.rm=TRUE )
+I <- ncol(resp)
+# specify guessing parameters, including a prior distribution
+est.guess <- 1:I
+est.guess[ maxK > 1 ] <- 0
+guess <- .2*(est.guess >0)
+guess.prior <- matrix( 0, nrow=I, ncol=2 )
+guess.prior[ est.guess  > 0, 1] <- 5
+guess.prior[ est.guess  > 0, 2] <- 17
+
+# fit model
+mod3 <- TAM::tam.mml.3pl( resp, gammaslope.des="2PL", est.guess=est.guess, guess=guess,
+           guess.prior=guess.prior,
+           control=list( maxiter=100, Msteps=10, fac.oldxsi=0.1,
+                        nodes=seq(-8,8,len=41) ),  est.variance=FALSE )
+summary(mod3)
+
+# information curves
+imod3 <- TAM::IRT.informationCurves( mod3 )
+imod3
+
+#*** estimate model in mirt package
+library(mirt)
+itemtype <- rep("gpcm", I)
+itemtype[ maxK==1] <- "3PL"
+mod3b <- mirt::mirt(resp, 1, itemtype=itemtype, verbose=TRUE )
+print(mod3b)
+}
+
+
-
-
-

Developed by Alexander Robitzsch.

+
+

Developed by Alexander Robitzsch.

-

Site built with pkgdown 1.5.1.

+

Site built with pkgdown 2.0.7.

-
-
+
- - + + diff --git a/docs/reference/IRT.irfprob.tam.html b/docs/reference/IRT.irfprob.tam.html index 90b5080..c81f4be 100644 --- a/docs/reference/IRT.irfprob.tam.html +++ b/docs/reference/IRT.irfprob.tam.html @@ -1,69 +1,14 @@ - - - - - - - -Extracting Item Response Functions — IRT.irfprob • TAM - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Extracting Item Response Functions — IRT.irfprob • TAM - - - - - - - - - - - - - + + -
-
- -
- -
+

Extracting Item Response Functions

@@ -117,77 +49,76 @@

Extracting Item Response Functions

Extracts item response functions for models -fitted in TAM. See CDM::IRT.irfprob +fitted in TAM. See CDM::IRT.irfprob for more details.

- 
# S3 method for tam
-IRT.irfprob(object, ...)
-
-# S3 method for tam.mml
-IRT.irfprob(object, ...)
-
-# S3 method for tam.mml.3pl
-IRT.irfprob(object, ...)
-
-# S3 method for tamaan
-IRT.irfprob(object, ...)
-
-# S3 method for tam.np
-IRT.irfprob(object, ...)
+
+ 
# S3 method for tam
+IRT.irfprob(object, ...)
+
+# S3 method for tam.mml
+IRT.irfprob(object, ...)
+
+# S3 method for tam.mml.3pl
+IRT.irfprob(object, ...)
+
+# S3 method for tamaan
+IRT.irfprob(object, ...)
+
+# S3 method for tam.np
+IRT.irfprob(object, ...)
+
-

Arguments

- - - - - - - - - - -
object

Object of class tam, tam.mml, -tam.mml.3pl, tam.np or tamaan.

...

Further arguments to be passed

+
+

Arguments

+
object
+

Object of class tam, tam.mml, +tam.mml.3pl, tam.np or tamaan.

-

Value

+
...
+

Further arguments to be passed

-

See CDM::IRT.irfprob.

+
+
+

Value

+ -

Examples

- 
#############################################################################
-# EXAMPLE 1: Dichotomous data data.sim.rasch - item response functions
-#############################################################################
+
See CDM::IRT.irfprob.

+
-data(data.sim.rasch) -# 1PL estimation -mod1 <- TAM::tam.mml(resp=data.sim.rasch) -IRT.irfprob(mod1) +
+

Examples

+ 
#############################################################################
+# EXAMPLE 1: Dichotomous data data.sim.rasch - item response functions
+#############################################################################
+
+data(data.sim.rasch)
+# 1PL estimation
+mod1 <- TAM::tam.mml(resp=data.sim.rasch)
+IRT.irfprob(mod1)
+
+
-
-
-

Developed by Alexander Robitzsch.

+
+

Developed by Alexander Robitzsch.

-

Site built with pkgdown 1.5.1.

+

Site built with pkgdown 2.0.7.

-
-
+
- - + + diff --git a/docs/reference/IRT.itemfit.html b/docs/reference/IRT.itemfit.html index 6908dc0..b5bbb57 100644 --- a/docs/reference/IRT.itemfit.html +++ b/docs/reference/IRT.itemfit.html @@ -1,71 +1,16 @@ - - - - - - - -RMSD Item Fit Statistics for <span class="pkg">TAM</span> Objects — IRT.itemfit.tam • TAM - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -TAM Objects — IRT.itemfit.tam" /> -RMSD Item Fit Statistics for TAM Objects — IRT.itemfit.tam • TAM - - - - - - - - - - - - - + + -
-
- -
- -
+

RMSD Item Fit Statistics for TAM Objects

@@ -121,124 +53,121 @@

RMSD Item Fit Statistics for TAM Objects

Computes the RMSD item fit statistic (formerly labeled as RMSEA; Yamamoto, Khorramdel, & von Davier, 2013) for fitted objects in the TAM package, see -CDM::IRT.itemfit and -CDM::IRT.RMSD.

+CDM::IRT.itemfit and +CDM::IRT.RMSD.

- 
# S3 method for tam.mml
-IRT.itemfit(object, method="RMSD", ...)
-
-# S3 method for tam.mml.2pl
-IRT.itemfit(object, method="RMSD", ...)
-
-# S3 method for tam.mml.mfr
-IRT.itemfit(object, method="RMSD", ...)
-
-# S3 method for tam.mml.3pl
-IRT.itemfit(object, method="RMSD", ...)
- -

Arguments

- - - - - - - - - - - - - - -
object

Object of class tam.mml, tam.mml.2pl, tam.mml.mfr -or tam.mml.3pl.

method

Requested method for item fit calculation. Currently, +

+ 
# S3 method for tam.mml
+IRT.itemfit(object, method="RMSD", ...)
+
+# S3 method for tam.mml.2pl
+IRT.itemfit(object, method="RMSD", ...)
+
+# S3 method for tam.mml.mfr
+IRT.itemfit(object, method="RMSD", ...)
+
+# S3 method for tam.mml.3pl
+IRT.itemfit(object, method="RMSD", ...)
+
+ +
+

Arguments

+
object
+

Object of class tam.mml, tam.mml.2pl, tam.mml.mfr +or tam.mml.3pl.

+ +
method
+

Requested method for item fit calculation. Currently, only the RMSD fit statistic (formerly labeled as the RMSEA statistic, -see CDM::IRT.RMSD) -can be used.

...

Further arguments to be passed.

+see CDM::IRT.RMSD) +can be used.

-

References

+
...
+

Further arguments to be passed.

+
+
+

References

Yamamoto, K., Khorramdel, L., & von Davier, M. (2013). Scaling PIAAC cognitive data. In OECD (Eds.). Technical Report of the Survey of Adults Skills (PIAAC) (Ch. 17). Paris: OECD.

-

See also

- -

CDM::IRT.itemfit, -CDM::IRT.RMSD

- -

Examples

- 
if (FALSE) {
-#############################################################################
-# EXAMPLE 1: RMSD item fit statistic data.read
-#############################################################################
-
-library(sirt)
-data(data.read,package="sirt")
-dat <- data.read
-
-#*** fit 1PL model
-mod1 <- TAM::tam.mml( dat )
-summary(mod1)
-
-#*** fit 2PL model
-mod2 <- TAM::tam.mml.2pl( dat )
-summary(mod2)
-
-#*** assess RMSEA item fit
-fmod1 <- IRT.itemfit(mod1)
-fmod2 <- IRT.itemfit(mod2)
-# summary of fit statistics
-summary( fmod1 )
-summary( fmod2 )
-
-#############################################################################
-# EXAMPLE 2: Simulated 2PL data and fit of 1PL model
-#############################################################################
-
-set.seed(987)
-N <- 1000    # 1000 persons
-I <- 10      # 10 items
-# define item difficulties and item slopes
-b <- seq(-2,2,len=I)
-a <- rep(1,I)
-a[c(3,8)] <- c( 1.7, .4 )
-# simulate 2PL data
-dat <- sirt::sim.raschtype( theta=rnorm(N), b=b, fixed.a=a)
-
-# fit 1PL model
-mod <- TAM::tam.mml( dat )
-
-# RMSEA item fit
-fmod <- IRT.itemfit(mod)
-round( fmod, 3 )
-}
+
+
+

See also

+

CDM::IRT.itemfit, +CDM::IRT.RMSD

+
+ +
+

Examples

+ 
if (FALSE) {
+#############################################################################
+# EXAMPLE 1: RMSD item fit statistic data.read
+#############################################################################
+
+library(sirt)
+data(data.read,package="sirt")
+dat <- data.read
+
+#*** fit 1PL model
+mod1 <- TAM::tam.mml( dat )
+summary(mod1)
+
+#*** fit 2PL model
+mod2 <- TAM::tam.mml.2pl( dat )
+summary(mod2)
+
+#*** assess RMSEA item fit
+fmod1 <- IRT.itemfit(mod1)
+fmod2 <- IRT.itemfit(mod2)
+# summary of fit statistics
+summary( fmod1 )
+summary( fmod2 )
+
+#############################################################################
+# EXAMPLE 2: Simulated 2PL data and fit of 1PL model
+#############################################################################
+
+set.seed(987)
+N <- 1000    # 1000 persons
+I <- 10      # 10 items
+# define item difficulties and item slopes
+b <- seq(-2,2,len=I)
+a <- rep(1,I)
+a[c(3,8)] <- c( 1.7, .4 )
+# simulate 2PL data
+dat <- sirt::sim.raschtype( theta=rnorm(N), b=b, fixed.a=a)
+
+# fit 1PL model
+mod <- TAM::tam.mml( dat )
+
+# RMSEA item fit
+fmod <- IRT.itemfit(mod)
+round( fmod, 3 )
+}
+
+
-
-
-

Developed by Alexander Robitzsch.

+
+

Developed by Alexander Robitzsch.

-

Site built with pkgdown 1.5.1.

+

Site built with pkgdown 2.0.7.

-
-
+
- - + + diff --git a/docs/reference/IRT.likelihood.tam.html b/docs/reference/IRT.likelihood.tam.html index c1a5631..033fc9b 100644 --- a/docs/reference/IRT.likelihood.tam.html +++ b/docs/reference/IRT.likelihood.tam.html @@ -1,69 +1,14 @@ - - - - - - - -Extracting Individual Likelihood and Individual Posterior — IRT.likelihood • TAM - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Extracting Individual Likelihood and Individual Posterior — IRT.likelihood • TAM - - - - - - - - - - - - - + + -
-
- -
- -
+

Extracting Individual Likelihood and Individual Posterior

@@ -117,96 +49,95 @@

Extracting Individual Likelihood and Individual Posterior

Extracts individual likelihood and posterior for models -fitted in TAM. See CDM::IRT.likelihood +fitted in TAM. See CDM::IRT.likelihood for more details.

- 
# S3 method for tam
-IRT.likelihood(object, ...)
-# S3 method for tam
-IRT.posterior(object, ...)
-
-# S3 method for tam.mml
-IRT.likelihood(object, ...)
-# S3 method for tam.mml
-IRT.posterior(object, ...)
-
-# S3 method for tam.mml.3pl
-IRT.likelihood(object, ...)
-# S3 method for tam.mml.3pl
-IRT.posterior(object, ...)
-
-# S3 method for tamaan
-IRT.likelihood(object, ...)
-# S3 method for tamaan
-IRT.posterior(object, ...)
-
-# S3 method for tam.latreg
-IRT.likelihood(object, ...)
-# S3 method for tam.latreg
-IRT.posterior(object, ...)
-
-# S3 method for tam.np
-IRT.likelihood(object, ...)
-# S3 method for tam.np
-IRT.posterior(object, ...)
- -

Arguments

- - - - - - - - - - -
object

Object of class tam, tam.mml, -tam.mml.3pl, tamaan, tam.np -or tam.latreg.

...

Further arguments to be passed

- -

Value

- -

See CDM::IRT.likelihood.

- -

Examples

- 
#############################################################################
-# EXAMPLE 1: Dichotomous data data.sim.rasch - extracting likelihood/posterior
-#############################################################################
-
-data(data.sim.rasch)
-# 1PL estimation
-mod1 <- TAM::tam.mml(resp=data.sim.rasch)
-lmod1 <- IRT.likelihood(mod1)
-str(lmod1)
-pmod1 <- IRT.posterior(mod1)
-str(pmod1)
+
+ 
# S3 method for tam
+IRT.likelihood(object, ...)
+# S3 method for tam
+IRT.posterior(object, ...)
+
+# S3 method for tam.mml
+IRT.likelihood(object, ...)
+# S3 method for tam.mml
+IRT.posterior(object, ...)
+
+# S3 method for tam.mml.3pl
+IRT.likelihood(object, ...)
+# S3 method for tam.mml.3pl
+IRT.posterior(object, ...)
+
+# S3 method for tamaan
+IRT.likelihood(object, ...)
+# S3 method for tamaan
+IRT.posterior(object, ...)
+
+# S3 method for tam.latreg
+IRT.likelihood(object, ...)
+# S3 method for tam.latreg
+IRT.posterior(object, ...)
+
+# S3 method for tam.np
+IRT.likelihood(object, ...)
+# S3 method for tam.np
+IRT.posterior(object, ...)
+
+ +
+

Arguments

+
object
+

Object of class tam, tam.mml, +tam.mml.3pl, tamaan, tam.np +or tam.latreg.

+ +
...
+

Further arguments to be passed

+ +
+
+

Value

+ + +

See CDM::IRT.likelihood.

+
+ +
+

Examples

+ 
#############################################################################
+# EXAMPLE 1: Dichotomous data data.sim.rasch - extracting likelihood/posterior
+#############################################################################
+
+data(data.sim.rasch)
+# 1PL estimation
+mod1 <- TAM::tam.mml(resp=data.sim.rasch)
+lmod1 <- IRT.likelihood(mod1)
+str(lmod1)
+pmod1 <- IRT.posterior(mod1)
+str(pmod1)
+
+
-
-
-

Developed by Alexander Robitzsch.

+
+

Developed by Alexander Robitzsch.

-

Site built with pkgdown 1.5.1.

+

Site built with pkgdown 2.0.7.

-
-
+
- - + + diff --git a/docs/reference/IRT.linearCFA.html b/docs/reference/IRT.linearCFA.html index e7ab064..e196056 100644 --- a/docs/reference/IRT.linearCFA.html +++ b/docs/reference/IRT.linearCFA.html @@ -1,71 +1,16 @@ - - - - - - - -Linear Approximation of a Confirmatory Factor Analysis — IRT.linearCFA • TAM - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Linear Approximation of a Confirmatory Factor Analysis — IRT.linearCFA • TAM - - - - - - - - - - - - - + + -
-
- -
- -
+

Linear Approximation of a Confirmatory Factor Analysis

@@ -125,78 +57,85 @@

Linear Approximation of a Confirmatory Factor Analysis

See Vermunt and Magidson (2005) for details.

- 
IRT.linearCFA( object, group=1)
-
-# S3 method for IRT.linearCFA
-summary(object,  ...)
- -

Arguments

- - - - - - - - - - - - - - -
object

Fitted item response model for which the IRT.expectedCounts -method is defined.

group

Group identifier which defines the selected group.

...

Further arguments to be passed.

- -

Value

- -

A list with following entries

-
loadings

Data frame with factor loadings. Mlat and +

+ 
IRT.linearCFA( object, group=1)
+
+# S3 method for IRT.linearCFA
+summary(object,  ...)
+
+ +
+

Arguments

+
object
+

Fitted item response model for which the IRT.expectedCounts +method is defined.

+ +
group
+

Group identifier which defines the selected group.

+ +
...
+

Further arguments to be passed.

+ +
+
+

Value

+ + +

A list with following entries

+
loadings
+

Data frame with factor loadings. Mlat and SDlat denote the model-implied item mean and standard deviation. The values ResidVar and h2 denote residual variances and item communality.

-
stand.loadings

Data frame with standardized factor loadings.

-
M.trait

Mean of factors

-
SD.trait

Standard deviations of factors

-

References

+
stand.loadings
+

Data frame with standardized factor loadings.

+ +
M.trait
+

Mean of factors

+
SD.trait
+

Standard deviations of factors

+ +
+
+

References

Vermunt, J. K., & Magidson, J. (2005). Factor Analysis with categorical indicators: A comparison between traditional and latent class approaches. In A. Van der Ark, M.A. Croon & K. Sijtsma (Eds.), New Developments in Categorical Data Analysis for the Social and Behavioral Sciences (pp. 41-62). Mahwah: Erlbaum

-

See also

- -

See tam.fa for confirmatory factor analysis in TAM.

+
+
+

See also

+

See tam.fa for confirmatory factor analysis in TAM.

+
-

Examples

- 

+    

+    
Examples

+    
+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/reference/IRT.residuals.html b/docs/reference/IRT.residuals.html
index ead7b64..9a0e80c 100644
--- a/docs/reference/IRT.residuals.html
+++ b/docs/reference/IRT.residuals.html
@@ -1,71 +1,16 @@
-
 
-
-  
-  
-
-
-
-Residuals in an IRT Model — IRT.residuals • TAM
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-Residuals in an IRT Model — IRT.residuals • TAM
-
-
-
-
-
-
-
-
-
-
-
-
-  
+
+    
 
-  
     

-      

-      
 
       
 
-      

-
-

+      

   

     

     
Residuals in an IRT Model

@@ -120,109 +52,120 @@ 
Residuals in an IRT Model

     

     
Defines an S3 method for the computation of observed residual values.
 The computation of residuals is based on weighted likelihood estimates as
-person parameters, see tam.wle.
+person parameters, see tam.wle.
 IRT.residuals can only be applied for unidimensional IRT models.
 The methods IRT.residuals and residuals are equivalent.

     

 
-    
IRT.residuals(object, ...)
-
-# S3 method for tam.mml
-IRT.residuals(object, ...)
-# S3 method for tam.mml
-residuals(object, ...)
-
-# S3 method for tam.mml.2pl
-IRT.residuals(object, ...)
-# S3 method for tam.mml.2pl
-residuals(object, ...)
-
-# S3 method for tam.mml.mfr
-IRT.residuals(object, ...)
-# S3 method for tam.mml.mfr
-residuals(object, ...)
-
-# S3 method for tam.jml
-IRT.residuals(object, ...)
-# S3 method for tam.jml
-residuals(object, ...)

-
-    
Arguments

-    
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
object
Object of class tam.mml, tam.mml.2pl or tam.mml.mfr.
...
Further arguments to be passed

-
-    
Value

-
-    
List with following entries

-
residuals
Residuals

-
stand_residuals
Standardized residuals

-  
X_exp
Expected value of the item response \(X_{pi}\)

-  
X_var
Variance of the item response \(X_{pi}\)

-  
theta
Used person parameter estimate

-
probs
Expected item response probabilities

-
-    
Note

+    

+    
IRT.residuals(object, ...)
+
+# S3 method for tam.mml
+IRT.residuals(object, ...)
+# S3 method for tam.mml
+residuals(object, ...)
+
+# S3 method for tam.mml.2pl
+IRT.residuals(object, ...)
+# S3 method for tam.mml.2pl
+residuals(object, ...)
+
+# S3 method for tam.mml.mfr
+IRT.residuals(object, ...)
+# S3 method for tam.mml.mfr
+residuals(object, ...)
+
+# S3 method for tam.jml
+IRT.residuals(object, ...)
+# S3 method for tam.jml
+residuals(object, ...)

+    

+
+    

+    
Arguments

+    
object

+
Object of class tam.mml, tam.mml.2pl or tam.mml.mfr.

+
+
...

+
Further arguments to be passed

+
+

+    

+    
Value

+    
+
+
List with following entries

+
residuals

+
Residuals

 
+
stand_residuals

+
Standardized residuals

+
+  
X_exp

+
Expected value of the item response \(X_{pi}\)

+
+  
X_var

+
Variance of the item response \(X_{pi}\)

+
+  
theta

+
Used person parameter estimate

+
+
probs

+
Expected item response probabilities

+
+

+    

+    
Note

     
Residuals can be used to inspect local dependencies in the item
 response data, for example using principle component analysis or
 factor analysis (see Example 1).

-    
See also

-
-    
See also the eRm::residuals (eRm) or
-residuals (mirt)
-functions.

-
See also predict.tam.mml.

-
-    
Examples

-    
if (FALSE) {
-#############################################################################
-# EXAMPLE 1: Residuals data.read
-#############################################################################
-
-library(sirt)
-data(data.read, package="sirt")
-dat <- data.read
-
-# for Rasch model
-mod <- TAM::tam.mml( dat )
-# extract residuals
-res <- TAM::IRT.residuals( mod )
-str(res)
-}

+    

+    

+    
See also

+    
See also the eRm::residuals (eRm) function or the
+mirt:residuals-method in the mirt package.

+
See also predict.tam.mml.

+    

+
+    

+    
Examples

+    
if (FALSE) {
+#############################################################################
+# EXAMPLE 1: Residuals data.read
+#############################################################################
+
+library(sirt)
+data(data.read, package="sirt")
+dat <- data.read
+
+# for Rasch model
+mod <- TAM::tam.mml( dat )
+# extract residuals
+res <- TAM::IRT.residuals( mod )
+str(res)
+}

+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/reference/IRT.simulate.html b/docs/reference/IRT.simulate.html
index 0237454..11a6e25 100644
--- a/docs/reference/IRT.simulate.html
+++ b/docs/reference/IRT.simulate.html
@@ -1,67 +1,12 @@
-
 
-
-  
-  
-
-
-
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-Simulating Item Response Models — IRT.simulate • TAM
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Simulating Item Response Models

@@ -117,180 +49,176 @@ 
Simulating Item Response Models

     
Defines an S3 method for simulation of item response models.

     

 
-    
IRT.simulate(object, ...)
-
-# S3 method for tam.mml
-IRT.simulate(object, iIndex=NULL, theta=NULL, nobs=NULL, ...)
-
-# S3 method for tam.mml.2pl
-IRT.simulate(object, iIndex=NULL, theta=NULL, nobs=NULL, ...)
-
-# S3 method for tam.mml.mfr
-IRT.simulate(object, iIndex=NULL, theta=NULL, nobs=NULL, ...)
-
-# S3 method for tam.mml.3pl
-IRT.simulate(object, iIndex=NULL, theta=NULL, nobs=NULL, ...)

-
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Arguments

-    
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object
An object of class tam.mml, tam.mml.2pl, tam.mml.mfr or
-tam.mml.3pl.
iIndex
Optional vector of item indices
theta
Optional matrix of theta values
nobs
Optional numeric containing the number of observations to be simulated.
...
Further objects to be passed

-
-    
Value

-
-    
Data frame with simulated item responses

-
-    
Examples

-    
#############################################################################
-# EXAMPLE 1: Simulating Rasch model
-#############################################################################
-
-data(data.sim.rasch)
-
-#** (1) estimate model
-mod1 <- TAM::tam.mml(resp=data.sim.rasch )
-
-#** (2) simulate data
-sim.dat <- TAM::IRT.simulate(mod1)
-
-if (FALSE) {
-#** (3) use a subset of items with the argument iIndex
-set.seed(976)
-iIndex <- sort(sample(ncol(data.sim.rasch), 15))  # randomly select 15 items
-sim.dat <- TAM::IRT.simulate(mod1, iIndex=iIndex)
-mod.sim.dat <- TAM::tam.mml(sim.dat)
-
-#** (4) specify number of persons in addition
-sim.dat <- TAM::IRT.simulate(mod1, nobs=1500, iIndex=iIndex)
-
-# Rasch - constraint="items" ----
-mod1 <- TAM::tam.mml(resp=data.sim.rasch,  constraint="items",
-                control=list( xsi.start0=1, fac.oldxsi=.5) )
-
-# provide abilities
-theta0 <- matrix( rnorm(1500, mean=0.5, sd=sqrt(mod1$variance)), ncol=1 )
-# simulate data
-data <- TAM::IRT.simulate(mod1, theta=theta0 )
-# estimate model based on simulated data
-xsi.fixed <- cbind(1:nrow(mod1$item), mod1$item$xsi.item)
-mod2 <- TAM::tam.mml(data, xsi.fixed=xsi.fixed )
-summary(mod2)
-
-#############################################################################
-# EXAMPLE 2: Simulating 2PL model
-#############################################################################
-
-data(data.sim.rasch)
-# estimate 2PL
-mod2 <- TAM::tam.mml.2pl(resp=data.sim.rasch, irtmodel="2PL")
-# simulate 2PL
-sim.dat <- TAM::IRT.simulate(mod2)
-mod.sim.dat <- TAM::tam.mml.2pl(resp=sim.dat, irtmodel="2PL")
-
-#############################################################################
-# EXAMPLE 3: Simulate multiple group model
-#############################################################################
+    

+    
IRT.simulate(object, ...)
+
+# S3 method for tam.mml
+IRT.simulate(object, iIndex=NULL, theta=NULL, nobs=NULL, ...)
+
+# S3 method for tam.mml.2pl
+IRT.simulate(object, iIndex=NULL, theta=NULL, nobs=NULL, ...)
+
+# S3 method for tam.mml.mfr
+IRT.simulate(object, iIndex=NULL, theta=NULL, nobs=NULL, ...)
+
+# S3 method for tam.mml.3pl
+IRT.simulate(object, iIndex=NULL, theta=NULL, nobs=NULL, ...)

+    

 
-# Multi-Group ----
-set.seed(6778)
-N <- 3000
-theta <- c( stats::rnorm(N/2,mean=0,sd=1.5), stats::rnorm(N/2,mean=.5,sd=1)  )
-I <- 20
-p1 <- stats::plogis( outer( theta, seq( -2, 2, len=I ), "-" ) )
-resp <- 1 * ( p1 > matrix( stats::runif( N*I ), nrow=N, ncol=I ) )
-colnames(resp) <- paste("I", 1:I, sep="")
-group <- rep(1:2, each=N/2 )
-mod3 <- TAM::tam.mml(resp, group=group)
+    

+    
Arguments

+    
object

+
An object of class tam.mml, tam.mml.2pl, tam.mml.mfr or
+tam.mml.3pl.

 
-# simulate data
-sim.dat.g1 <- TAM::IRT.simulate(mod3,
-                   theta=matrix( stats::rnorm(N/2, mean=0, sd=1.5), ncol=1) )
-sim.dat.g2 <- TAM::IRT.simulate(mod3,
-                   theta=matrix( stats::rnorm(N/2, mean=.5, sd=1), ncol=1) )
-sim.dat <- rbind( sim.dat.g1, sim.dat.g2)
-# estimate model
-mod3s <- TAM::tam.mml( sim.dat, group=group)
+
iIndex

+
Optional vector of item indices

 
-#############################################################################
-# EXAMPLE 4: Multidimensional model and latent regression
-#############################################################################
+
theta

+
Optional matrix of theta values

 
-set.seed(6778)
-N <- 2000
-Y <- cbind( stats::rnorm(N), stats::rnorm(N))
-theta <- mvtnorm::rmvnorm(N, mean=c(0,0), sigma=matrix(c(1,.5,.5,1), 2, 2))
-theta[,1] <- theta[,1] + .4 * Y[,1] + .2 * Y[,2]  # latent regression model
-theta[,2] <- theta[,2] + .8 * Y[,1] + .5 * Y[,2]  # latent regression model
-I <- 20
-p1 <- stats::plogis(outer(theta[, 1], seq(-2, 2, len=I), "-"))
-resp1 <- 1 * (p1 > matrix(stats::runif(N * I), nrow=N, ncol=I))
-p1 <- stats::plogis(outer(theta[, 2], seq(-2, 2, len=I ), "-" ))
-resp2 <- 1 * (p1 > matrix(stats::runif(N * I), nrow=N, ncol=I))
-resp <- cbind(resp1, resp2)
-colnames(resp) <- paste("I", 1 : (2 * I), sep="")
+
nobs

+
Optional numeric containing the number of observations to be simulated.

 
-# (2) define loading Matrix
-Q <- array(0, dim=c(2 * I, 2))
-Q[cbind(1:(2*I), c(rep(1, I), rep(2, I)))] <- 1
-Q
+  
...

+
Further objects to be passed

 
-# (3) estimate models
-mod4 <- TAM::tam.mml(resp=resp, Q=Q, Y=Y, control=list(  maxiter=15))
+

+    

+    
Value

+    
 
-# simulate new item responses
-theta <- mvtnorm::rmvnorm(N, mean=c(0,0), sigma=matrix(c(1,.5,.5,1), 2, 2))
-theta[,1] <- theta[,1] + .4 * Y[,1] + .2 * Y[,2]  # latent regression model
-theta[,2] <- theta[,2] + .8 * Y[,1] + .5 * Y[,2]  # latent regression model
+
Data frame with simulated item responses

+    

 
-sim.dat <- TAM::IRT.simulate(mod4, theta=theta)
-mod.sim.dat <- TAM::tam.mml(resp=sim.dat, Q=Q, Y=Y, control=list( maxiter=15))
-}

+    

+    
Examples

+    
#############################################################################
+# EXAMPLE 1: Simulating Rasch model
+#############################################################################
+
+data(data.sim.rasch)
+
+#** (1) estimate model
+mod1 <- TAM::tam.mml(resp=data.sim.rasch )
+
+#** (2) simulate data
+sim.dat <- TAM::IRT.simulate(mod1)
+
+if (FALSE) {
+#** (3) use a subset of items with the argument iIndex
+set.seed(976)
+iIndex <- sort(sample(ncol(data.sim.rasch), 15))  # randomly select 15 items
+sim.dat <- TAM::IRT.simulate(mod1, iIndex=iIndex)
+mod.sim.dat <- TAM::tam.mml(sim.dat)
+
+#** (4) specify number of persons in addition
+sim.dat <- TAM::IRT.simulate(mod1, nobs=1500, iIndex=iIndex)
+
+# Rasch - constraint="items" ----
+mod1 <- TAM::tam.mml(resp=data.sim.rasch,  constraint="items",
+                control=list( xsi.start0=1, fac.oldxsi=.5) )
+
+# provide abilities
+theta0 <- matrix( rnorm(1500, mean=0.5, sd=sqrt(mod1$variance)), ncol=1 )
+# simulate data
+data <- TAM::IRT.simulate(mod1, theta=theta0 )
+# estimate model based on simulated data
+xsi.fixed <- cbind(1:nrow(mod1$item), mod1$item$xsi.item)
+mod2 <- TAM::tam.mml(data, xsi.fixed=xsi.fixed )
+summary(mod2)
+
+#############################################################################
+# EXAMPLE 2: Simulating 2PL model
+#############################################################################
+
+data(data.sim.rasch)
+# estimate 2PL
+mod2 <- TAM::tam.mml.2pl(resp=data.sim.rasch, irtmodel="2PL")
+# simulate 2PL
+sim.dat <- TAM::IRT.simulate(mod2)
+mod.sim.dat <- TAM::tam.mml.2pl(resp=sim.dat, irtmodel="2PL")
+
+#############################################################################
+# EXAMPLE 3: Simulate multiple group model
+#############################################################################
+
+# Multi-Group ----
+set.seed(6778)
+N <- 3000
+theta <- c( stats::rnorm(N/2,mean=0,sd=1.5), stats::rnorm(N/2,mean=.5,sd=1)  )
+I <- 20
+p1 <- stats::plogis( outer( theta, seq( -2, 2, len=I ), "-" ) )
+resp <- 1 * ( p1 > matrix( stats::runif( N*I ), nrow=N, ncol=I ) )
+colnames(resp) <- paste("I", 1:I, sep="")
+group <- rep(1:2, each=N/2 )
+mod3 <- TAM::tam.mml(resp, group=group)
+
+# simulate data
+sim.dat.g1 <- TAM::IRT.simulate(mod3,
+                   theta=matrix( stats::rnorm(N/2, mean=0, sd=1.5), ncol=1) )
+sim.dat.g2 <- TAM::IRT.simulate(mod3,
+                   theta=matrix( stats::rnorm(N/2, mean=.5, sd=1), ncol=1) )
+sim.dat <- rbind( sim.dat.g1, sim.dat.g2)
+# estimate model
+mod3s <- TAM::tam.mml( sim.dat, group=group)
+
+#############################################################################
+# EXAMPLE 4: Multidimensional model and latent regression
+#############################################################################
+
+set.seed(6778)
+N <- 2000
+Y <- cbind( stats::rnorm(N), stats::rnorm(N))
+theta <- mvtnorm::rmvnorm(N, mean=c(0,0), sigma=matrix(c(1,.5,.5,1), 2, 2))
+theta[,1] <- theta[,1] + .4 * Y[,1] + .2 * Y[,2]  # latent regression model
+theta[,2] <- theta[,2] + .8 * Y[,1] + .5 * Y[,2]  # latent regression model
+I <- 20
+p1 <- stats::plogis(outer(theta[, 1], seq(-2, 2, len=I), "-"))
+resp1 <- 1 * (p1 > matrix(stats::runif(N * I), nrow=N, ncol=I))
+p1 <- stats::plogis(outer(theta[, 2], seq(-2, 2, len=I ), "-" ))
+resp2 <- 1 * (p1 > matrix(stats::runif(N * I), nrow=N, ncol=I))
+resp <- cbind(resp1, resp2)
+colnames(resp) <- paste("I", 1 : (2 * I), sep="")
+
+# (2) define loading Matrix
+Q <- array(0, dim=c(2 * I, 2))
+Q[cbind(1:(2*I), c(rep(1, I), rep(2, I)))] <- 1
+Q
+
+# (3) estimate models
+mod4 <- TAM::tam.mml(resp=resp, Q=Q, Y=Y, control=list(  maxiter=15))
+
+# simulate new item responses
+theta <- mvtnorm::rmvnorm(N, mean=c(0,0), sigma=matrix(c(1,.5,.5,1), 2, 2))
+theta[,1] <- theta[,1] + .4 * Y[,1] + .2 * Y[,2]  # latent regression model
+theta[,2] <- theta[,2] + .8 * Y[,1] + .5 * Y[,2]  # latent regression model
+
+sim.dat <- TAM::IRT.simulate(mod4, theta=theta)
+mod.sim.dat <- TAM::tam.mml(resp=sim.dat, Q=Q, Y=Y, control=list( maxiter=15))
+}

+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/reference/IRT.threshold.html b/docs/reference/IRT.threshold.html
index 2337c27..5e191a7 100644
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+++ b/docs/reference/IRT.threshold.html
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-
 
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-Thurstonian Thresholds and Wright Map for Item Response Models — IRT.threshold • TAM
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Thurstonian Thresholds and Wright Map for Item Response Models

@@ -122,162 +54,172 @@ 
Thurstonian Thresholds and Wright Map for Item Response Models

     

     
The function IRT.threshold computes Thurstonian thresholds
 for item response models. It is only based on fitted models
-for which the IRT.irfprob does exist.

+for which the [CDM:IRT.irfprob]CDM::IRT.irfprob class does exist.

 
The function IRT.WrightMap creates a Wright map and works as a wrapper to the
-WrightMap::wrightMap function in
+WrightMap::wrightMap function in
 the WrightMap package. Wright maps operate
 on objects of class IRT.threshold.

     

 
-    
IRT.threshold(object, prob.lvl=.5, type="category")
-
-# S3 method for IRT.threshold
-print(x, ...)
+    

+    
IRT.threshold(object, prob.lvl=.5, type="category")
+
+# S3 method for IRT.threshold
+print(x, ...)
+
+IRT.WrightMap(object, ...)
+
+# S3 method for IRT.threshold
+IRT.WrightMap(object, label.items=NULL, ...)

+    

 
-IRT.WrightMap(object, ...)
+    

+    
Arguments

+    
object

+
Object of fitted models for which [CDM:IRT.irfprob]CDM::IRT.irfprob
+ exists.

 
-# S3 method for IRT.threshold
-IRT.WrightMap(object, label.items=NULL, ...)

+
prob.lvl

+
Requested probability level of thresholds.

 
-    
Arguments

-    
-    
-    
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-    
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object
Object of fitted models for which IRT.irfprob exists.
prob.lvl
Requested probability level of thresholds.
type
Type of thresholds to be calculated. The default is
+
type

+
Type of thresholds to be calculated. The default is
     category-wise calculation. If only one threshold per item should
     be calculated, then choose type="item". If an item possesses
     a maximum score of \(K_i\), then a threshold is defined as a
     value which produces an expected value of \(K_i /2\)
-    (see Ali, Chang & Anderson, 2015).
x
Object of class IRT.threshold
label.items
Vector of item labels
...
Further arguments to be passed.

-
-    
Value

-
-    
Function IRT.threshold:

-Matrix with Thurstonian thresholds

-
Function IRT.WrightMap: 

-A Wright map generated by the WrightMap package.

-    
References

-
-    
Ali, U. S., Chang, H.-H., & Anderson, C. J. (2015). Location indices for ordinal
-polytomous items based on item response theory (Research
-Report No. RR-15-20). Princeton, NJ: Educational Testing Service.
-doi: 10.1002/ets2.12065

-    
See also

-
-    
See the WrightMap::wrightMap function in
-the WrightMap package.

+    (see Ali, Chang & Anderson, 2015).

 
-    
Examples

-    
if (FALSE) {
-#############################################################################
-# EXAMPLE 1: Fitted unidimensional model with gdm
-#############################################################################
+
x

+
Object of class IRT.threshold

 
-data(data.Students)
-dat <- data.Students
+
label.items

+
Vector of item labels

 
-# select part of the dataset
-resp <- dat[, paste0("sc",1:4) ]
-resp[ paste(resp[,1])==3,1] <-  2
-psych::describe(resp)
+
...

+
Further arguments to be passed.

 
-# Model 1: Partial credit model in gdm
-theta.k <- seq( -5, 5, len=21 )   # discretized ability
-mod1 <- CDM::gdm( dat=resp, irtmodel="1PL", theta.k=theta.k, skillspace="normal",
-              centered.latent=TRUE)
+

+    

+    
Value

+    
 
-# compute thresholds
-thresh1 <- TAM::IRT.threshold(mod1)
-print(thresh1)
-IRT.WrightMap(thresh1)
+
Function IRT.threshold:

 
-#############################################################################
-# EXAMPLE 2: Fitted mutidimensional model with gdm
-#############################################################################
 
-data( data.fraction2 )
-dat <- data.fraction2$data
-Qmatrix <- data.fraction2$q.matrix3
+
Matrix with Thurstonian thresholds

 
-# Model 1: 3-dimensional Rasch Model (normal distribution)
-theta.k <- seq( -4, 4, len=11 )   # discretized ability
-mod1 <- CDM::gdm( dat, irtmodel="1PL", theta.k=theta.k, Qmatrix=Qmatrix,
-              centered.latent=TRUE, maxiter=10 )
-summary(mod1)
 
-# compute thresholds
-thresh1 <- TAM::IRT.threshold(mod1)
-print(thresh1)
+
Function IRT.WrightMap: 

 
-#############################################################################
-# EXAMPLE 3: Item-wise thresholds
-#############################################################################
 
-data(data.timssAusTwn.scored)
-dat <- data.timssAusTwn.scored
-dat <- dat[, grep("M03", colnames(dat) ) ]
-summary(dat)
+
A Wright map generated by the WrightMap package.

+    

+    

+    
References

+    
Ali, U. S., Chang, H.-H., & Anderson, C. J. (2015). Location indices for ordinal
+polytomous items based on item response theory (Research
+Report No. RR-15-20). Princeton, NJ: Educational Testing Service.
+doi:10.1002/ets2.12065

+    

+    

+    
Author

+    
The IRT.WrightMap function is based on the
+WrightMap::wrightMap function
+in the WrightMap package.

+    

+    

+    
See also

+    
See the WrightMap::wrightMap function in
+the WrightMap package.

+    

 
-# fit partial credit model
-mod <- TAM::tam.mml( dat )
-# compute thresholds with tam.threshold function
-t1mod <- TAM::tam.threshold( mod )
-t1mod
-# compute thresholds with IRT.threshold function
-t2mod <- TAM::IRT.threshold( mod )
-t2mod
-# compute item-wise thresholds
-t3mod <- TAM::IRT.threshold( mod, type="item")
-t3mod
-}
+    

+    
Examples

+    
if (FALSE) {
+#############################################################################
+# EXAMPLE 1: Fitted unidimensional model with gdm
+#############################################################################
+
+data(data.Students)
+dat <- data.Students
+
+# select part of the dataset
+resp <- dat[, paste0("sc",1:4) ]
+resp[ paste(resp[,1])==3,1] <-  2
+psych::describe(resp)
+
+# Model 1: Partial credit model in gdm
+theta.k <- seq( -5, 5, len=21 )   # discretized ability
+mod1 <- CDM::gdm( dat=resp, irtmodel="1PL", theta.k=theta.k, skillspace="normal",
+              centered.latent=TRUE)
+
+# compute thresholds
+thresh1 <- TAM::IRT.threshold(mod1)
+print(thresh1)
+IRT.WrightMap(thresh1)
+
+#############################################################################
+# EXAMPLE 2: Fitted mutidimensional model with gdm
+#############################################################################
+
+data( data.fraction2 )
+dat <- data.fraction2$data
+Qmatrix <- data.fraction2$q.matrix3
+
+# Model 1: 3-dimensional Rasch Model (normal distribution)
+theta.k <- seq( -4, 4, len=11 )   # discretized ability
+mod1 <- CDM::gdm( dat, irtmodel="1PL", theta.k=theta.k, Qmatrix=Qmatrix,
+              centered.latent=TRUE, maxiter=10 )
+summary(mod1)
+
+# compute thresholds
+thresh1 <- TAM::IRT.threshold(mod1)
+print(thresh1)
+
+#############################################################################
+# EXAMPLE 3: Item-wise thresholds
+#############################################################################
+
+data(data.timssAusTwn.scored)
+dat <- data.timssAusTwn.scored
+dat <- dat[, grep("M03", colnames(dat) ) ]
+summary(dat)
+
+# fit partial credit model
+mod <- TAM::tam.mml( dat )
+# compute thresholds with tam.threshold function
+t1mod <- TAM::tam.threshold( mod )
+t1mod
+# compute thresholds with IRT.threshold function
+t2mod <- TAM::IRT.threshold( mod )
+t2mod
+# compute item-wise thresholds
+t3mod <- TAM::IRT.threshold( mod, type="item")
+t3mod
+}

+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/reference/IRT.truescore.html b/docs/reference/IRT.truescore.html
index c3d8983..78a9c22 100644
--- a/docs/reference/IRT.truescore.html
+++ b/docs/reference/IRT.truescore.html
@@ -1,72 +1,17 @@
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-Converts a \(\theta\) Score into a True Score \(\tau ( \theta)\) — IRT.truescore • TAM
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Converts a \(\theta\) Score into a True Score \(\tau ( \theta)\)

@@ -127,112 +59,110 @@ 
Converts a \(\theta\) Score into a True Score \(\tau ( \theta)\)

 \(q_{ih}\) in the matrix Q.

     

 
-    
IRT.truescore(object, iIndex=NULL, theta=NULL, Q=NULL)

-
-    
Arguments

-    
-    
-    
-      
-      
-    
-    
-      
-      
-    
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-      
-      
-    
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-      
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object
Object for which the
-CDM::IRT.irfprob S3 method is defined
iIndex
Optional vector with item indices
theta
Optional vector with \(\theta\) values
Q
Optional weighting matrix

-
-    
Value

-
-    
Data frame containing \(\theta\) values and corresponding
-true scores \(\tau( \theta ) \).

-    
See also

+    

+    
IRT.truescore(object, iIndex=NULL, theta=NULL, Q=NULL)

+    

+
+    

+    
Arguments

+    
object

+
Object for which the
+CDM::IRT.irfprob S3 method is defined

+
+  
iIndex

+
Optional vector with item indices

 
-    
See also sirt::truescore.irt
+  
theta

+
Optional vector with \(\theta\) values

+
+
Q

+
Optional weighting matrix

+
+

+    

+    
Value

+    
+
+
Data frame containing \(\theta\) values and corresponding
+true scores \(\tau( \theta ) \).

+    

+    

+    
See also

+    
See also sirt::truescore.irt
 for a conversion function for generalized partial credit models.

+    

 
-    
Examples

-    
#############################################################################
-# EXAMPLE 1: True score conversion for a test with polytomous items
-#############################################################################
-
-data(data.Students, package="CDM")
-dat <- data.Students[, paste0("mj",1:4) ]
-
-# fit partial credit model
-mod1 <- TAM::tam.mml( dat,control=list(maxiter=20) )
-summary(mod1)
-
-# true score conversion
-tmod1 <- TAM::IRT.truescore( mod1 )
-round( tmod1, 4 )
-# true score conversion with user-defined theta grid
-tmod1b <- TAM::IRT.truescore( mod1, theta=seq( -8,8, len=33 ) )
-# plot results
-plot( tmod1$theta, tmod1$truescore, type="l",
-            xlab=expression(theta), ylab=expression(tau( theta ) ) )
-points( tmod1b$theta, tmod1b$truescore, pch=16, col="brown" )
-
-if (FALSE) {
-#############################################################################
-# EXAMPLE 2: True scores with different category weightings
-#############################################################################
-
-data(data.timssAusTwn.scored)
-dat <- data.timssAusTwn.scored
-# extract item response data
-dat <- dat[, grep("M03", colnames(dat) ) ]
-# select items with do have maximum score of 2 (polytomous items)
-ind <- which( apply( dat,  2, max, na.rm=TRUE )==2 )
-I <- ncol(dat)
-# define Q-matrix with scoring variant
-Q <- matrix( 1, nrow=I, ncol=1 )
-Q[ ind, 1 ] <- .5    # score of 0.5 for polyomous items
-
-# estimate model
-mod1 <- TAM::tam.mml( dat, Q=Q, irtmodel="PCM2", control=list( nodes=seq(-10,10,len=61) ) )
-summary(mod1)
-
-# true score with scoring (0,1,2) which is the default of the function
-tmod1 <- TAM::IRT.truescore(mod1)
-# true score with user specified weighting matrix
-Q <- mod1$B[,,1]
-tmod2 <- TAM::IRT.truescore(mod1, Q=Q)
-}

+    

+    
Examples

+    
#############################################################################
+# EXAMPLE 1: True score conversion for a test with polytomous items
+#############################################################################
+
+data(data.Students, package="CDM")
+dat <- data.Students[, paste0("mj",1:4) ]
+
+# fit partial credit model
+mod1 <- TAM::tam.mml( dat,control=list(maxiter=20) )
+summary(mod1)
+
+# true score conversion
+tmod1 <- TAM::IRT.truescore( mod1 )
+round( tmod1, 4 )
+# true score conversion with user-defined theta grid
+tmod1b <- TAM::IRT.truescore( mod1, theta=seq( -8,8, len=33 ) )
+# plot results
+plot( tmod1$theta, tmod1$truescore, type="l",
+            xlab=expression(theta), ylab=expression(tau( theta ) ) )
+points( tmod1b$theta, tmod1b$truescore, pch=16, col="brown" )
+
+if (FALSE) {
+#############################################################################
+# EXAMPLE 2: True scores with different category weightings
+#############################################################################
+
+data(data.timssAusTwn.scored)
+dat <- data.timssAusTwn.scored
+# extract item response data
+dat <- dat[, grep("M03", colnames(dat) ) ]
+# select items with do have maximum score of 2 (polytomous items)
+ind <- which( apply( dat,  2, max, na.rm=TRUE )==2 )
+I <- ncol(dat)
+# define Q-matrix with scoring variant
+Q <- matrix( 1, nrow=I, ncol=1 )
+Q[ ind, 1 ] <- .5    # score of 0.5 for polyomous items
+
+# estimate model
+mod1 <- TAM::tam.mml( dat, Q=Q, irtmodel="PCM2", control=list( nodes=seq(-10,10,len=61) ) )
+summary(mod1)
+
+# true score with scoring (0,1,2) which is the default of the function
+tmod1 <- TAM::IRT.truescore(mod1)
+# true score with user specified weighting matrix
+Q <- mod1$B[,,1]
+tmod2 <- TAM::IRT.truescore(mod1, Q=Q)
+}

+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/reference/IRTLikelihood.cfa.html b/docs/reference/IRTLikelihood.cfa.html
index 1bfb8be..1831f25 100644
--- a/docs/reference/IRTLikelihood.cfa.html
+++ b/docs/reference/IRTLikelihood.cfa.html
@@ -1,74 +1,19 @@
-
 
-
-  
-  
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-
-
-Individual Likelihood for Confirmatory Factor Analysis — IRTLikelihood.cfa • TAM
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-Individual Likelihood for Confirmatory Factor Analysis — IRTLikelihood.cfa • TAM
-
-
-
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-
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-
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-
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-  
+
+    
 
-  
     

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-      
 
       
 
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+      

   

     

     
Individual Likelihood for Confirmatory Factor Analysis

@@ -131,134 +63,129 @@ 
Individual Likelihood for Confirmatory Factor Analysis

 can be used for drawing plausible values.

     

 
-    
IRTLikelihood.cfa(data, cfaobj=NULL, theta=NULL, L=NULL, nu=NULL,
-    psi=NULL, snodes=NULL, snodes.adj=2, version=1)

+    

+    
IRTLikelihood.cfa(data, cfaobj=NULL, theta=NULL, L=NULL, nu=NULL,
+    psi=NULL, snodes=NULL, snodes.adj=2, version=1)

+    

 
-    
Arguments

-    
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
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-    
-      
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-    
-    
data
Dataset with item responses
cfaobj
Fitted lavaan::cfa (lavaan) object
theta
Optional matrix containing the theta values
-used for evaluating the individual likelihood
L
Matrix of item loadings (if cfaobj is not provided)
nu
Vector of item intercepts (if cfaobj is not provided)
psi
Matrix with residual covariances
-(if cfaobj is not provided)
snodes
Number of theta values used for the approximation
-of the distribution of latent variables.
snodes.adj
Adjustment factor for quasi monte carlo nodes for
-more than two latent variables.
version
Function version. version=1 is based on a
-    Rcpp implementation while version=0 is
-    a pure R implementation.

+    

+    
Arguments

+    
data

+
Dataset with item responses

 
-    
Value

+  
cfaobj

+
Fitted lavaan::cfa (lavaan) object

 
-    
Individual likelihood evaluated at theta

-    
See also

+  
theta

+
Optional matrix containing the theta values
+used for evaluating the individual likelihood

 
-    
CDM::IRT.likelihood

+  
L

+
Matrix of item loadings (if cfaobj is not provided)

 
-    
Examples

-    
if (FALSE) {
-#############################################################################
-# EXAMPLE 1: Two-dimensional CFA data.Students
-#############################################################################
+  
nu

+
Vector of item intercepts (if cfaobj is not provided)

 
-library(lavaan)
-library(CDM)
+  
psi

+
Matrix with residual covariances
+(if cfaobj is not provided)

 
-data(data.Students, package="CDM")
-dat <- data.Students
+  
snodes

+
Number of theta values used for the approximation
+of the distribution of latent variables.

 
-dat2 <- dat[, c(paste0("mj",1:4), paste0("sc",1:4)) ]
-# lavaan model with DO operator
-lavmodel <- "
-DO(1,4,1)
-   mj=~ mj%
-   sc=~ sc%
-DOEND
-   mj ~~ sc
-   mj ~~ 1*mj
-   sc ~~ 1*sc
-     "
-lavmodel <- TAM::lavaanify.IRT( lavmodel, data=dat2 )$lavaan.syntax
-cat(lavmodel)
+  
snodes.adj

+
Adjustment factor for quasi monte carlo nodes for
+more than two latent variables.

+
+
version

+
Function version. version=1 is based on a
+    Rcpp implementation while version=0 is
+    a pure R implementation.

 
-mod4 <- lavaan::cfa( lavmodel, data=dat2, std.lv=TRUE )
-summary(mod4, standardized=TRUE, rsquare=TRUE )
-# extract item parameters
-res4 <- TAM::cfa.extract.itempars( mod4 )
-# create theta grid
-theta0 <- seq( -6, 6, len=15)
-theta <- expand.grid( theta0, theta0 )
-L <- res4$L
-nu <- res4$nu
-psi <- res4$psi
-data <- dat2
-# evaluate likelihood using item parameters
-like2 <- TAM::IRTLikelihood.cfa( data=dat2, theta=theta, L=L, nu=nu, psi=psi )
-# The likelihood can also be obtained by direct evaluation
-# of the fitted cfa object "mod4"
-like4 <- TAM::IRTLikelihood.cfa( data=dat2, cfaobj=mod4 )
-attr( like4, "theta")
-# the theta grid is automatically created if theta is not
-# supplied as an argument
-}

+

+    

+    
Value

+    
+
+
Individual likelihood evaluated at theta

+
+
+    

+    

+    
See also

+    
CDM::IRT.likelihood

+    

+
+    

+    
Examples

+    
if (FALSE) {
+#############################################################################
+# EXAMPLE 1: Two-dimensional CFA data.Students
+#############################################################################
+
+library(lavaan)
+library(CDM)
+
+data(data.Students, package="CDM")
+dat <- data.Students
+
+dat2 <- dat[, c(paste0("mj",1:4), paste0("sc",1:4)) ]
+# lavaan model with DO operator
+lavmodel <- "
+DO(1,4,1)
+   mj=~ mj%
+   sc=~ sc%
+DOEND
+   mj ~~ sc
+   mj ~~ 1*mj
+   sc ~~ 1*sc
+     "
+lavmodel <- TAM::lavaanify.IRT( lavmodel, data=dat2 )$lavaan.syntax
+cat(lavmodel)
+
+mod4 <- lavaan::cfa( lavmodel, data=dat2, std.lv=TRUE )
+summary(mod4, standardized=TRUE, rsquare=TRUE )
+# extract item parameters
+res4 <- TAM::cfa.extract.itempars( mod4 )
+# create theta grid
+theta0 <- seq( -6, 6, len=15)
+theta <- expand.grid( theta0, theta0 )
+L <- res4$L
+nu <- res4$nu
+psi <- res4$psi
+data <- dat2
+# evaluate likelihood using item parameters
+like2 <- TAM::IRTLikelihood.cfa( data=dat2, theta=theta, L=L, nu=nu, psi=psi )
+# The likelihood can also be obtained by direct evaluation
+# of the fitted cfa object "mod4"
+like4 <- TAM::IRTLikelihood.cfa( data=dat2, cfaobj=mod4 )
+attr( like4, "theta")
+# the theta grid is automatically created if theta is not
+# supplied as an argument
+}

+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/reference/IRTLikelihood.ctt.html b/docs/reference/IRTLikelihood.ctt.html
index de0ea28..fe12ac4 100644
--- a/docs/reference/IRTLikelihood.ctt.html
+++ b/docs/reference/IRTLikelihood.ctt.html
@@ -1,68 +1,13 @@
-
 
-
-  
-  
-
-
-
-Computes Individual Likelihood from Classical Test Theory Estimates — IRTLikelihood.ctt • TAM
-
-
-
-
-
-
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-
-Computes Individual Likelihood from Classical Test Theory Estimates — IRTLikelihood.ctt • TAM
-
-
-
-  
+
+    
 
-  
     

-      

-      
 
       
 
-      

-
-

+      

   

     

     
Computes Individual Likelihood from Classical Test Theory Estimates

@@ -119,95 +51,95 @@ 
Computes Individual Likelihood from Classical Test Theory Estimates

 under a unidimensional normal distribution of measurement errors.

     

 
-    
IRTLikelihood.ctt(y, errvar, theta=NULL)

-
-    
Arguments

-    
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
y
Vector of observed scores
errvar
Vector of error variances
theta
Optional vector for \(\theta\) grid.

-
-    
Value

-
-    
Object of class IRT.likelihood

-
-    
Examples

-    
#############################################################################
-# EXAMPLE 1: Individual likelihood and latent regression in CTT
-#############################################################################
-
-set.seed(75)
-
-#--- simulate data
-N <- 2000
-x1 <- stats::rnorm(N)
-x2 <- .7 * x1 + stats::runif(N)
-# simulate true score
-theta <- 1.2 + .6*x1 + .3 *x2 + stats::rnorm(N, sd=sqrt(.50) )
-var(theta)
-# simulate measurement error variances
-errvar <- stats::runif( N, min=.6, max=.9 )
-# simulate observed scores
-y <- theta + stats::rnorm( N, sd=sqrt( errvar) )
-
-#--- create likelihood object
-like1 <- TAM::IRTLikelihood.ctt( y=y, errvar=errvar, theta=NULL )
-
-#--- estimate latent regression
-X <- data.frame(x1,x2)
-mod1 <- TAM::tam.latreg( like=like1, Y=X )
-
-if (FALSE) {
-#--- draw plausible values
-pv1 <- TAM::tam.pv( mod1, normal.approx=TRUE )
-
-#--- create datalist
-datlist1 <- TAM::tampv2datalist( pv1, pvnames="thetaPV", Y=X )
-
-#--- statistical inference on plausible values using mitools package
-library(mitools)
-datlist1a <- mitools::imputationList(datlist1)
-
-# fit linear regression and apply Rubin formulas
-mod2 <- with( datlist1a, stats::lm( thetaPV ~ x1 + x2 ) )
-summary( mitools::MIcombine(mod2) )
-}

+    

+    
IRTLikelihood.ctt(y, errvar, theta=NULL)

+    

+
+    

+    
Arguments

+    
y

+
Vector of observed scores

+
+  
errvar

+
Vector of error variances

+
+  
theta

+
Optional vector for \(\theta\) grid.

+
+

+    

+    
Value

+    
+
+
Object of class IRT.likelihood

+
+
+    

+
+    

+    
Examples

+    
#############################################################################
+# EXAMPLE 1: Individual likelihood and latent regression in CTT
+#############################################################################
+
+set.seed(75)
+
+#--- simulate data
+N <- 2000
+x1 <- stats::rnorm(N)
+x2 <- .7 * x1 + stats::runif(N)
+# simulate true score
+theta <- 1.2 + .6*x1 + .3 *x2 + stats::rnorm(N, sd=sqrt(.50) )
+var(theta)
+# simulate measurement error variances
+errvar <- stats::runif( N, min=.6, max=.9 )
+# simulate observed scores
+y <- theta + stats::rnorm( N, sd=sqrt( errvar) )
+
+#--- create likelihood object
+like1 <- TAM::IRTLikelihood.ctt( y=y, errvar=errvar, theta=NULL )
+
+#--- estimate latent regression
+X <- data.frame(x1,x2)
+mod1 <- TAM::tam.latreg( like=like1, Y=X )
+
+if (FALSE) {
+#--- draw plausible values
+pv1 <- TAM::tam.pv( mod1, normal.approx=TRUE )
+
+#--- create datalist
+datlist1 <- TAM::tampv2datalist( pv1, pvnames="thetaPV", Y=X )
+
+#--- statistical inference on plausible values using mitools package
+library(mitools)
+datlist1a <- mitools::imputationList(datlist1)
+
+# fit linear regression and apply Rubin formulas
+mod2 <- with( datlist1a, stats::lm( thetaPV ~ x1 + x2 ) )
+summary( mitools::MIcombine(mod2) )
+}

+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/reference/Scale.html b/docs/reference/Scale.html
index fb31e4f..37506c9 100644
--- a/docs/reference/Scale.html
+++ b/docs/reference/Scale.html
@@ -1,67 +1,12 @@
-
 
-
-  
-  
-
-
-
-S3 Method for Standardizations and Transformations of Variables — Scale • TAM
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-S3 Method for Standardizations and Transformations of Variables — Scale • TAM
-
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-  
+
+    
 
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-      

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+      

   

     

     
S3 Method for Standardizations and Transformations of Variables

@@ -117,50 +49,45 @@ 
S3 Method for Standardizations and Transformations of Variables

     
S3 method for standardizations and transformations of variables

     

 
-    
Scale(object, ...)

+    

+    
Scale(object, ...)

+    

 
-    
Arguments

-    
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
object
An object
...
Further arguments to be passed

+    

+    
Arguments

+    
object

+
An object

 
-    
See also

+  
...

+
Further arguments to be passed

 
-    
base::scale

+

+    

+    
See also

+    
base::scale

+    

 
   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/reference/TAM-defunct.html b/docs/reference/TAM-defunct.html
index fddc66b..7794b02 100644
--- a/docs/reference/TAM-defunct.html
+++ b/docs/reference/TAM-defunct.html
@@ -1,68 +1,13 @@
-
 
-
-  
-  
-
-
-
-Defunct <span class="pkg">TAM</span> Functions — TAM-defunct • TAM
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-Defunct TAM Functions — TAM-defunct • TAM
-
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-  
+
+    
 
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+      

   

     

     
Defunct TAM Functions

@@ -119,47 +51,43 @@ 
Defunct TAM Functions

 package.

     

 
-    
tam.jml2(...)

-
-    
Arguments

-    
-    
-    
-      
-      
-    
-    
...
Arguments to be passed.

+    

+    
tam.jml2(...)

+    

 
-    
Details

+    

+    
Arguments

+    
...

+
Arguments to be passed.

 
+

+    

+    
Details

     
The tam.jml2 is included as the default in
-tam.jml.

+tam.jml.

+    

 
   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/reference/TAM-package.html b/docs/reference/TAM-package.html
index e764eff..7ae18b1 100644
--- a/docs/reference/TAM-package.html
+++ b/docs/reference/TAM-package.html
@@ -1,46 +1,5 @@
-
 
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-  
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+    
 
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+      

   

     

     
Test Analysis Modules

@@ -140,57 +72,61 @@ 
Test Analysis Modules

     

 
 
-
-    
Details

-
-    
See http://www.edmeasurementsurveys.com/TAM/Tutorials/ for
+    

+    
Author

+    
Alexander Robitzsch [aut,cre] (<https://orcid.org/0000-0002-8226-3132>),
+    Thomas Kiefer [aut], 
+    Margaret Wu [aut]

+
Maintainer: Alexander Robitzsch <robitzsch@ipn.uni-kiel.de>

+    

+    

+    
Details

+    
See http://www.edmeasurementsurveys.com/TAM/Tutorials/ for
 tutorials of the TAM package.

-    
References

-
+    

+    

+    
References

     
Adams, R. J., Wilson, M., & Wang, W. C. (1997). The multidimensional random coefficients
 multinomial logit model. Applied Psychological Measurement, 21(1), 1-23.
-doi: 10.1177/0146621697211001

+doi:10.1177/0146621697211001

 
Adams, R. J., Wilson, M., & Wu, M. (1997).
 Multilevel item response models: An approach to errors in
 variables regression. Journal of Educational and Behavioral
-Statistics, 22(1), 47-76. doi: 10.3102/10769986022001047

+Statistics, 22(1), 47-76. doi:10.3102/10769986022001047

 
Adams, R. J., & Wu, M. L. (2007). The mixed-coefficients multinomial logit model.
 A generalized form of the Rasch model. In M. von Davier & C. H. Carstensen (Eds.):
 Multivariate and mixture distribution Rasch models: Extensions and applications
 (pp. 55-76). New York: Springer.
-doi: 10.1007/978-0-387-49839-3_4

+doi:10.1007/978-0-387-49839-3_4

 
Formann, A. K. (1982). Linear logistic latent class analysis.
 Biometrical Journal, 24(2), 171-190.
-doi: 10.1002/bimj.4710240209

+doi:10.1002/bimj.4710240209

 
Formann, A. K. (1992). Linear logistic latent class analysis for polytomous data.
 Journal of the American Statistical Association, 87(418), 476-486.
-doi: 10.1080/01621459.1992.10475229

+doi:10.1080/01621459.1992.10475229

+    

 
   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
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+  
 
+  
 
diff --git a/docs/reference/TAM-utilities.html b/docs/reference/TAM-utilities.html
index d47999d..b38991f 100644
--- a/docs/reference/TAM-utilities.html
+++ b/docs/reference/TAM-utilities.html
@@ -1,67 +1,12 @@
-
 
-
-  
-  
-
-
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-Utility Functions in <span class="pkg">TAM</span> — TAM-utilities • TAM
-
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-Utility Functions in TAM — TAM-utilities • TAM
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Utility Functions in TAM

@@ -117,339 +49,278 @@ 
Utility Functions in TAM

     
Utility functions in TAM.

     

 
-    
## RISE item fit statistic of two models
-IRT.RISE( mod_p, mod_np, use_probs=TRUE )
-## model-implied means
-tam_model_implied_means(mod)
-
-## information about used package version
-tam_packageinfo(pack)
-## call statement in a string format
-tam_print_call(CALL)
-## information about R session
-tam_rsessinfo()
-## grep list of arguments for a specific variable
-tam_args_CALL_search(args_CALL, variable, default_value)
-## requireNamespace with message of needed installation
-require_namespace_msg(pkg)
-## add leading zeroes
-add.lead(x, width=max(nchar(x)))
-## round some columns in a data frame
-tam_round_data_frame(obji, from=1, to=ncol(obji), digits=3, rownames_null=FALSE)
-## round some columns in a data frame and print this data frame
-tam_round_data_frame_print(obji, from=1, to=ncol(obji), digits=3, rownames_null=FALSE)
-## copy of CDM::osink
-tam_osink(file, suffix=".Rout")
-## copy of CDM::csink
-tam_csink(file)
-
-## base::matrix function with argument value byrow=TRUE
-tam_matrix2(x, nrow=NULL, ncol=NULL)
-## more efficient base::outer functions for operations "*", "+" and "-"
-tam_outer(x, y, op="*")
-## row normalization of a matrix
-tam_normalize_matrix_rows(x)
-## row normalization of a vector
-tam_normalize_vector(x)
-## aggregate function for mean and sum based on base::rowsum
-tam_aggregate(x, group, mean=FALSE, na.rm=TRUE)
-## column index when a value in a matrix is exceeded (used in TAM::tam.pv)
-tam_interval_index(matr, rn)
-## cumulative sum of row entries in a matrix
-tam_rowCumsums(matr)
-## extension of mvtnorm::dmvnorm to matrix entries of mean
-tam_dmvnorm(x, mean, sigma, log=FALSE )
-## Bayesian bootstrap in TAM (used in tam.pv.mcmc)
-tam_bayesian_bootstrap(N, sample_integers=FALSE, do_boot=TRUE)
-## weighted covariance matrix
-tam_cov_wt(x, wt=NULL, method="ML")
-## weighted correlation matrix
-tam_cor_wt(x, wt=NULL, method="ML")
-## generalized inverse
-tam_ginv(x, eps=.05)
-## generalized inverse with scaled matrix using MASS::ginv
-tam_ginv_scaled(x, use_MASS=TRUE)
-
-## remove items or persons with complete missing entries
-tam_remove_missings( dat, items, elim_items=TRUE, elim_persons=TRUE )
-## compute AXsi given A and xsi
-tam_AXsi_compute(A, xsi)
-## fit xsi given A and AXsi
-tam_AXsi_fit(A, AXsi)
-
-## maximum absolute difference between objects
-tam_max_abs( list1, list2, label )
-tam_max_abs_list( list1, list2)
-
-## trimming increments in iterations
-tam_trim_increment(increment, max.increment, trim_increment="cut",
-     trim_incr_factor=2, eps=1E-10, avoid_na=FALSE)
-## numerical differentiation by central difference
-tam_difference_quotient(d0, d0p, d0m, h)
-## assign elements of a list in an environment
-tam_assign_list_elements(x, envir)

-
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Arguments

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-    
-    
mod_p
Fitted model
mod_np
Fitted model
mod
Fitted model
use_probs
Logical
pack
An R package
CALL
An R call
args_CALL
Arguments obtained from as.list( sys.call() )
variable
Name of a variable
default_value
Default value of a variable
pkg
String
x
Vector or matrix or list
width
Number of zeroes before decimal
obji
Data frame or vector
from
Integer
to
Integer
digits
Integer
rownames_null
Logical
file
File name
suffix
Suffix for file name of summary output
nrow
Number of rows
ncol
Number of columns
y
Vector
op
An operation "*", "+" or "-"
group
Vector of grouping identifiers
mean
Logical indicating whether mean should be calculated or the sum or
-vector or matrix
na.rm
Logical indicating whether missing values should be removed
matr
Matrix
sigma
Matrix
log
Logical
N
Integer
sample_integers
Logical indicating whether weights for complete cases
-should be sampled in bootstrap
do_boot
Logical
wt
Optional vector containing weights
method
Method, see stats::cov.wt
rn
Vector
dat
Data frame
items
Vector
elim_items
Logical
elim_persons
Logical
A
Array
xsi
Vector
AXsi
Matrix
increment
Vector
max.increment
Numeric
trim_increment
One of the methods "half" or "cut"
trim_incr_factor
Factor of trimming in method "half"
eps
Small number preventing from division by zero
use_MASS
Logical indicating whether MASS package should be used.
avoid_na
Logical indicating whether missing values should be set to zero.
d0
Vector
d0p
Vector
d0m
Vector
h
Vector
envir
Environment variable
list1
List
list2
List
label
Element of a list

+    

+    
## RISE item fit statistic of two models
+IRT.RISE( mod_p, mod_np, use_probs=TRUE )
+## model-implied means
+tam_model_implied_means(mod)
+
+## information about used package version
+tam_packageinfo(pack)
+## call statement in a string format
+tam_print_call(CALL)
+## information about R session
+tam_rsessinfo()
+## grep list of arguments for a specific variable
+tam_args_CALL_search(args_CALL, variable, default_value)
+## requireNamespace with message of needed installation
+require_namespace_msg(pkg)
+## add leading zeroes
+add.lead(x, width=max(nchar(x)))
+## round some columns in a data frame
+tam_round_data_frame(obji, from=1, to=ncol(obji), digits=3, rownames_null=FALSE)
+## round some columns in a data frame and print this data frame
+tam_round_data_frame_print(obji, from=1, to=ncol(obji), digits=3, rownames_null=FALSE)
+## copy of CDM::osink
+tam_osink(file, suffix=".Rout")
+## copy of CDM::csink
+tam_csink(file)
+
+## base::matrix function with argument value byrow=TRUE
+tam_matrix2(x, nrow=NULL, ncol=NULL)
+## more efficient base::outer functions for operations "*", "+" and "-"
+tam_outer(x, y, op="*")
+## row normalization of a matrix
+tam_normalize_matrix_rows(x)
+## row normalization of a vector
+tam_normalize_vector(x)
+## aggregate function for mean and sum based on base::rowsum
+tam_aggregate(x, group, mean=FALSE, na.rm=TRUE)
+## column index when a value in a matrix is exceeded (used in TAM::tam.pv)
+tam_interval_index(matr, rn)
+## cumulative sum of row entries in a matrix
+tam_rowCumsums(matr)
+## extension of mvtnorm::dmvnorm to matrix entries of mean
+tam_dmvnorm(x, mean, sigma, log=FALSE )
+## Bayesian bootstrap in TAM (used in tam.pv.mcmc)
+tam_bayesian_bootstrap(N, sample_integers=FALSE, do_boot=TRUE)
+## weighted covariance matrix
+tam_cov_wt(x, wt=NULL, method="ML")
+## weighted correlation matrix
+tam_cor_wt(x, wt=NULL, method="ML")
+## generalized inverse
+tam_ginv(x, eps=.05)
+## generalized inverse with scaled matrix using MASS::ginv
+tam_ginv_scaled(x, use_MASS=TRUE)
+
+## remove items or persons with complete missing entries
+tam_remove_missings( dat, items, elim_items=TRUE, elim_persons=TRUE )
+## compute AXsi given A and xsi
+tam_AXsi_compute(A, xsi)
+## fit xsi given A and AXsi
+tam_AXsi_fit(A, AXsi)
+
+## maximum absolute difference between objects
+tam_max_abs( list1, list2, label )
+tam_max_abs_list( list1, list2)
+
+## trimming increments in iterations
+tam_trim_increment(increment, max.increment, trim_increment="cut",
+     trim_incr_factor=2, eps=1E-10, avoid_na=FALSE)
+## numerical differentiation by central difference
+tam_difference_quotient(d0, d0p, d0m, h)
+## assign elements of a list in an environment
+tam_assign_list_elements(x, envir)

+    

+
+    

+    
Arguments

+    
mod_p

+
Fitted model

+
+
mod_np

+
Fitted model

+
+
mod

+
Fitted model

+
+
use_probs

+
Logical

+
+
pack

+
An R package

+
+
CALL

+
An R call

+
+
args_CALL

+
Arguments obtained from as.list( sys.call() )

+
+
variable

+
Name of a variable

+
+
default_value

+
Default value of a variable

+
+
pkg

+
String

+
+
x

+
Vector or matrix or list

+
+
width

+
Number of zeroes before decimal

+
+
obji

+
Data frame or vector

+
+
from

+
Integer

+
+
to

+
Integer

 
+
digits

+
Integer

+
+
rownames_null

+
Logical

+
+
file

+
File name

+
+
suffix

+
Suffix for file name of summary output

+
+
nrow

+
Number of rows

+
+
ncol

+
Number of columns

+
+
y

+
Vector

+
+
op

+
An operation "*", "+" or "-"

+
+
group

+
Vector of grouping identifiers

+
+
mean

+
Logical indicating whether mean should be calculated or the sum or
+vector or matrix

+
+
na.rm

+
Logical indicating whether missing values should be removed

+
+
matr

+
Matrix

+
+
sigma

+
Matrix

+
+
log

+
Logical

+
+
N

+
Integer

+
+
sample_integers

+
Logical indicating whether weights for complete cases
+should be sampled in bootstrap

+
+
do_boot

+
Logical

+
+
wt

+
Optional vector containing weights

+
+
method

+
Method, see stats::cov.wt

+
+
rn

+
Vector

+
+
dat

+
Data frame

+
+
items

+
Vector

+
+
elim_items

+
Logical

+
+
elim_persons

+
Logical

+
+
A

+
Array

+
+
xsi

+
Vector

+
+
AXsi

+
Matrix

+
+
increment

+
Vector

+
+
max.increment

+
Numeric

+
+
trim_increment

+
One of the methods "half" or "cut"

+
+
trim_incr_factor

+
Factor of trimming in method "half"

+
+
eps

+
Small number preventing from division by zero

+
+
use_MASS

+
Logical indicating whether MASS package should be used.

+
+
avoid_na

+
Logical indicating whether missing values should be set to zero.

+
+
d0

+
Vector

+
+
d0p

+
Vector

+
+
d0m

+
Vector

+
+
h

+
Vector

+
+
envir

+
Environment variable

+
+
list1

+
List

+
+
list2

+
List

+
+
label

+
Element of a list

+
+

 
   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/reference/WLErel.html b/docs/reference/WLErel.html
index 69f4da6..1c0f43f 100644
--- a/docs/reference/WLErel.html
+++ b/docs/reference/WLErel.html
@@ -1,67 +1,12 @@
-
 
-
-  
-  
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-
-Reliability Estimation in <span class="pkg">TAM</span> — WLErel • TAM
-
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-Reliability Estimation in TAM — WLErel • TAM
-
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Reliability Estimation in TAM

@@ -117,86 +49,85 @@ 
Reliability Estimation in TAM

     
Functions for computing reliability estimates.

     

 
-    
WLErel(theta, error, w=rep(1, length(theta)), select=NULL)
-
-EAPrel(theta, error, w=rep(1, length(theta)), select=NULL)

-
-    
Arguments

-    
-    
-    
-      
-      
-    
-    
-      
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-      
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-      
-      
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-    
theta
Vector with theta estimates
error
Vector with standard errors of theta estimates
w
Optional vector of person weights
select
Optional vector for selecting cases

-
-    
Details

+    

+    
WLErel(theta, error, w=rep(1, length(theta)), select=NULL)
+
+EAPrel(theta, error, w=rep(1, length(theta)), select=NULL)

+    

+
+    

+    
Arguments

+    
theta

+
Vector with theta estimates

+
+
error

+
Vector with standard errors of theta estimates

+
+  
w

+
Optional vector of person weights

 
+
select

+
Optional vector for selecting cases

+
+

+    

+    
Details

     
The reliability formulas follow Adams (2005). Let \(v\) denote
 the variance of theta estimates and let \(s\) denote
 the average of the squared error. Then, the WLE reliability is
 defined as \(1-s/v=(v-s)/v\) while the EAP reliability is defined as
 \(1 - s/(s+v)=v/(s+v)\).

-    
Value

-
-    
Numeric value

-    
References

+    

+    

+    
Value

+    
 
+
Numeric value

+    

+    

+    
References

     
Adams, R. J. (2005). Reliability as a measurement design effect.
 Studies in Educational Evaluation, 31(2), 162-172.
-doi: 10.1016/j.stueduc.2005.05.008

-
-    
Examples

-    
#############################################################################
-# EXAMPLE 1: Toy example for reliability functions
-#############################################################################
-
-set.seed(9897)
-N <- 100
-# simulate theta and error SDs
-x <- stats::rnorm(N,sd=2)
-error <- stats::runif(N, .7, 1.3)
-# compute WLE reliability
-WLErel(x,error)
-# compute EAP reliaility
-EAPrel(x,error)

+doi:10.1016/j.stueduc.2005.05.008

+    

+
+    

+    
Examples

+    
#############################################################################
+# EXAMPLE 1: Toy example for reliability functions
+#############################################################################
+
+set.seed(9897)
+N <- 100
+# simulate theta and error SDs
+x <- stats::rnorm(N,sd=2)
+error <- stats::runif(N, .7, 1.3)
+# compute WLE reliability
+WLErel(x,error)
+# compute EAP reliaility
+EAPrel(x,error)

+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/reference/anova.tam.html b/docs/reference/anova.tam.html
index 37d0769..27869cc 100644
--- a/docs/reference/anova.tam.html
+++ b/docs/reference/anova.tam.html
@@ -1,72 +1,17 @@
-
 
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-  
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-Likelihood Ratio Test for Model Comparisons and Log-Likelihood Value — anova-logLik • TAM
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-Likelihood Ratio Test for Model Comparisons and Log-Likelihood Value — anova-logLik • TAM
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+
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Likelihood Ratio Test for Model Comparisons and Log-Likelihood Value

@@ -119,126 +51,125 @@ 
Likelihood Ratio Test for Model Comparisons and Log-Likelihood Value

     

 
     

-    
The anova function compares two models estimated of class tam,
-tam.mml or tam.mml.3pl using a likelihood ratio test.
+    
The anova function compares two models estimated of class tam,
+tam.mml or tam.mml.3pl using a likelihood ratio test.
 The logLik function extracts the value of the log-Likelihood.

-
The function can be applied for values of tam.mml,
-tam.mml.2pl, tam.mml.mfr, tam.fa,
-tam.mml.3pl, tam.latreg or tamaan.

+
The function can be applied for values of tam.mml,
+tam.mml.2pl, tam.mml.mfr, tam.fa,
+tam.mml.3pl, tam.latreg or tamaan.

     

 
-    
# S3 method for tam
-anova(object, ...)
-# S3 method for tam
-logLik(object, ...)
-
-# S3 method for tam.mml
-anova(object, ...)
-# S3 method for tam.mml
-logLik(object, ...)
-
-# S3 method for tam.mml.3pl
-anova(object, ...)
-# S3 method for tam.mml.3pl
-logLik(object, ...)
-
-# S3 method for tamaan
-anova(object, ...)
-# S3 method for tamaan
-logLik(object, ...)
-
-# S3 method for tam.latreg
-anova(object, ...)
-# S3 method for tam.latreg
-logLik(object, ...)
-
-# S3 method for tam.np
-anova(object, ...)
-# S3 method for tam.np
-logLik(object, ...)

-
-    
Arguments

-    
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
object
Object of class tam, tam.mml,
-tam.mml.3pl, tam.latreg, tam.np,
-or tamaan. Note that for anova two objects
-(fitted models) must be provided.
...
Further arguments to be passed

-
-    
Value

-
-    
A data frame containing the likelihood ratio test statistic and
+    

+    
# S3 method for tam
+anova(object, ...)
+# S3 method for tam
+logLik(object, ...)
+
+# S3 method for tam.mml
+anova(object, ...)
+# S3 method for tam.mml
+logLik(object, ...)
+
+# S3 method for tam.mml.3pl
+anova(object, ...)
+# S3 method for tam.mml.3pl
+logLik(object, ...)
+
+# S3 method for tamaan
+anova(object, ...)
+# S3 method for tamaan
+logLik(object, ...)
+
+# S3 method for tam.latreg
+anova(object, ...)
+# S3 method for tam.latreg
+logLik(object, ...)
+
+# S3 method for tam.np
+anova(object, ...)
+# S3 method for tam.np
+logLik(object, ...)

+    

+
+    

+    
Arguments

+    
object

+
Object of class tam, tam.mml,
+tam.mml.3pl, tam.latreg, tam.np,
+or tamaan. Note that for anova two objects
+(fitted models) must be provided.

+
+
...

+
Further arguments to be passed

+
+

+    

+    
Value

+    
+
+
A data frame containing the likelihood ratio test statistic and
 information criteria.

+    

 
-    
Examples

-    
#############################################################################
-# EXAMPLE 1: Dichotomous data sim.rasch - 1PL vs. 2PL model
-#############################################################################
-
-data(data.sim.rasch)
-# 1PL estimation
-mod1 <- TAM::tam.mml(resp=data.sim.rasch)
-logLik(mod1)
-# 2PL estimation
-mod2 <- TAM::tam.mml.2pl(resp=data.sim.rasch, irtmodel="2PL")
-logLik(mod2)
-# Model comparison
-anova( mod1, mod2 )
-  ##     Model   loglike Deviance Npars      AIC      BIC    Chisq df       p
-  ##   1  mod1 -42077.88 84155.77    41 84278.77 84467.40 54.05078 39 0.05508
-  ##   2  mod2 -42050.86 84101.72    80 84341.72 84709.79       NA NA      NA
-
-if (FALSE) {
-#############################################################################
-# EXAMPLE 2: Dataset reading (sirt package): 1- vs. 2-dimensional model
-#############################################################################
-
-data(data.read, package="sirt")
-
-# 1-dimensional model
-mod1 <- TAM::tam.mml.2pl(resp=data.read )
-# 2-dimensional model
-mod2 <- TAM::tam.fa(resp=data.read, irtmodel="efa", nfactors=2,
-             control=list(maxiter=150) )
-# Model comparison
-anova( mod1, mod2 )
-  ##       Model   loglike Deviance Npars      AIC      BIC    Chisq df  p
-  ##   1    mod1 -1954.888 3909.777    24 3957.777 4048.809 76.66491 11  0
-  ##   2    mod2 -1916.556 3833.112    35 3903.112 4035.867       NA NA NA
-}

+    

+    
Examples

+    
#############################################################################
+# EXAMPLE 1: Dichotomous data sim.rasch - 1PL vs. 2PL model
+#############################################################################
+
+data(data.sim.rasch)
+# 1PL estimation
+mod1 <- TAM::tam.mml(resp=data.sim.rasch)
+logLik(mod1)
+# 2PL estimation
+mod2 <- TAM::tam.mml.2pl(resp=data.sim.rasch, irtmodel="2PL")
+logLik(mod2)
+# Model comparison
+anova( mod1, mod2 )
+  ##     Model   loglike Deviance Npars      AIC      BIC    Chisq df       p
+  ##   1  mod1 -42077.88 84155.77    41 84278.77 84467.40 54.05078 39 0.05508
+  ##   2  mod2 -42050.86 84101.72    80 84341.72 84709.79       NA NA      NA
+
+if (FALSE) {
+#############################################################################
+# EXAMPLE 2: Dataset reading (sirt package): 1- vs. 2-dimensional model
+#############################################################################
+
+data(data.read, package="sirt")
+
+# 1-dimensional model
+mod1 <- TAM::tam.mml.2pl(resp=data.read )
+# 2-dimensional model
+mod2 <- TAM::tam.fa(resp=data.read, irtmodel="efa", nfactors=2,
+             control=list(maxiter=150) )
+# Model comparison
+anova( mod1, mod2 )
+  ##       Model   loglike Deviance Npars      AIC      BIC    Chisq df  p
+  ##   1    mod1 -1954.888 3909.777    24 3957.777 4048.809 76.66491 11  0
+  ##   2    mod2 -1916.556 3833.112    35 3903.112 4035.867       NA NA NA
+}

+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/reference/cfa.extract.itempars.html b/docs/reference/cfa.extract.itempars.html
index 75996bc..7f45941 100644
--- a/docs/reference/cfa.extract.itempars.html
+++ b/docs/reference/cfa.extract.itempars.html
@@ -1,71 +1,16 @@
-
 
-
-  
-  
-
-
-
-Extracting Item Parameters from a Fitted <code>cfa</code> Object in <span class="pkg">lavaan</span> — cfa.extract.itempars • TAM
-
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-
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-lavaan — cfa.extract.itempars" />
-Extracting Item Parameters from a Fitted cfa Object in lavaan — cfa.extract.itempars • TAM
-
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-  
+
+    
 
-  
     

-      

-      
 
       
 
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+      

   

     

     
Extracting Item Parameters from a Fitted cfa Object in lavaan

@@ -119,128 +51,140 @@ 
Extracting Item Parameters from a Fitted cfa Object in 
     
This function extract item parameters from a fitted
-lavaan::cfa object in lavaan. It
+lavaan::cfa object in lavaan. It
 extract item loadings, item intercepts and the mean
 and covariance matrix of latent variables in a
 confirmatory factor analysis model.

     

 
-    
cfa.extract.itempars(object)

+    

+    
cfa.extract.itempars(object)

+    

 
-    
Arguments

-    
-    
-    
-      
-      
-    
-    
object
Fitted cfa object

+    

+    
Arguments

+    
object

+
Fitted cfa object

 
-    
Value

+

+    

+    
Value

+    
 
-    
List with following entries

-
L
Matrix of item loadings

-
nu
Vector of item intercepts

-
psi
Residual covariance matrix

-
Sigma
Covariance matrix of latent variables

-
nu
Vector of means of latent variables

-
...
Further values

+
List with following entries

+
L

+
Matrix of item loadings

 
-    
See also

+
nu

+
Vector of item intercepts

 
-    
See IRTLikelihood.cfa for extracting the
+
psi

+
Residual covariance matrix

+
+
Sigma

+
Covariance matrix of latent variables

+
+
nu

+
Vector of means of latent variables

+
+
...

+
Further values

+
+

+    

+    
See also

+    
See IRTLikelihood.cfa for extracting the
 individual likelihood from fitted confirmatory
 factor analyses.

-
lavaan::cfa

-
-    
Examples

-    
#############################################################################
-# EXAMPLE 1: CFA data.Students
-#############################################################################
-
-library(lavaan)
-library(CDM)
-
-data(data.Students, package="CDM")
-dat <- data.Students
-
-dat1 <- dat[, paste0( "mj", 1:4 ) ]
-
-#*** Model 1: Unidimensional model scale mj
-lavmodel <- "
-   mj=~ mj1 + mj2 + mj3 + mj4
-   mj ~~ mj
-     "
-mod1 <- lavaan::cfa( lavmodel, data=dat1, std.lv=TRUE )
-summary(mod1, standardized=TRUE, rsquare=TRUE )
-# extract parameters
-res1 <- TAM::cfa.extract.itempars( mod1 )
-
-if (FALSE) {
-#*** Model 2: Scale mj - explicit modelling of item intercepts
-lavmodel <- "
-   mj=~ mj1 + mj2 + mj3 + mj4
-   mj ~~ mj
-   mj1 ~ 1
-     "
-mod2 <- lavaan::cfa( lavmodel, data=dat1, std.lv=TRUE )
-summary(mod2, standardized=TRUE, rsquare=TRUE )
-res2 <- TAM::cfa.extract.itempars( mod2 )
-
-#*** Model 3: Tau-parallel measurements scale mj
-lavmodel <- "
-   mj=~ a*mj1 + a*mj2 + a*mj3 + a*mj4
-   mj ~~ 1*mj
-   mj1 ~ b*1
-   mj2 ~ b*1
-   mj3 ~ b*1
-   mj4 ~ b*1
-     "
-mod3 <- lavaan::cfa( lavmodel, data=dat1, std.lv=TRUE )
-summary(mod3, standardized=TRUE, rsquare=TRUE )
-res3 <- TAM::cfa.extract.itempars( mod3 )
-
-#*** Model 4: Two-dimensional CFA with scales mj and sc
-dat2 <- dat[, c(paste0("mj",1:4), paste0("sc",1:4)) ]
-# lavaan model with shortage "__" operator
-lavmodel <- "
-   mj=~ mj1__mj4
-   sc=~ sc1__sc4
-   mj ~~ sc
-   mj ~~ 1*mj
-   sc ~~ 1*sc
-     "
-lavmodel <- TAM::lavaanify.IRT( lavmodel, data=dat2 )$lavaan.syntax
-cat(lavmodel)
-mod4 <- lavaan::cfa( lavmodel, data=dat2, std.lv=TRUE )
-summary(mod4, standardized=TRUE, rsquare=TRUE )
-res4 <- TAM::cfa.extract.itempars( mod4 )
-}

+
lavaan::cfa

+    

+
+    

+    
Examples

+    
#############################################################################
+# EXAMPLE 1: CFA data.Students
+#############################################################################
+
+library(lavaan)
+library(CDM)
+
+data(data.Students, package="CDM")
+dat <- data.Students
+
+dat1 <- dat[, paste0( "mj", 1:4 ) ]
+
+#*** Model 1: Unidimensional model scale mj
+lavmodel <- "
+   mj=~ mj1 + mj2 + mj3 + mj4
+   mj ~~ mj
+     "
+mod1 <- lavaan::cfa( lavmodel, data=dat1, std.lv=TRUE )
+summary(mod1, standardized=TRUE, rsquare=TRUE )
+# extract parameters
+res1 <- TAM::cfa.extract.itempars( mod1 )
+
+if (FALSE) {
+#*** Model 2: Scale mj - explicit modelling of item intercepts
+lavmodel <- "
+   mj=~ mj1 + mj2 + mj3 + mj4
+   mj ~~ mj
+   mj1 ~ 1
+     "
+mod2 <- lavaan::cfa( lavmodel, data=dat1, std.lv=TRUE )
+summary(mod2, standardized=TRUE, rsquare=TRUE )
+res2 <- TAM::cfa.extract.itempars( mod2 )
+
+#*** Model 3: Tau-parallel measurements scale mj
+lavmodel <- "
+   mj=~ a*mj1 + a*mj2 + a*mj3 + a*mj4
+   mj ~~ 1*mj
+   mj1 ~ b*1
+   mj2 ~ b*1
+   mj3 ~ b*1
+   mj4 ~ b*1
+     "
+mod3 <- lavaan::cfa( lavmodel, data=dat1, std.lv=TRUE )
+summary(mod3, standardized=TRUE, rsquare=TRUE )
+res3 <- TAM::cfa.extract.itempars( mod3 )
+
+#*** Model 4: Two-dimensional CFA with scales mj and sc
+dat2 <- dat[, c(paste0("mj",1:4), paste0("sc",1:4)) ]
+# lavaan model with shortage "__" operator
+lavmodel <- "
+   mj=~ mj1__mj4
+   sc=~ sc1__sc4
+   mj ~~ sc
+   mj ~~ 1*mj
+   sc ~~ 1*sc
+     "
+lavmodel <- TAM::lavaanify.IRT( lavmodel, data=dat2 )$lavaan.syntax
+cat(lavmodel)
+mod4 <- lavaan::cfa( lavmodel, data=dat2, std.lv=TRUE )
+summary(mod4, standardized=TRUE, rsquare=TRUE )
+res4 <- TAM::cfa.extract.itempars( mod4 )
+}

+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/reference/data.cqc.html b/docs/reference/data.cqc.html
index b633fac..4b719bb 100644
--- a/docs/reference/data.cqc.html
+++ b/docs/reference/data.cqc.html
@@ -1,68 +1,13 @@
-
 
-
-  
-  
-
-
-
-More Datasets and Examples (Similar to ConQuest Examples) — data.cqc • TAM
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-More Datasets and Examples (Similar to ConQuest Examples) — data.cqc • TAM
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+
+    
 
-  
     

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-      
 
       
 
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+      

   

     

     
More Datasets and Examples (Similar to ConQuest Examples)

@@ -119,308 +51,278 @@ 
More Datasets and Examples (Similar to ConQuest Examples)

 (Wu, Adams, Wilson, & Haldane, 2007).

     

 
-    
data(data.cqc01)
-data(data.cqc02)
-data(data.cqc03)
-data(data.cqc04)
-data(data.cqc05)

-
-
-    
Format

+    

+    
data(data.cqc01)
+data(data.cqc02)
+data(data.cqc03)
+data(data.cqc04)
+data(data.cqc05)

+    

 
+    

+    
Format

     
 
-
    
-
  • data.cqc01 contains 512 persons on
+
    • data.cqc01 contains 512 persons on
 12 dichotomous items of following format
      
-
      'data.frame':   512 obs. of  12 variables: 
      
- $ BSMMA01: int  1 1 0 1 1 1 1 1 0 0 ... 
      
- $ BSMMA02: int  1 0 1 1 0 1 1 1 0 0 ... 
      
- $ BSMMA03: int  1 1 0 1 1 1 1 1 1 0 ... 
      
- [...] 
      
- $ BSMSA12: int  0 0 0 0 1 0 1 1 0 0 ... 
      • 
+
      'data.frame':   512 obs. of  12 variables: 
       $ BSMMA01: int  1 1 0 1 1 1 1 1 0 0 ... 
       $ BSMMA02: int  1 0 1 1 0 1 1 1 0 0 ... 
       $ BSMMA03: int  1 1 0 1 1 1 1 1 1 0 ... 
       [...] 
       $ BSMSA12: int  0 0 0 0 1 0 1 1 0 0 ... 
      
 
    • data.cqc02 contains 431 persons on 8 polytomous
 variables of following format
      
-
      'data.frame':   431 obs. of  8 variables: 
      
- $ It1: int  1 1 2 0 2 1 2 2 2 1 ... 
      
- $ It2: int  3 0 1 2 2 3 2 2 1 1 ... 
      
- $ It3: int  1 1 1 0 1 1 0 0 1 0 ... 
      
- [...] 
      
- $ It8: int  3 1 0 0 3 1 3 0 3 0 ... 
      • 
+
      'data.frame':   431 obs. of  8 variables: 
       $ It1: int  1 1 2 0 2 1 2 2 2 1 ... 
       $ It2: int  3 0 1 2 2 3 2 2 1 1 ... 
       $ It3: int  1 1 1 0 1 1 0 0 1 0 ... 
       [...] 
       $ It8: int  3 1 0 0 3 1 3 0 3 0 ... 
      
 
    • data.cqc03 contains 11200 observations for
 5600 persons, 16 raters and 2 items (crit1 and crit2)
      
-
      'data.frame':   11200 obs. of  4 variables: 
      
- $ pid  : num  10001 10001 10002 10002 10003 ... 
      
- $ rater: chr  "R11" "R12" "R13" "R14" ... 
      
- $ crit1: int  2 2 2 1 3 2 2 1 1 1 ... 
      
- $ crit2: int  3 3 2 1 2 2 2 2 2 1 ... 
      • 
+
      'data.frame':   11200 obs. of  4 variables: 
       $ pid  : num  10001 10001 10002 10002 10003 ... 
       $ rater: chr  "R11" "R12" "R13" "R14" ... 
       $ crit1: int  2 2 2 1 3 2 2 1 1 1 ... 
       $ crit2: int  3 3 2 1 2 2 2 2 2 1 ... 
      
 
    • data.cqc04 contains 1452 observations for 363 persons,
 4 raters, 4 topics and 5 items (spe, coh, str,
  gra,  con)
      
-
      'data.frame':   1452 obs. of  8 variables: 
      
- $ pid  : num  10010 10010 10010 10010 10016 ... 
      
- $ rater: chr  "BE" "CO" "BE" "CO" ... 
      
- $ topic: chr  "Spor" "Spor" "Spor" "Spor" ... 
      
- $ spe  : int  2 0 2 1 3 3 3 3 3 2 ... 
      
- $ coh  : int  1 1 2 0 3 3 3 3 3 3 ... 
      
- $ str  : int  0 1 3 0 3 2 3 2 3 0 ... 
      
- $ gra  : int  0 0 2 0 3 3 3 3 2 1 ... 
      
- $ con  : int  0 0 0 0 3 1 2 2 3 0 ... 
      • 
+
      'data.frame':   1452 obs. of  8 variables: 
       $ pid  : num  10010 10010 10010 10010 10016 ... 
       $ rater: chr  "BE" "CO" "BE" "CO" ... 
       $ topic: chr  "Spor" "Spor" "Spor" "Spor" ... 
       $ spe  : int  2 0 2 1 3 3 3 3 3 2 ... 
       $ coh  : int  1 1 2 0 3 3 3 3 3 3 ... 
       $ str  : int  0 1 3 0 3 2 3 2 3 0 ... 
       $ gra  : int  0 0 2 0 3 3 3 3 2 1 ... 
       $ con  : int  0 0 0 0 3 1 2 2 3 0 ... 
      
 
    • data.cqc05 contains 1500 persons,
 3 covariates and 157 items.
      
-
      'data.frame':   1500 obs. of  160 variables: 
      
- $ gender: int  1 0 1 0 0 0 0 1 0 1 ... 
      
- $ level : int  0 1 1 0 0 0 1 0 1 1 ... 
      
- $ gbyl  : int  0 0 1 0 0 0 0 0 0 1 ... 
      
- $ A001  : num  0 0 0 1 0 1 1 1 0 1 ... 
      
- $ A002  : num  1 1 0 1 1 1 1 1 1 0 ... 
      
- $ A003  : num  0 0 0 0 1 1 1 0 0 1 ... 
      
-[...] 
      • 
-
    
-
-    
    See also
    
-
-    
    See the sirt::R2conquest function
+
    'data.frame':   1500 obs. of  160 variables: 
     $ gender: int  1 0 1 0 0 0 0 1 0 1 ... 
     $ level : int  0 1 1 0 0 0 1 0 1 1 ... 
     $ gbyl  : int  0 0 1 0 0 0 0 0 0 1 ... 
     $ A001  : num  0 0 0 1 0 1 1 1 0 1 ... 
     $ A002  : num  1 1 0 1 1 1 1 1 1 0 ... 
     $ A003  : num  0 0 0 0 1 1 1 0 0 1 ... 
    [...] 
    • 
+

+    

+    
See also

+    
See the sirt::R2conquest function
 for running ConQuest software from within R.

-
See the WrightMap package for functions
+
See the WrightMap package for functions
 connected to reading ConQuest files and creating Wright maps.
 ConQuest output files can be read into R with the help of
-the WrightMap::CQmodel function.
-See also the IRT.WrightMap function in TAM.

-
See also the eat package (https://r-forge.r-project.org/projects/eat/)
+the WrightMap::CQmodel function.
+See also the IRT.WrightMap function in TAM.

+
See also the eat package (https://r-forge.r-project.org/projects/eat/)
 for elaborate functionality for communication of ConQuest with R.

-    
References

-
+    

+    

+    
References

     
Wu, M. L., Adams, R. J., Wilson, M. R. & Haldane, S. (2007).
 ACER ConQuest Version 2.0. Mulgrave.
 https://shop.acer.edu.au/acer-shop/group/CON3.

+    

 
-    
Examples

-    
if (FALSE) {
-
-library(sirt)
-library(WrightMap)
-# In the following, ConQuest will also be used for estimation.
-path.conquest <- "C:/Conquest"             # path of the ConQuest console.exe
-setwd( "p:/my_files/ConQuest_analyses" )  # working directory
-
-#############################################################################
-# EXAMPLE 01: Rasch model data.cqc01
-#############################################################################
-
-data(data.cqc01)
-dat <- data.cqc01
-
-#********************************************
-#*** Model 01: Estimate Rasch model
-mod01 <- TAM::tam.mml(dat)
-summary(mod01)
-
-#------- ConQuest
-
-# estimate model
-cmod01 <- sirt::R2conquest( dat, name="mod01", path.conquest=path.conquest)
-summary(cmod01)   # summary output
-# read shw file with some terms
-shw01a <- sirt::read.show( "mod01.shw" )
-cmod01$shw.itemparameter
-# read person item maps
-pi01a <- sirt::read.pimap( "mod01.shw" )
-cmod01$shw.pimap
-# read plausible values (npv=10 plausible values)
-pv01a <- sirt::read.pv(pvfile="mod01.pv", npv=10)
-cmod01$person
-
-# read ConQuest model
-res01a <- WrightMap::CQmodel(p.est="mod01.wle", show="mod01.shw", p.type="WLE" )
-print(res01a)
-# plot item fit
-WrightMap::fitgraph(res01a)
-# Wright map
-plot(res01a, label.items.srt=90 )
-
-#############################################################################
-# EXAMPLE 02: Partial credit model and rating scale model data.cqc02
-#############################################################################
-
-data(data.cqc02)
-dat <- data.cqc02
-
-#********************************************
-# Model 02a: Partial credit model in ConQuest parametrization 'item+item*step'
-mod02a <- TAM::tam.mml( dat, irtmodel="PCM2" )
-summary(mod02a, file="mod02a")
-fit02a <- TAM::tam.fit(mod02a)
-summary(fit02a)
-
-#--- ConQuest
-# estimate model
-maxK <- max( dat, na.rm=TRUE )
-cmod02a <- sirt::R2conquest( dat, itemcodes=0:maxK, model="item+item*step",
-               name="mod02a", path.conquest=path.conquest)
-summary(cmod02a)   # summary output
-
-# read ConQuest model
-res02a <- WrightMap::CQmodel(p.est="mod02a.wle", show="mod02a.shw", p.type="WLE" )
-print(res02a)
-# Wright map
-plot(res02a, label.items.srt=90 )
-plot(res02a, item.table="item")
-
-#********************************************
-# Model 02b: Rating scale model
-mod02b <- TAM::tam.mml( dat, irtmodel="RSM" )
-summary( mod02b )
-
-#############################################################################
-# EXAMPLE 03: Faceted Rasch model for rating data data.cqc03
-#############################################################################
-
-data(data.cqc03)
-# select items
-resp <- data.cqc03[, c("crit1","crit2") ]
-
-#********************************************
-# Model 03a: 'item+step+rater'
-mod03a <- TAM::tam.mml.mfr( resp, facets=data.cqc03[,"rater",drop=FALSE],
-            formulaA=~ item+step+rater, pid=data.cqc03$pid )
-summary( mod03a )
-
-#--- ConQuest
-X <- data.cqc03[,"rater",drop=FALSE]
-X$rater <- as.numeric(substring( X$rater, 2 )) # convert 'rater' in numeric format
-maxK <- max( resp, na.rm=TRUE)
-cmod03a <- sirt::R2conquest( resp,  X=X, regression="",  model="item+step+rater",
-             name="mod03a", path.conquest=path.conquest, set.constraints="cases" )
-summary(cmod03a)   # summary output
-
-# read ConQuest model
-res03a <- WrightMap::CQmodel(p.est="mod03a.wle", show="mod03a.shw", p.type="WLE" )
-print(res03a)
-# Wright map
-plot(res03a)
-
-#********************************************
-# Model 03b: 'item:step+rater'
-mod03b <- TAM::tam.mml.mfr( resp, facets=data.cqc03[,"rater",drop=FALSE],
-            formulaA=~ item + item:step+rater, pid=data.cqc03$pid )
-summary( mod03b )
-
-#********************************************
-# Model 03c: 'step+rater' for first item 'crit1'
-# Restructuring the data is necessary.
-# Define raters as items in the new dataset 'dat1'.
-persons <- unique( data.cqc03$pid )
-raters <- unique( data.cqc03$rater )
-dat1 <- matrix( NA, nrow=length(persons), ncol=length(raters) + 1 )
-dat1 <- as.data.frame(dat1)
-colnames(dat1) <- c("pid", raters )
-dat1$pid <- persons
-for (rr in raters){
-    dat1.rr <- data.cqc03[ data.cqc03$rater==rr, ]
-    dat1[ match(dat1.rr$pid, persons),rr] <- dat1.rr$crit1
-        }
-  ##   > head(dat1)
-  ##       pid R11 R12 R13 R14 R15 R16 R17 R18 R19 R20 R21 R22 R23 R24 R25 R26
-  ##   1 10001   2   2  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA
-  ##   2 10002  NA  NA   2   1  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA
-  ##   3 10003  NA  NA   3   2  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA
-  ##   4 10004  NA  NA   2   1  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA
-  ##   5 10005  NA  NA   1   1  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA
-  ##   6 10006  NA  NA   1   1  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA
-# estimate model 03c
-mod03c <- TAM::tam.mml( dat1[,-1], pid=dat1$pid )
-summary( mod03c )
-
-#############################################################################
-# EXAMPLE 04: Faceted Rasch model for rating data data.cqc04
-#############################################################################
-
-data(data.cqc04)
-resp <- data.cqc04[,4:8]
-facets <- data.cqc04[, c("rater", "topic") ]
-
-#********************************************
-# Model 04a: 'item*step+rater+topic'
-formulaA <- ~ item*step + rater + topic
-mod04a <- TAM::tam.mml.mfr( resp, facets=facets,
-            formulaA=formulaA, pid=data.cqc04$pid )
-summary( mod04a )
-
-#********************************************
-# Model 04b: 'item*step+rater+topic+item*rater+item*topic'
-formulaA <- ~ item*step + rater + topic + item*rater + item*topic
-mod04b <- TAM::tam.mml.mfr( resp, facets=facets,
-            formulaA=formulaA, pid=data.cqc04$pid )
-summary( mod04b )
-
-#********************************************
-# Model 04c: 'item*step' with fixing rater and topic parameters to zero
-formulaA <- ~ item*step + rater + topic
-mod04c0 <- TAM::tam.mml.mfr( resp, facets=facets,
-            formulaA=formulaA, pid=data.cqc04$pid, control=list(maxiter=4) )
-summary( mod04c0 )
-# fix rater and topic parameter to zero
-xsi.est <- mod04c0$xsi
-xsi.fixed <- cbind( seq(1,nrow(xsi.est)), xsi.est$xsi )
-rownames(xsi.fixed) <- rownames(xsi.est)
-xsi.fixed <- xsi.fixed[ c(8:13),]
-xsi.fixed[,2] <- 0
-  ##   > xsi.fixed
-  ##             [,1] [,2]
-  ##   raterAM      8    0
-  ##   raterBE      9    0
-  ##   raterCO     10    0
-  ##   topicFami   11    0
-  ##   topicScho   12    0
-  ##   topicSpor   13    0
-mod04c1 <- TAM::tam.mml.mfr( resp, facets=facets,
-             formulaA=formulaA, pid=data.cqc04$pid, xsi.fixed=xsi.fixed )
-summary( mod04c1 )
-
-#############################################################################
-# EXAMPLE 05: Partial credit model with latent regression and
-#             plausible value imputation
-#############################################################################
-
-data(data.cqc05)
-resp <- data.cqc05[, -c(1:3) ] # select item responses
-
-#********************************************
-# Model 05a: Partial credit model
-mod05a <-tam.mml(resp=resp, irtmodel="PCM2" )
-
-#********************************************
-# Model 05b: Partial credit model with latent regressors
-mod05b <-tam.mml(resp=resp, irtmodel="PCM2",  Y=data.cqc05[,1:3] )
-# Plausible value imputation
-pvmod05b <- TAM::tam.pv( mod05b )
-}

+    

+    
Examples

+    
if (FALSE) {
+
+library(sirt)
+library(WrightMap)
+# In the following, ConQuest will also be used for estimation.
+path.conquest <- "C:/Conquest"             # path of the ConQuest console.exe
+setwd( "p:/my_files/ConQuest_analyses" )  # working directory
+
+#############################################################################
+# EXAMPLE 01: Rasch model data.cqc01
+#############################################################################
+
+data(data.cqc01)
+dat <- data.cqc01
+
+#********************************************
+#*** Model 01: Estimate Rasch model
+mod01 <- TAM::tam.mml(dat)
+summary(mod01)
+
+#------- ConQuest
+
+# estimate model
+cmod01 <- sirt::R2conquest( dat, name="mod01", path.conquest=path.conquest)
+summary(cmod01)   # summary output
+# read shw file with some terms
+shw01a <- sirt::read.show( "mod01.shw" )
+cmod01$shw.itemparameter
+# read person item maps
+pi01a <- sirt::read.pimap( "mod01.shw" )
+cmod01$shw.pimap
+# read plausible values (npv=10 plausible values)
+pv01a <- sirt::read.pv(pvfile="mod01.pv", npv=10)
+cmod01$person
+
+# read ConQuest model
+res01a <- WrightMap::CQmodel(p.est="mod01.wle", show="mod01.shw", p.type="WLE" )
+print(res01a)
+# plot item fit
+WrightMap::fitgraph(res01a)
+# Wright map
+plot(res01a, label.items.srt=90 )
+
+#############################################################################
+# EXAMPLE 02: Partial credit model and rating scale model data.cqc02
+#############################################################################
+
+data(data.cqc02)
+dat <- data.cqc02
+
+#********************************************
+# Model 02a: Partial credit model in ConQuest parametrization 'item+item*step'
+mod02a <- TAM::tam.mml( dat, irtmodel="PCM2" )
+summary(mod02a, file="mod02a")
+fit02a <- TAM::tam.fit(mod02a)
+summary(fit02a)
+
+#--- ConQuest
+# estimate model
+maxK <- max( dat, na.rm=TRUE )
+cmod02a <- sirt::R2conquest( dat, itemcodes=0:maxK, model="item+item*step",
+               name="mod02a", path.conquest=path.conquest)
+summary(cmod02a)   # summary output
+
+# read ConQuest model
+res02a <- WrightMap::CQmodel(p.est="mod02a.wle", show="mod02a.shw", p.type="WLE" )
+print(res02a)
+# Wright map
+plot(res02a, label.items.srt=90 )
+plot(res02a, item.table="item")
+
+#********************************************
+# Model 02b: Rating scale model
+mod02b <- TAM::tam.mml( dat, irtmodel="RSM" )
+summary( mod02b )
+
+#############################################################################
+# EXAMPLE 03: Faceted Rasch model for rating data data.cqc03
+#############################################################################
+
+data(data.cqc03)
+# select items
+resp <- data.cqc03[, c("crit1","crit2") ]
+
+#********************************************
+# Model 03a: 'item+step+rater'
+mod03a <- TAM::tam.mml.mfr( resp, facets=data.cqc03[,"rater",drop=FALSE],
+            formulaA=~ item+step+rater, pid=data.cqc03$pid )
+summary( mod03a )
+
+#--- ConQuest
+X <- data.cqc03[,"rater",drop=FALSE]
+X$rater <- as.numeric(substring( X$rater, 2 )) # convert 'rater' in numeric format
+maxK <- max( resp, na.rm=TRUE)
+cmod03a <- sirt::R2conquest( resp,  X=X, regression="",  model="item+step+rater",
+             name="mod03a", path.conquest=path.conquest, set.constraints="cases" )
+summary(cmod03a)   # summary output
+
+# read ConQuest model
+res03a <- WrightMap::CQmodel(p.est="mod03a.wle", show="mod03a.shw", p.type="WLE" )
+print(res03a)
+# Wright map
+plot(res03a)
+
+#********************************************
+# Model 03b: 'item:step+rater'
+mod03b <- TAM::tam.mml.mfr( resp, facets=data.cqc03[,"rater",drop=FALSE],
+            formulaA=~ item + item:step+rater, pid=data.cqc03$pid )
+summary( mod03b )
+
+#********************************************
+# Model 03c: 'step+rater' for first item 'crit1'
+# Restructuring the data is necessary.
+# Define raters as items in the new dataset 'dat1'.
+persons <- unique( data.cqc03$pid )
+raters <- unique( data.cqc03$rater )
+dat1 <- matrix( NA, nrow=length(persons), ncol=length(raters) + 1 )
+dat1 <- as.data.frame(dat1)
+colnames(dat1) <- c("pid", raters )
+dat1$pid <- persons
+for (rr in raters){
+    dat1.rr <- data.cqc03[ data.cqc03$rater==rr, ]
+    dat1[ match(dat1.rr$pid, persons),rr] <- dat1.rr$crit1
+        }
+  ##   > head(dat1)
+  ##       pid R11 R12 R13 R14 R15 R16 R17 R18 R19 R20 R21 R22 R23 R24 R25 R26
+  ##   1 10001   2   2  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA
+  ##   2 10002  NA  NA   2   1  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA
+  ##   3 10003  NA  NA   3   2  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA
+  ##   4 10004  NA  NA   2   1  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA
+  ##   5 10005  NA  NA   1   1  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA
+  ##   6 10006  NA  NA   1   1  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA
+# estimate model 03c
+mod03c <- TAM::tam.mml( dat1[,-1], pid=dat1$pid )
+summary( mod03c )
+
+#############################################################################
+# EXAMPLE 04: Faceted Rasch model for rating data data.cqc04
+#############################################################################
+
+data(data.cqc04)
+resp <- data.cqc04[,4:8]
+facets <- data.cqc04[, c("rater", "topic") ]
+
+#********************************************
+# Model 04a: 'item*step+rater+topic'
+formulaA <- ~ item*step + rater + topic
+mod04a <- TAM::tam.mml.mfr( resp, facets=facets,
+            formulaA=formulaA, pid=data.cqc04$pid )
+summary( mod04a )
+
+#********************************************
+# Model 04b: 'item*step+rater+topic+item*rater+item*topic'
+formulaA <- ~ item*step + rater + topic + item*rater + item*topic
+mod04b <- TAM::tam.mml.mfr( resp, facets=facets,
+            formulaA=formulaA, pid=data.cqc04$pid )
+summary( mod04b )
+
+#********************************************
+# Model 04c: 'item*step' with fixing rater and topic parameters to zero
+formulaA <- ~ item*step + rater + topic
+mod04c0 <- TAM::tam.mml.mfr( resp, facets=facets,
+            formulaA=formulaA, pid=data.cqc04$pid, control=list(maxiter=4) )
+summary( mod04c0 )
+# fix rater and topic parameter to zero
+xsi.est <- mod04c0$xsi
+xsi.fixed <- cbind( seq(1,nrow(xsi.est)), xsi.est$xsi )
+rownames(xsi.fixed) <- rownames(xsi.est)
+xsi.fixed <- xsi.fixed[ c(8:13),]
+xsi.fixed[,2] <- 0
+  ##   > xsi.fixed
+  ##             [,1] [,2]
+  ##   raterAM      8    0
+  ##   raterBE      9    0
+  ##   raterCO     10    0
+  ##   topicFami   11    0
+  ##   topicScho   12    0
+  ##   topicSpor   13    0
+mod04c1 <- TAM::tam.mml.mfr( resp, facets=facets,
+             formulaA=formulaA, pid=data.cqc04$pid, xsi.fixed=xsi.fixed )
+summary( mod04c1 )
+
+#############################################################################
+# EXAMPLE 05: Partial credit model with latent regression and
+#             plausible value imputation
+#############################################################################
+
+data(data.cqc05)
+resp <- data.cqc05[, -c(1:3) ] # select item responses
+
+#********************************************
+# Model 05a: Partial credit model
+mod05a <-tam.mml(resp=resp, irtmodel="PCM2" )
+
+#********************************************
+# Model 05b: Partial credit model with latent regressors
+mod05b <-tam.mml(resp=resp, irtmodel="PCM2",  Y=data.cqc05[,1:3] )
+# Plausible value imputation
+pvmod05b <- TAM::tam.pv( mod05b )
+}

+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
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+  
 
+  
 
diff --git a/docs/reference/data.ctest.html b/docs/reference/data.ctest.html
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Some C-Test Datasets

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Some C-Test Datasets

     
Some C-Test datasets.

     

 
-    
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-data(data.ctest2)

-
-
-    
Format

+    

+    
data(data.ctest1)
+data(data.ctest2)

+    

 
+    

+    
Format

     
 
-
    
-
  • The dataset data.ctest1 contains item responses of C-tests
+
    • The dataset data.ctest1 contains item responses of C-tests
 at two time points. The format is
      
-
      'data.frame':   1675 obs. of  42 variables: 
      
- $ idstud : num  100101 100102 100103 100104 100105 ... 
      
- $ idclass: num  1001 1001 1001 1001 1001 ... 
      
- $ A01T1  : int  0 1 0 1 1 NA 1 0 1 1 ... 
      
- $ A02T1  : int  0 1 0 1 0 NA 0 1 1 0 ... 
      
- $ A03T1  : int  0 1 1 1 0 NA 0 1 1 1 ... 
      
- $ A04T1  : int  1 0 0 0 0 NA 0 0 0 0 ... 
      
- $ A05T1  : int  0 0 0 1 1 NA 0 0 1 1 ... 
      
- $ B01T1  : int  1 1 0 1 1 NA 0 0 1 0 ... 
      
- $ B02T1  : int  0 0 0 1 0 NA 0 0 1 1 ... 
      
- [...] 
      
- $ C02T2  : int  0 1 1 1 1 0 1 0 1 1 ... 
      
- $ C03T2  : int  1 1 0 1 0 0 0 0 1 0 ... 
      
- $ C04T2  : int  0 0 1 0 0 0 0 1 0 0 ... 
      
- $ C05T2  : int  0 1 0 0 1 0 1 0 0 1 ... 
      
- $ D01T2  : int  0 1 1 1 0 1 1 1 1 1 ... 
      
- $ D02T2  : int  0 1 1 1 1 1 0 1 1 1 ... 
      
- $ D03T2  : int  1 0 0 0 1 0 0 0 0 0 ... 
      
- $ D04T2  : int  1 0 1 1 1 0 1 0 1 1 ... 
      
- $ D05T2  : int  1 0 1 1 1 1 1 1 1 1 ... 
      • 
+
      'data.frame':   1675 obs. of  42 variables: 
       $ idstud : num  100101 100102 100103 100104 100105 ... 
       $ idclass: num  1001 1001 1001 1001 1001 ... 
       $ A01T1  : int  0 1 0 1 1 NA 1 0 1 1 ... 
       $ A02T1  : int  0 1 0 1 0 NA 0 1 1 0 ... 
       $ A03T1  : int  0 1 1 1 0 NA 0 1 1 1 ... 
       $ A04T1  : int  1 0 0 0 0 NA 0 0 0 0 ... 
       $ A05T1  : int  0 0 0 1 1 NA 0 0 1 1 ... 
       $ B01T1  : int  1 1 0 1 1 NA 0 0 1 0 ... 
       $ B02T1  : int  0 0 0 1 0 NA 0 0 1 1 ... 
       [...] 
       $ C02T2  : int  0 1 1 1 1 0 1 0 1 1 ... 
       $ C03T2  : int  1 1 0 1 0 0 0 0 1 0 ... 
       $ C04T2  : int  0 0 1 0 0 0 0 1 0 0 ... 
       $ C05T2  : int  0 1 0 0 1 0 1 0 0 1 ... 
       $ D01T2  : int  0 1 1 1 0 1 1 1 1 1 ... 
       $ D02T2  : int  0 1 1 1 1 1 0 1 1 1 ... 
       $ D03T2  : int  1 0 0 0 1 0 0 0 0 0 ... 
       $ D04T2  : int  1 0 1 1 1 0 1 0 1 1 ... 
       $ D05T2  : int  1 0 1 1 1 1 1 1 1 1 ... 
      
 
    • The dataset data.ctest2 contains two datasets
 ($data1 containing item responses, $data2
 containing sum scores of each C-test) and
 a data frame $ITEM with item informations.
      
-
      List of 3 
      
- $ data1:'data.frame':  933 obs. of  102 variables: 
      
-  ..$ idstud: num [1:933] 10001 10002 10003 10004 10005 ... 
      
-  ..$ female: num [1:933] 1 1 0 0 0 0 1 1 0 1 ... 
      
-  ..$ A101  : int [1:933] NA NA NA NA NA NA NA NA NA NA ... 
      
-  ..$ A102  : int [1:933] NA NA NA NA NA NA NA NA NA NA ... 
      
-  ..$ A103  : int [1:933] NA NA NA NA NA NA NA NA NA NA ... 
      
-  ..$ A104  : int [1:933] NA NA NA NA NA NA NA NA NA NA ... 
      
-  ..$ A105  : int [1:933] NA NA NA NA NA NA NA NA NA NA ... 
      
-  ..$ A106  : int [1:933] NA NA NA NA NA NA NA NA NA NA ... 
      
-  ..$ E115  : int [1:933] NA NA NA NA NA NA NA NA NA NA ... 
      
-  ..$ E116  : int [1:933] NA NA NA NA NA NA NA NA NA NA ... 
      
-  ..$ E117  : int [1:933] NA NA NA NA NA NA NA NA NA NA ... 
      
-  .. [list output truncated] 
      
- $ data2:'data.frame':  933 obs. of  7 variables: 
      
-  ..$ idstud: num [1:933] 10001 10002 10003 10004 10005 ... 
      
-  ..$ female: num [1:933] 1 1 0 0 0 0 1 1 0 1 ... 
      
-  ..$ A     : num [1:933] NA NA NA NA NA NA NA NA NA NA ... 
      
-  ..$ B     : num [1:933] 16 14 15 13 17 11 11 18 19 13 ... 
      
-  ..$ C     : num [1:933] 17 15 17 14 17 13 9 15 17 12 ... 
      
-  ..$ D     : num [1:933] NA NA NA NA NA NA NA NA NA NA ... 
      
-  ..$ E     : num [1:933] NA NA NA NA NA NA NA NA NA NA ... 
      
- $ ITEM :'data.frame':  100 obs. of  3 variables: 
      
-  ..$ item   : chr [1:100] "A101" "A102" "A103" "A104" ... 
      
-  ..$ ctest  : chr [1:100] "A" "A" "A" "A" ... 
      
-  ..$ testlet: int [1:100] 1 1 2 2 2 3 3 3 NA 4 ... 
      • 
-
    
-
+
    List of 3 
     $ data1:'data.frame':  933 obs. of  102 variables: 
      ..$ idstud: num [1:933] 10001 10002 10003 10004 10005 ... 
      ..$ female: num [1:933] 1 1 0 0 0 0 1 1 0 1 ... 
      ..$ A101  : int [1:933] NA NA NA NA NA NA NA NA NA NA ... 
      ..$ A102  : int [1:933] NA NA NA NA NA NA NA NA NA NA ... 
      ..$ A103  : int [1:933] NA NA NA NA NA NA NA NA NA NA ... 
      ..$ A104  : int [1:933] NA NA NA NA NA NA NA NA NA NA ... 
      ..$ A105  : int [1:933] NA NA NA NA NA NA NA NA NA NA ... 
      ..$ A106  : int [1:933] NA NA NA NA NA NA NA NA NA NA ... 
      ..$ E115  : int [1:933] NA NA NA NA NA NA NA NA NA NA ... 
      ..$ E116  : int [1:933] NA NA NA NA NA NA NA NA NA NA ... 
      ..$ E117  : int [1:933] NA NA NA NA NA NA NA NA NA NA ... 
      .. [list output truncated] 
     $ data2:'data.frame':  933 obs. of  7 variables: 
      ..$ idstud: num [1:933] 10001 10002 10003 10004 10005 ... 
      ..$ female: num [1:933] 1 1 0 0 0 0 1 1 0 1 ... 
      ..$ A     : num [1:933] NA NA NA NA NA NA NA NA NA NA ... 
      ..$ B     : num [1:933] 16 14 15 13 17 11 11 18 19 13 ... 
      ..$ C     : num [1:933] 17 15 17 14 17 13 9 15 17 12 ... 
      ..$ D     : num [1:933] NA NA NA NA NA NA NA NA NA NA ... 
      ..$ E     : num [1:933] NA NA NA NA NA NA NA NA NA NA ... 
     $ ITEM :'data.frame':  100 obs. of  3 variables: 
      ..$ item   : chr [1:100] "A101" "A102" "A103" "A104" ... 
      ..$ ctest  : chr [1:100] "A" "A" "A" "A" ... 
      ..$ testlet: int [1:100] 1 1 2 2 2 3 3 3 NA 4 ... 
    • 
+

 
   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
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+  
 
+  
 
diff --git a/docs/reference/data.examples.html b/docs/reference/data.examples.html
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Datasets data.ex in TAM Package

     
Datasets included in the TAM package

     

 
-    
data(data.ex08)
-data(data.ex10)
-data(data.ex11)
-data(data.ex12)
-data(data.ex14)
-data(data.ex15)
-data(data.exJ03)

-
-
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Format

+    

+    
data(data.ex08)
+data(data.ex10)
+data(data.ex11)
+data(data.ex12)
+data(data.ex14)
+data(data.ex15)
+data(data.exJ03)

+    

 
+    

+    
Format

     
-
    
-
  • Data data.ex08 for Example 8 in tam.mml
+
    • Data data.ex08 for Example 8 in tam.mml
 has the following format:
      
-
      List of 2 
      
- $ facets:'data.frame': 1000 obs. of  1 variable: 
      
-  ..$ female: int [1:1000] 1 1 1 1 1 1 1 1 1 1 ... 
      
- $ resp  : num [1:1000, 1:10] 1 1 1 0 1 0 1 1 0 1 ... 
      
-  ..- attr(*, "dimnames")=List of 2 
      
-  .. ..$ : NULL 
      
-  .. ..$ : chr [1:10] "I0001" "I0002" "I0003" "I0004" ... 
      • 
-
    • Data data.ex10 for Example 10 in tam.mml
+
      List of 2 
       $ facets:'data.frame': 1000 obs. of  1 variable: 
        ..$ female: int [1:1000] 1 1 1 1 1 1 1 1 1 1 ... 
       $ resp  : num [1:1000, 1:10] 1 1 1 0 1 0 1 1 0 1 ... 
        ..- attr(*, "dimnames")=List of 2 
        .. ..$ : NULL 
        .. ..$ : chr [1:10] "I0001" "I0002" "I0003" "I0004" ... 
      • 
+
    • Data data.ex10 for Example 10 in tam.mml
 has the following format:
      
-
      'data.frame':   675 obs. of  7 variables: 
      
- $ pid  : int  1 1 1 2 2 3 3 4 4 5 ... 
      
- $ rater: int  1 2 3 2 3 1 2 1 3 1 ... 
      
- $ I0001: num  0 1 1 1 1 1 1 1 1 1 ... 
      
- $ I0002: num  1 1 1 1 1 0 1 1 1 1 ... 
      
- $ I0003: num  1 1 1 1 0 0 0 1 0 1 ... 
      
- $ I0004: num  0 1 0 0 1 0 1 0 1 0 ... 
      
- $ I0005: num  0 0 1 1 1 0 0 1 0 1 ... 
      
+
      'data.frame':   675 obs. of  7 variables: 
       $ pid  : int  1 1 1 2 2 3 3 4 4 5 ... 
       $ rater: int  1 2 3 2 3 1 2 1 3 1 ... 
       $ I0001: num  0 1 1 1 1 1 1 1 1 1 ... 
       $ I0002: num  1 1 1 1 1 0 1 1 1 1 ... 
       $ I0003: num  1 1 1 1 0 0 0 1 0 1 ... 
       $ I0004: num  0 1 0 0 1 0 1 0 1 0 ... 
       $ I0005: num  0 0 1 1 1 0 0 1 0 1 ... 
      
 
      • 
-
    • Data data.ex11 for Example 11 in tam.mml
+
    • Data data.ex11 for Example 11 in tam.mml
 has the following format:
      
-
      'data.frame':   3400 obs. of  13 variables: 
      
- $ booklet: chr  "B1" "B1" "B3" "B2" ... 
      
- $ M133   : int  1 1 NA 1 NA 1 NA 1 0 1 ... 
      
- $ M176   : int  1 0 1 NA 0 0 0 NA NA NA ... 
      
- $ M202   : int  NA NA NA 0 NA NA NA 0 0 0 ... 
      
- $ M212   : int  NA NA 1 0 0 NA 0 1 0 0 ... 
      
- $ M214   : int  1 0 1 1 0 0 0 0 1 0 ... 
      
- $ M259   : int  NA NA 1 1 1 NA 1 1 1 1 ... 
      
- $ M303   : int  NA NA 1 1 1 NA 1 1 1 0 ... 
      
- $ M353   : int  NA NA NA 1 NA NA NA 1 1 9 ... 
      
- $ M355   : int  NA NA NA 1 NA NA NA 1 1 0 ... 
      
- $ M444   : int  0 0 0 NA 0 0 0 NA NA NA ... 
      
- $ M446   : int  1 0 0 1 0 1 1 1 0 0 ... 
      
- $ M449   : int  NA NA NA 1 NA NA NA 1 1 1 ...
      
+
      'data.frame':   3400 obs. of  13 variables: 
       $ booklet: chr  "B1" "B1" "B3" "B2" ... 
       $ M133   : int  1 1 NA 1 NA 1 NA 1 0 1 ... 
       $ M176   : int  1 0 1 NA 0 0 0 NA NA NA ... 
       $ M202   : int  NA NA NA 0 NA NA NA 0 0 0 ... 
       $ M212   : int  NA NA 1 0 0 NA 0 1 0 0 ... 
       $ M214   : int  1 0 1 1 0 0 0 0 1 0 ... 
       $ M259   : int  NA NA 1 1 1 NA 1 1 1 1 ... 
       $ M303   : int  NA NA 1 1 1 NA 1 1 1 0 ... 
       $ M353   : int  NA NA NA 1 NA NA NA 1 1 9 ... 
       $ M355   : int  NA NA NA 1 NA NA NA 1 1 0 ... 
       $ M444   : int  0 0 0 NA 0 0 0 NA NA NA ... 
       $ M446   : int  1 0 0 1 0 1 1 1 0 0 ... 
       $ M449   : int  NA NA NA 1 NA NA NA 1 1 1 ...
      
 
      Missing responses by design are coded as NA, omitted
-responses are coded as 9. 
      
+responses are coded as 9. 
      
 
      • 
-
    • Data data.ex12 for Example 12 in tam.mml
+
    • Data data.ex12 for Example 12 in tam.mml
 has the following format:
      
-
       num [1:100, 1:10] 1 1 1 1 1 1 1 1 1 1 ... 
      
- - attr(*, "dimnames")=List of 2 
      
-  ..$ : NULL 
      
-  ..$ : chr [1:10] "I0001" "I0002" "I0003" "I0004" ... 
      
+
       num [1:100, 1:10] 1 1 1 1 1 1 1 1 1 1 ... 
       - attr(*, "dimnames")=List of 2 
        ..$ : NULL 
        ..$ : chr [1:10] "I0001" "I0002" "I0003" "I0004" ... 
      
 
      • 
-
    • Data data.ex14 for Example 14 in tam.mml
+
    • Data data.ex14 for Example 14 in tam.mml
 has the following format:
      
-
      'data.frame':   1110 obs. of  11 variables: 
      
- $ pid  : num  1001 1001 1001 1001 1001 ... 
      
- $ X1   : num  1 1 1 1 1 1 0 0 0 0 ... 
      
- $ X2   : int  1 1 1 1 1 1 1 1 1 1 ... 
      
- $ rater: int  4 4 4 4 4 4 4 4 4 4 ... 
      
- $ crit1: int  0 0 2 1 1 2 0 0 0 0 ... 
      
- $ crit2: int  0 0 0 0 0 0 0 0 0 0 ... 
      
- $ crit3: int  0 1 1 0 0 1 0 0 1 0 ... 
      
- $ crit4: int  0 0 0 1 0 0 0 0 0 0 ... 
      
- $ crit5: int  0 0 0 0 1 1 0 0 0 0 ... 
      
- $ crit6: int  0 0 0 0 1 0 0 0 0 0 ... 
      
- $ crit7: int  1 0 2 0 0 0 0 0 0 0 ... 
      
+
      'data.frame':   1110 obs. of  11 variables: 
       $ pid  : num  1001 1001 1001 1001 1001 ... 
       $ X1   : num  1 1 1 1 1 1 0 0 0 0 ... 
       $ X2   : int  1 1 1 1 1 1 1 1 1 1 ... 
       $ rater: int  4 4 4 4 4 4 4 4 4 4 ... 
       $ crit1: int  0 0 2 1 1 2 0 0 0 0 ... 
       $ crit2: int  0 0 0 0 0 0 0 0 0 0 ... 
       $ crit3: int  0 1 1 0 0 1 0 0 1 0 ... 
       $ crit4: int  0 0 0 1 0 0 0 0 0 0 ... 
       $ crit5: int  0 0 0 0 1 1 0 0 0 0 ... 
       $ crit6: int  0 0 0 0 1 0 0 0 0 0 ... 
       $ crit7: int  1 0 2 0 0 0 0 0 0 0 ... 
      
 
      • 
-
    • Data data.ex15 for Example 15 in tam.mml
+
    • Data data.ex15 for Example 15 in tam.mml
 has the following format:
      
-
      'data.frame':   2155 obs. of  182 variables: 
      
- $ pid    : num  10001 10002 10003 10004 10005 ... 
      
- $ group  : num  1 1 0 0 1 0 1 0 1 1 ... 
      
- $ Item001: num  0 NA NA 0 NA NA NA 0 0 NA ... 
      
- $ Item002: num  1 NA NA 1 NA NA NA NA 1 NA ... 
      
- $ Item003: num  NA NA NA NA 1 NA NA NA NA 1 ... 
      
- $ Item004: num  NA NA 0 NA NA NA NA NA NA NA ... 
      
- $ Item005: num  NA NA 1 NA NA NA NA NA NA NA ... 
      
-[...]
      
+
      'data.frame':   2155 obs. of  182 variables: 
       $ pid    : num  10001 10002 10003 10004 10005 ... 
       $ group  : num  1 1 0 0 1 0 1 0 1 1 ... 
       $ Item001: num  0 NA NA 0 NA NA NA 0 0 NA ... 
       $ Item002: num  1 NA NA 1 NA NA NA NA 1 NA ... 
       $ Item003: num  NA NA NA NA 1 NA NA NA NA 1 ... 
       $ Item004: num  NA NA 0 NA NA NA NA NA NA NA ... 
       $ Item005: num  NA NA 1 NA NA NA NA NA NA NA ... 
      [...]
      
 
      This dataset shows an atypical convergence behavior. Look at Example 15
 to fix convergence problems using arguments increment.factor and
-fac.oldxsi. 
      
+fac.oldxsi. 
      
 
      • 
-
    • Data data.exJ03 for Example 4 in tam.jml
+
    • Data data.exJ03 for Example 4 in tam.jml
 has the following format:
      
-
      List of 2 
      
- $ resp:'data.frame':   40 obs. of  20 variables: 
      
-  ..$ I104: int [1:40] 4 5 6 5 3 4 3 5 4 6 ... 
      
-  ..$ I118: int [1:40] 6 4 6 5 3 2 5 3 5 4 ... 
      
-[...]
-  ..$ I326: int [1:40] 6 1 5 1 4 2 4 1 6 1 ... 
      
-  ..$ I338: int [1:40] 6 2 6 1 6 2 4 1 6 1 ... 
      
- $ X   :'data.frame':   40 obs. of  4 variables: 
      
-  ..$ rater : int [1:40] 40 40 96 96 123 123 157 157 164 164 ... 
      
-  ..$ gender: int [1:40] 2 2 1 1 1 1 2 2 2 2 ... 
      
-  ..$ region: num [1:40] 1 1 1 1 2 2 1 1 1 1 ... 
      
-  ..$ leader: int [1:40] 1 2 1 2 1 2 1 2 1 2 ...
      
-
      It is a rating dataset (a subset of a dataset provided by Matt Barney). 
      
+
      List of 2 
       $ resp:'data.frame':   40 obs. of  20 variables: 
        ..$ I104: int [1:40] 4 5 6 5 3 4 3 5 4 6 ... 
        ..$ I118: int [1:40] 6 4 6 5 3 2 5 3 5 4 ... 
      [...]
+  ..$ I326: int [1:40] 6 1 5 1 4 2 4 1 6 1 ... 
        ..$ I338: int [1:40] 6 2 6 1 6 2 4 1 6 1 ... 
       $ X   :'data.frame':   40 obs. of  4 variables: 
        ..$ rater : int [1:40] 40 40 96 96 123 123 157 157 164 164 ... 
        ..$ gender: int [1:40] 2 2 1 1 1 1 2 2 2 2 ... 
        ..$ region: num [1:40] 1 1 1 1 2 2 1 1 1 1 ... 
        ..$ leader: int [1:40] 1 2 1 2 1 2 1 2 1 2 ...
      
+
      It is a rating dataset (a subset of a dataset provided by Matt Barney). 
      
 
      • 
 
    • Data data.ex16 contains dichotomous item response data from
 three studies corresponding to three grades.
      
-
      'data.frame':   3235 obs. of  25 variables: 
      
- $ idstud: num  1e+05 1e+05 1e+05 1e+05 1e+05 ... 
      
- $ grade : num  1 1 1 1 1 1 1 1 1 1 ... 
      
- $ A1    : int  1 1 1 1 1 1 1 1 1 1 ... 
      
- $ B1    : int  1 1 1 1 1 1 1 1 1 1 ... 
      
- $ C1    : int  1 1 1 1 1 1 1 1 1 1 ... 
      
- $ D1    : int  1 1 1 1 1 1 1 1 1 1 ... 
      
- $ E1    : int  0 0 1 0 1 1 1 0 1 1 ... 
      
- $ E2    : int  1 1 1 1 1 1 1 0 1 1 ... 
      
- $ E3    : int  1 1 1 1 1 1 1 0 1 1 ... 
      
- $ F1    : int  1 0 1 1 0 0 1 0 1 1 ... 
      
- $ G1    : int  0 1 1 1 1 0 1 0 1 1 ... 
      
- $ G2    : int  1 1 1 1 1 0 0 0 1 1 ... 
      
- $ G3    : int  1 0 1 1 1 0 0 0 1 1 ... 
      
- $ H1    : int  1 0 1 1 1 0 0 0 1 1 ... 
      
- $ H2    : int  1 0 1 1 1 0 0 0 1 1 ... 
      
- $ I1    : int  1 0 1 0 1 0 0 0 1 1 ... 
      
- $ I2    : int  1 0 1 0 1 0 0 0 1 1 ... 
      
- $ J1    : int  NA NA NA NA NA NA NA NA NA NA ... 
      
- $ K1    : int  NA NA NA NA NA NA NA NA NA NA ... 
      
- $ L1    : int  NA NA NA NA NA NA NA NA NA NA ... 
      
- $ L2    : int  NA NA NA NA NA NA NA NA NA NA ... 
      
- $ L3    : int  NA NA NA NA NA NA NA NA NA NA ... 
      
- $ M1    : int  NA NA NA NA NA NA NA NA NA NA ... 
      
- $ M2    : int  NA NA NA NA NA NA NA NA NA NA ... 
      
- $ M3    : int  NA NA NA NA NA NA NA NA NA NA ... 
      
+
      'data.frame':   3235 obs. of  25 variables: 
       $ idstud: num  1e+05 1e+05 1e+05 1e+05 1e+05 ... 
       $ grade : num  1 1 1 1 1 1 1 1 1 1 ... 
       $ A1    : int  1 1 1 1 1 1 1 1 1 1 ... 
       $ B1    : int  1 1 1 1 1 1 1 1 1 1 ... 
       $ C1    : int  1 1 1 1 1 1 1 1 1 1 ... 
       $ D1    : int  1 1 1 1 1 1 1 1 1 1 ... 
       $ E1    : int  0 0 1 0 1 1 1 0 1 1 ... 
       $ E2    : int  1 1 1 1 1 1 1 0 1 1 ... 
       $ E3    : int  1 1 1 1 1 1 1 0 1 1 ... 
       $ F1    : int  1 0 1 1 0 0 1 0 1 1 ... 
       $ G1    : int  0 1 1 1 1 0 1 0 1 1 ... 
       $ G2    : int  1 1 1 1 1 0 0 0 1 1 ... 
       $ G3    : int  1 0 1 1 1 0 0 0 1 1 ... 
       $ H1    : int  1 0 1 1 1 0 0 0 1 1 ... 
       $ H2    : int  1 0 1 1 1 0 0 0 1 1 ... 
       $ I1    : int  1 0 1 0 1 0 0 0 1 1 ... 
       $ I2    : int  1 0 1 0 1 0 0 0 1 1 ... 
       $ J1    : int  NA NA NA NA NA NA NA NA NA NA ... 
       $ K1    : int  NA NA NA NA NA NA NA NA NA NA ... 
       $ L1    : int  NA NA NA NA NA NA NA NA NA NA ... 
       $ L2    : int  NA NA NA NA NA NA NA NA NA NA ... 
       $ L3    : int  NA NA NA NA NA NA NA NA NA NA ... 
       $ M1    : int  NA NA NA NA NA NA NA NA NA NA ... 
       $ M2    : int  NA NA NA NA NA NA NA NA NA NA ... 
       $ M3    : int  NA NA NA NA NA NA NA NA NA NA ... 
      
 
 
      • 
 
    • Data data.ex17 contains polytomous item response data from
 three studies corresponding to three grades.
      
-
      'data.frame':   3235 obs. of  15 variables: 
      
- $ idstud: num  1e+05 1e+05 1e+05 1e+05 1e+05 ... 
      
- $ grade : num  1 1 1 1 1 1 1 1 1 1 ... 
      
- $ A     : int  1 1 1 1 1 1 1 1 1 1 ... 
      
- $ B     : int  1 1 1 1 1 1 1 1 1 1 ... 
      
- $ C     : int  1 1 1 1 1 1 1 1 1 1 ... 
      
- $ D     : int  1 1 1 1 1 1 1 1 1 1 ... 
      
- $ E     : num  2 2 3 2 3 3 3 0 3 3 ... 
      
- $ F     : int  1 0 1 1 0 0 1 0 1 1 ... 
      
- $ G     : num  2 2 3 3 3 0 1 0 3 3 ... 
      
- $ H     : num  2 0 2 2 2 0 0 0 2 2 ... 
      
- $ I     : num  2 0 2 0 2 0 0 0 2 2 ... 
      
- $ J     : int  NA NA NA NA NA NA NA NA NA NA ... 
      
- $ K     : int  NA NA NA NA NA NA NA NA NA NA ... 
      
- $ L     : num  NA NA NA NA NA NA NA NA NA NA ... 
      
- $ M     : num  NA NA NA NA NA NA NA NA NA NA ... 
      • 
+
      'data.frame':   3235 obs. of  15 variables: 
       $ idstud: num  1e+05 1e+05 1e+05 1e+05 1e+05 ... 
       $ grade : num  1 1 1 1 1 1 1 1 1 1 ... 
       $ A     : int  1 1 1 1 1 1 1 1 1 1 ... 
       $ B     : int  1 1 1 1 1 1 1 1 1 1 ... 
       $ C     : int  1 1 1 1 1 1 1 1 1 1 ... 
       $ D     : int  1 1 1 1 1 1 1 1 1 1 ... 
       $ E     : num  2 2 3 2 3 3 3 0 3 3 ... 
       $ F     : int  1 0 1 1 0 0 1 0 1 1 ... 
       $ G     : num  2 2 3 3 3 0 1 0 3 3 ... 
       $ H     : num  2 0 2 2 2 0 0 0 2 2 ... 
       $ I     : num  2 0 2 0 2 0 0 0 2 2 ... 
       $ J     : int  NA NA NA NA NA NA NA NA NA NA ... 
       $ K     : int  NA NA NA NA NA NA NA NA NA NA ... 
       $ L     : num  NA NA NA NA NA NA NA NA NA NA ... 
       $ M     : num  NA NA NA NA NA NA NA NA NA NA ... 
      
 
    
-    
    See also
    
-
-    
    These examples are used in the tam.mml Examples.
    
+    

+    

+    
See also

+    
These examples are used in the tam.mml Examples.

+    

 
   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/reference/data.fims.Aus.Jpn.html b/docs/reference/data.fims.Aus.Jpn.html
index 2a61826..1dc9f3b 100644
--- a/docs/reference/data.fims.Aus.Jpn.html
+++ b/docs/reference/data.fims.Aus.Jpn.html
@@ -1,69 +1,14 @@
-
 
-
-  
-  
-
-
-
-Dataset FIMS Study with Responses of Australian and Japanese Students — data.fims.Aus.Jpn.scored • TAM
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-Dataset FIMS Study with Responses of Australian and Japanese Students — data.fims.Aus.Jpn.scored • TAM
-
-
-
-
-
-
-
-
-
-
-
-
-  
+
+    
 
-  
     

-      

-      
 
       
 
-      

-
-

+      

   

     

     
Dataset FIMS Study with Responses of Australian and Japanese Students

@@ -121,102 +53,132 @@ 
Dataset FIMS Study with Responses of Australian and Japanese Students

 Japanese Students.

     

 
-    
data(data.fims.Aus.Jpn.raw)
-data(data.fims.Aus.Jpn.scored)

-
-
-    
Format

-
-    
A data frame with 6371 observations on the following 16 variables.

-    
SEX
Gender: 1 -- male, 2 -- female

-    
M1PTI1
A Mathematics item

-    
M1PTI2
A Mathematics item

-    
M1PTI3
A Mathematics item

-    
M1PTI6
A Mathematics item

-    
M1PTI7
A Mathematics item

-    
M1PTI11
A Mathematics item

-    
M1PTI12
A Mathematics item

-    
M1PTI14
A Mathematics item

-    
M1PTI17
A Mathematics item

-    
M1PTI18
A Mathematics item

-    
M1PTI19
A Mathematics item

-    
M1PTI21
A Mathematics item

-    
M1PTI22
A Mathematics item

-    
M1PTI23
A Mathematics item

-    
country
Country: 1 -- Australia, 2 -- Japan

+    

+    
data(data.fims.Aus.Jpn.raw)
+data(data.fims.Aus.Jpn.scored)

+    

+
+    

+    
Format

+    
A data frame with 6371 observations on the following 16 variables.
SEX

+
Gender: 1 -- male, 2 -- female

+
+    
M1PTI1

+
A Mathematics item

+
+    
M1PTI2

+
A Mathematics item

+
+    
M1PTI3

+
A Mathematics item

+
+    
M1PTI6

+
A Mathematics item

+
+    
M1PTI7

+
A Mathematics item

+
+    
M1PTI11

+
A Mathematics item

+
+    
M1PTI12

+
A Mathematics item

+
+    
M1PTI14

+
A Mathematics item

+
+    
M1PTI17

+
A Mathematics item

+
+    
M1PTI18

+
A Mathematics item

+
+    
M1PTI19

+
A Mathematics item

+
+    
M1PTI21

+
A Mathematics item

+
+    
M1PTI22

+
A Mathematics item

+
+    
M1PTI23

+
A Mathematics item

+
+    
country

+
Country: 1 -- Australia, 2 -- Japan

+
   
-

-
-    
See also

-
-    
http://www.edmeasurementsurveys.com/TAM/Tutorials/7DIF.htm

-
-    
Examples

-    
if (FALSE) {
-data(data.fims.Aus.Jpn.scored)
-#*****
-# Model 1: Differential Item Functioning Gender for Australian students
-
-# extract Australian students
-scored <- data.fims.Aus.Jpn.scored[ data.fims.Aus.Jpn.scored$country==1, ]
-
-# select items
-items <- grep("M1", colnames(data.fims.Aus.Jpn.scored), value=TRUE)
-##   > items
-##    [1] "M1PTI1"  "M1PTI2"  "M1PTI3"  "M1PTI6"  "M1PTI7"  "M1PTI11" "M1PTI12"
-##    [8] "M1PTI14" "M1PTI17" "M1PTI18" "M1PTI19" "M1PTI21" "M1PTI22" "M1PTI23"
-
-# Run partial credit model
-mod1 <- TAM::tam.mml(scored[,items])
-
-# extract values of the gender variable into a variable called "gender".
-gender <- scored[,"SEX"]
-# computes the test score for each student by calculating the row sum
-# of each student's scored responses.
-raw_score <- rowSums(scored[,items] )
-
-# compute the mean test score for each gender group: 1=male, and 2=female
-stats::aggregate(raw_score,by=list(gender),FUN=mean)
-# The mean test score is 6.12 for group 1 (males) and 6.27 for group 2 (females).
-# That is, the two groups performed similarly, with girls having a slightly
-# higher mean test score. The step of computing raw test scores is not necessary
-# for the IRT analyses. But it's always a good practice to explore the data
-# a little before delving into more complex analyses.
-
-# Facets analysis
-# To conduct a DIF analysis, we set up the variable "gender" as a facet and
-# re-run the IRT analysis.
-formulaA <- ~item+gender+item*gender    # define facets analysis
-facets <- as.data.frame(gender)         # data frame with student covariates
-# facets model for studying differential item functioning
-mod2 <- TAM::tam.mml.mfr( resp=scored[,items], facets=facets, formulaA=formulaA )
-summary(mod2)
-}

+

+    
+
+    

+    
Examples

+    
if (FALSE) {
+data(data.fims.Aus.Jpn.scored)
+#*****
+# Model 1: Differential Item Functioning Gender for Australian students
+
+# extract Australian students
+scored <- data.fims.Aus.Jpn.scored[ data.fims.Aus.Jpn.scored$country==1, ]
+
+# select items
+items <- grep("M1", colnames(data.fims.Aus.Jpn.scored), value=TRUE)
+##   > items
+##    [1] "M1PTI1"  "M1PTI2"  "M1PTI3"  "M1PTI6"  "M1PTI7"  "M1PTI11" "M1PTI12"
+##    [8] "M1PTI14" "M1PTI17" "M1PTI18" "M1PTI19" "M1PTI21" "M1PTI22" "M1PTI23"
+
+# Run partial credit model
+mod1 <- TAM::tam.mml(scored[,items])
+
+# extract values of the gender variable into a variable called "gender".
+gender <- scored[,"SEX"]
+# computes the test score for each student by calculating the row sum
+# of each student's scored responses.
+raw_score <- rowSums(scored[,items] )
+
+# compute the mean test score for each gender group: 1=male, and 2=female
+stats::aggregate(raw_score,by=list(gender),FUN=mean)
+# The mean test score is 6.12 for group 1 (males) and 6.27 for group 2 (females).
+# That is, the two groups performed similarly, with girls having a slightly
+# higher mean test score. The step of computing raw test scores is not necessary
+# for the IRT analyses. But it's always a good practice to explore the data
+# a little before delving into more complex analyses.
+
+# Facets analysis
+# To conduct a DIF analysis, we set up the variable "gender" as a facet and
+# re-run the IRT analysis.
+formulaA <- ~item+gender+item*gender    # define facets analysis
+facets <- as.data.frame(gender)         # data frame with student covariates
+# facets model for studying differential item functioning
+mod2 <- TAM::tam.mml.mfr( resp=scored[,items], facets=facets, formulaA=formulaA )
+summary(mod2)
+}

+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/reference/data.geiser.html b/docs/reference/data.geiser.html
index 472a515..4f94774 100644
--- a/docs/reference/data.geiser.html
+++ b/docs/reference/data.geiser.html
@@ -1,68 +1,13 @@
-
 
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-Dataset from Geiser et al. (2006) — data.geiser • TAM
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Dataset from Geiser et al. (2006)

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Dataset from Geiser et al. (2006)

 Geiser and Eid (2010).

     

 
-    
data(data.geiser)

-
-
-    
Format

+    

+    
data(data.geiser)

+    

 
+    

+    
Format

     
A data frame with 519 observations on the following 24 variables

-
'data.frame':   519 obs. of  24 variables: 

- $ mrt1 : num  0 0 0 0 0 0 0 0 0 0 ... 

- $ mrt2 : num  0 0 0 0 0 0 0 0 0 0 ... 

- $ mrt3 : num  0 0 0 0 0 0 0 0 1 0 ... 

- $ mrt4 : num  0 0 0 0 0 1 0 0 0 0 ... 

-[...] 

- $ mrt23: num  0 0 0 0 0 0 0 1 0 0 ... 

- $ mrt24: num  0 0 0 0 0 0 0 0 0 0 ... 

-    
References

-
+
'data.frame':   519 obs. of  24 variables: 
 $ mrt1 : num  0 0 0 0 0 0 0 0 0 0 ... 
 $ mrt2 : num  0 0 0 0 0 0 0 0 0 0 ... 
 $ mrt3 : num  0 0 0 0 0 0 0 0 1 0 ... 
 $ mrt4 : num  0 0 0 0 0 1 0 0 0 0 ... 
[...] 
 $ mrt23: num  0 0 0 0 0 0 0 1 0 0 ... 
 $ mrt24: num  0 0 0 0 0 0 0 0 0 0 ... 

+    

+    

+    
References

     
Geiser, C., & Eid, M. (2010). Item-Response-Theorie.
 In C. Wolf & H. Best (Hrsg.). Handbuch der sozialwissenschaftlichen
 Datenanalyse (S. 311-332). VS Verlag fuer Sozialwissenschaften.

 
Geiser, C., Lehmann, W., & Eid, M. (2006). Separating rotators from
 nonrotators in the mental rotations test: A multigroup latent class analysis.
 Multivariate Behavioral Research, 41(3), 261-293.
-doi: 10.1207/s15327906mbr4103_2

-
-    
Examples

-    
if (FALSE) {
-#############################################################################
-# EXAMPLE 1: Latent trait and latent class models (Geiser et al., 2006, MBR)
-#############################################################################
-
-data(data.geiser)
-dat <- data.geiser
-
-#**********************************************
-# Model 1: Rasch model
-tammodel <- "
-  LAVAAN MODEL:
-    F=~ 1*mrt1__mrt12
-    F ~~ F
-  ITEM TYPE:
-    ALL(Rasch)
-    "
-mod1 <- TAM::tamaan( tammodel, dat)
-summary(mod1)
-
-#**********************************************
-# Model 2: 2PL model
-tammodel <- "
-  LAVAAN MODEL:
-    F=~ mrt1__mrt12
-    F ~~ 1*F
-    "
-mod2 <- TAM::tamaan( tammodel, dat)
-summary(mod2)
-
-# model comparison Rasch vs. 2PL
-anova(mod1,mod2)
-
-#*********************************************************************
-#*** Model 3: Latent class analysis with four classes
-
-tammodel <- "
-ANALYSIS:
-  TYPE=LCA;
-  NCLASSES(4);   # 4 classes
-  NSTARTS(10,20); # 10 random starts with 20 iterations
-LAVAAN MODEL:
-  F=~ mrt1__mrt12
-    "
-mod3 <- TAM::tamaan( tammodel, resp=dat  )
-summary(mod3)
-
-# extract item response functions
-imod2 <- IRT.irfprob(mod3)[,2,]
-# plot class specific probabilities
-matplot( imod2, type="o", pch=1:4, xlab="Item", ylab="Probability" )
-legend( 10,1, paste0("Class",1:4), lty=1:4, col=1:4, pch=1:4 )
-
-#*********************************************************************
-#*** Model 4: Latent class analysis with five classes
-
-tammodel <- "
-ANALYSIS:
-  TYPE=LCA;
-  NCLASSES(5);
-  NSTARTS(10,20);
-LAVAAN MODEL:
-  F=~ mrt1__mrt12
-    "
-mod4 <- TAM::tamaan( tammodel, resp=dat )
-summary(mod4)
-
-# compare different models
-AIC(mod1); AIC(mod2); AIC(mod3); AIC(mod4)
-BIC(mod1); BIC(mod2); BIC(mod3); BIC(mod4)
-# more condensed form
-IRT.compareModels(mod1, mod2, mod3, mod4)
-
-#############################################################################
-# EXAMPLE 2: Rasch model and mixture Rasch model (Geiser & Eid, 2010)
-#############################################################################
-
-data(data.geiser)
-dat <- data.geiser
-
-#*********************************************************************
-#*** Model 1: Rasch model
-tammodel <- "
-LAVAAN MODEL:
-  F=~ mrt1__mrt6
-  F ~~ F
-ITEM TYPE:
-  ALL(Rasch);
-    "
-mod1 <- TAM::tamaan( tammodel, resp=dat  )
-summary(mod1)
-
-#*********************************************************************
-#*** Model 2: Mixed Rasch model with two classes
-tammodel <- "
-ANALYSIS:
-  TYPE=MIXTURE ;
-  NCLASSES(2);
-  NSTARTS(20,25);
-LAVAAN MODEL:
-  F=~ mrt1__mrt6
-  F ~~ F
-ITEM TYPE:
-  ALL(Rasch);
-    "
-mod2 <- TAM::tamaan( tammodel, resp=dat  )
-summary(mod2)
-
-# plot item parameters
-ipars <- mod2$itempartable_MIXTURE[ 1:6, ]
-plot( 1:6, ipars[,3], type="o", ylim=c(-3,2), pch=16,
-        xlab="Item", ylab="Item difficulty")
-lines( 1:6, ipars[,4], type="l", col=2, lty=2)
-points( 1:6, ipars[,4],  col=2, pch=2)
-
-# extract individual posterior distribution
-post2 <- IRT.posterior(mod2)
-str(post2)
-# num [1:519, 1:30] 0.000105 0.000105 0.000105 0.000105 0.000105 ...
-# - attr(*, "theta")=num [1:30, 1:30] 1 0 0 0 0 0 0 0 0 0 ...
-# - attr(*, "prob.theta")=num [1:30, 1] 1.21e-05 2.20e-04 2.29e-03 1.37e-02 4.68e-02 ...
-# - attr(*, "G")=num 1
-
-# There are 2 classes and 15 theta grid points for each class
-# The loadings of the theta grid on items are as follows
-mod2$E[1,2,,"mrt1_F_load_Cl1"]
-mod2$E[1,2,,"mrt1_F_load_Cl2"]
-
-# compute individual posterior probability for class 1 (first 15 columns)
-round( rowSums( post2[, 1:15] ), 3 )
-# columns 16 to 30 refer to class 2
-
-#*********************************************************************
-#*** Model 3: Mixed Rasch model with three classes
-tammodel <- "
-ANALYSIS:
-  TYPE=MIXTURE ;
-  NCLASSES(3);
-  NSTARTS(20,25);
-LAVAAN MODEL:
-  F=~ mrt1__mrt6
-  F ~~ F
-ITEM TYPE:
-  ALL(Rasch);
-    "
-mod3 <- TAM::tamaan( tammodel, resp=dat  )
-summary(mod3)
-
-# plot item parameters
-ipars <- mod3$itempartable_MIXTURE[ 1:6, ]
-plot( 1:6, ipars[,3], type="o", ylim=c(-3.7,2), pch=16,
-        xlab="Item", ylab="Item difficulty")
-lines( 1:6, ipars[,4], type="l", col=2, lty=2)
-points( 1:6, ipars[,4],  col=2, pch=2)
-lines( 1:6, ipars[,5], type="l", col=3, lty=3)
-points( 1:6, ipars[,5],  col=3, pch=17)
+doi:10.1207/s15327906mbr4103_2

+    

 
-# model comparison
-IRT.compareModels( mod1, mod2, mod3 )
-}
+    

+    
Examples

+    
if (FALSE) {
+#############################################################################
+# EXAMPLE 1: Latent trait and latent class models (Geiser et al., 2006, MBR)
+#############################################################################
+
+data(data.geiser)
+dat <- data.geiser
+
+#**********************************************
+# Model 1: Rasch model
+tammodel <- "
+  LAVAAN MODEL:
+    F=~ 1*mrt1__mrt12
+    F ~~ F
+  ITEM TYPE:
+    ALL(Rasch)
+    "
+mod1 <- TAM::tamaan( tammodel, dat)
+summary(mod1)
+
+#**********************************************
+# Model 2: 2PL model
+tammodel <- "
+  LAVAAN MODEL:
+    F=~ mrt1__mrt12
+    F ~~ 1*F
+    "
+mod2 <- TAM::tamaan( tammodel, dat)
+summary(mod2)
+
+# model comparison Rasch vs. 2PL
+anova(mod1,mod2)
+
+#*********************************************************************
+#*** Model 3: Latent class analysis with four classes
+
+tammodel <- "
+ANALYSIS:
+  TYPE=LCA;
+  NCLASSES(4);   # 4 classes
+  NSTARTS(10,20); # 10 random starts with 20 iterations
+LAVAAN MODEL:
+  F=~ mrt1__mrt12
+    "
+mod3 <- TAM::tamaan( tammodel, resp=dat  )
+summary(mod3)
+
+# extract item response functions
+imod2 <- IRT.irfprob(mod3)[,2,]
+# plot class specific probabilities
+matplot( imod2, type="o", pch=1:4, xlab="Item", ylab="Probability" )
+legend( 10,1, paste0("Class",1:4), lty=1:4, col=1:4, pch=1:4 )
+
+#*********************************************************************
+#*** Model 4: Latent class analysis with five classes
+
+tammodel <- "
+ANALYSIS:
+  TYPE=LCA;
+  NCLASSES(5);
+  NSTARTS(10,20);
+LAVAAN MODEL:
+  F=~ mrt1__mrt12
+    "
+mod4 <- TAM::tamaan( tammodel, resp=dat )
+summary(mod4)
+
+# compare different models
+AIC(mod1); AIC(mod2); AIC(mod3); AIC(mod4)
+BIC(mod1); BIC(mod2); BIC(mod3); BIC(mod4)
+# more condensed form
+IRT.compareModels(mod1, mod2, mod3, mod4)
+
+#############################################################################
+# EXAMPLE 2: Rasch model and mixture Rasch model (Geiser & Eid, 2010)
+#############################################################################
+
+data(data.geiser)
+dat <- data.geiser
+
+#*********************************************************************
+#*** Model 1: Rasch model
+tammodel <- "
+LAVAAN MODEL:
+  F=~ mrt1__mrt6
+  F ~~ F
+ITEM TYPE:
+  ALL(Rasch);
+    "
+mod1 <- TAM::tamaan( tammodel, resp=dat  )
+summary(mod1)
+
+#*********************************************************************
+#*** Model 2: Mixed Rasch model with two classes
+tammodel <- "
+ANALYSIS:
+  TYPE=MIXTURE ;
+  NCLASSES(2);
+  NSTARTS(20,25);
+LAVAAN MODEL:
+  F=~ mrt1__mrt6
+  F ~~ F
+ITEM TYPE:
+  ALL(Rasch);
+    "
+mod2 <- TAM::tamaan( tammodel, resp=dat  )
+summary(mod2)
+
+# plot item parameters
+ipars <- mod2$itempartable_MIXTURE[ 1:6, ]
+plot( 1:6, ipars[,3], type="o", ylim=c(-3,2), pch=16,
+        xlab="Item", ylab="Item difficulty")
+lines( 1:6, ipars[,4], type="l", col=2, lty=2)
+points( 1:6, ipars[,4],  col=2, pch=2)
+
+# extract individual posterior distribution
+post2 <- IRT.posterior(mod2)
+str(post2)
+# num [1:519, 1:30] 0.000105 0.000105 0.000105 0.000105 0.000105 ...
+# - attr(*, "theta")=num [1:30, 1:30] 1 0 0 0 0 0 0 0 0 0 ...
+# - attr(*, "prob.theta")=num [1:30, 1] 1.21e-05 2.20e-04 2.29e-03 1.37e-02 4.68e-02 ...
+# - attr(*, "G")=num 1
+
+# There are 2 classes and 15 theta grid points for each class
+# The loadings of the theta grid on items are as follows
+mod2$E[1,2,,"mrt1_F_load_Cl1"]
+mod2$E[1,2,,"mrt1_F_load_Cl2"]
+
+# compute individual posterior probability for class 1 (first 15 columns)
+round( rowSums( post2[, 1:15] ), 3 )
+# columns 16 to 30 refer to class 2
+
+#*********************************************************************
+#*** Model 3: Mixed Rasch model with three classes
+tammodel <- "
+ANALYSIS:
+  TYPE=MIXTURE ;
+  NCLASSES(3);
+  NSTARTS(20,25);
+LAVAAN MODEL:
+  F=~ mrt1__mrt6
+  F ~~ F
+ITEM TYPE:
+  ALL(Rasch);
+    "
+mod3 <- TAM::tamaan( tammodel, resp=dat  )
+summary(mod3)
+
+# plot item parameters
+ipars <- mod3$itempartable_MIXTURE[ 1:6, ]
+plot( 1:6, ipars[,3], type="o", ylim=c(-3.7,2), pch=16,
+        xlab="Item", ylab="Item difficulty")
+lines( 1:6, ipars[,4], type="l", col=2, lty=2)
+points( 1:6, ipars[,4],  col=2, pch=2)
+lines( 1:6, ipars[,5], type="l", col=3, lty=3)
+points( 1:6, ipars[,5],  col=3, pch=17)
+
+# model comparison
+IRT.compareModels( mod1, mod2, mod3 )
+}

+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
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+  
 
+  
 
diff --git a/docs/reference/data.gpcm.html b/docs/reference/data.gpcm.html
index dfe5b6c..a50da05 100644
--- a/docs/reference/data.gpcm.html
+++ b/docs/reference/data.gpcm.html
@@ -1,67 +1,12 @@
-
 
-
-  
-  
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-
-Dataset with Ordered Indicators — data.gpcm • TAM
-
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-Dataset with Ordered Indicators — data.gpcm • TAM
-
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+    
 
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+      

   

     

     
Dataset with Ordered Indicators

@@ -117,50 +49,54 @@ 
Dataset with Ordered Indicators

     
Dataset with ordered values of 3 indicators

     

 
-    
data(data.gpcm)

+    

+    
data(data.gpcm)

+    

 
+    

+    
Format

+    
A data frame with 392 observations on the following 3 items.
Comfort

+
a numeric vector

 
-    
Format

+    
Work

+
a numeric vector

 
-    
A data frame with 392 observations on the following 3 items.

-    
Comfort
a numeric vector

-    
Work
a numeric vector

-    
Benefit
a numeric vector

-  
-

-
-    
Source

+    
Benefit

+
a numeric vector

 
+  
+

+    

+    
Source

     
The dataset is copied from the ltm package.

+    

 
-    
Examples

-    
data(data.gpcm)
-summary(data.gpcm)

+    

+    
Examples

+    
data(data.gpcm)
+summary(data.gpcm)

+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/reference/data.janssen.html b/docs/reference/data.janssen.html
index f8377a0..ee16f98 100644
--- a/docs/reference/data.janssen.html
+++ b/docs/reference/data.janssen.html
@@ -1,67 +1,12 @@
-
 
-
-  
-  
-
-
-
-Dataset from Janssen and Geiser (2010) — data.janssen • TAM
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-Dataset from Janssen and Geiser (2010) — data.janssen • TAM
-
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Dataset from Janssen and Geiser (2010)

@@ -117,124 +49,109 @@ 
Dataset from Janssen and Geiser (2010)

     
Dataset used in Janssen and Geiser (2010).

     

 
-    
data(data.janssen)
-data(data.janssen2)

-
-
-    
Format

+    

+    
data(data.janssen)
+data(data.janssen2)

+    

 
+    

+    
Format

     
-
    
-
  • data.janssen is a data frame with 346 observations on the 8
+
    • data.janssen is a data frame with 346 observations on the 8
 items of the following format
      
-
      'data.frame':   346 obs. of  8 variables: 
      
- $ PIS1 : num  1 1 1 0 0 1 1 1 0 1 ... 
      
- $ PIS3 : num  0 1 1 1 1 1 0 1 1 1 ... 
      
- $ PIS4 : num  1 1 1 1 1 1 1 1 1 1 ... 
      
- $ PIS5 : num  0 1 1 0 1 1 1 1 1 0 ... 
      
- $ SCR6 : num  1 1 1 1 1 1 1 1 1 0 ... 
      
- $ SCR9 : num  1 1 1 1 0 0 0 1 0 0 ... 
      
- $ SCR10: num  0 0 0 0 0 0 0 0 0 0 ... 
      
- $ SCR17: num  0 0 0 0 0 1 0 0 0 0 ... 
      • 
+
      'data.frame':   346 obs. of  8 variables: 
       $ PIS1 : num  1 1 1 0 0 1 1 1 0 1 ... 
       $ PIS3 : num  0 1 1 1 1 1 0 1 1 1 ... 
       $ PIS4 : num  1 1 1 1 1 1 1 1 1 1 ... 
       $ PIS5 : num  0 1 1 0 1 1 1 1 1 0 ... 
       $ SCR6 : num  1 1 1 1 1 1 1 1 1 0 ... 
       $ SCR9 : num  1 1 1 1 0 0 0 1 0 0 ... 
       $ SCR10: num  0 0 0 0 0 0 0 0 0 0 ... 
       $ SCR17: num  0 0 0 0 0 1 0 0 0 0 ... 
      
 
    • data.janssen2 contains 20 IST items:
      
-
      'data.frame':   346 obs. of  20 variables: 
      
- $ IST01 : num  1 1 1 0 0 1 1 1 0 1 ... 
      
- $ IST02 : num  1 0 1 0 1 1 1 1 0 1 ... 
      
- $ IST03 : num  0 1 1 1 1 1 0 1 1 1 ... 
      
-[...] 
      
- $ IST020: num  0 0 0 1 1 0 0 0 0 0 ... 
      • 
-
    
-
-    
    References
    
-
+
    'data.frame':   346 obs. of  20 variables: 
     $ IST01 : num  1 1 1 0 0 1 1 1 0 1 ... 
     $ IST02 : num  1 0 1 0 1 1 1 1 0 1 ... 
     $ IST03 : num  0 1 1 1 1 1 0 1 1 1 ... 
    [...] 
     $ IST020: num  0 0 0 1 1 0 0 0 0 0 ... 
    • 
+

+    

+    
References

     
Janssen, A. B., & Geiser, C. (2010). On the relationship between solution
 strategies in two mental rotation tasks.
 Learning and Individual Differences, 20(5), 473-478.
-doi: 10.1016/j.lindif.2010.03.002

-
-    
Examples

-    
if (FALSE) {
-#############################################################################
-# EXAMPLE 1: CCT data, Janssen and Geiser (2010, LID)
-#            Latent class analysis based on data.janssen
-#############################################################################
-
-data(data.janssen)
-dat <- data.janssen
-colnames(dat)
-  ##   [1] "PIS1"  "PIS3"  "PIS4"  "PIS5"  "SCR6"  "SCR9"  "SCR10" "SCR17"
-
-#*********************************************************************
-#*** Model 1: Latent class analysis with two classes
-
-tammodel <- "
-ANALYSIS:
-  TYPE=LCA;
-  NCLASSES(2);
-  NSTARTS(10,20);
-LAVAAN MODEL:
-  # missing item numbers (e.g. PIS2) are ignored in the model
-  F=~ PIS1__PIS5 + SCR6__SCR17
-    "
-mod3 <- TAM::tamaan( tammodel, resp=dat  )
-summary(mod3)
-
-# extract item response functions
-imod2 <- IRT.irfprob(mod3)[,2,]
-# plot class specific probabilities
-ncl <- 2
-matplot( imod2, type="o", pch=1:ncl, xlab="Item", ylab="Probability" )
-legend( 1, .3, paste0("Class",1:ncl), lty=1:ncl, col=1:ncl, pch=1:ncl )
-
-#*********************************************************************
-#*** Model 2: Latent class analysis with three classes
-
-tammodel <- "
-ANALYSIS:
-  TYPE=LCA;
-  NCLASSES(3);
-  NSTARTS(10,20);
-LAVAAN MODEL:
-  F=~ PIS1__PIS5 + SCR6__SCR17
-    "
-mod3 <- TAM::tamaan( tammodel, resp=dat  )
-summary(mod3)
-
-# extract item response functions
-imod2 <- IRT.irfprob(mod3)[,2,]
-# plot class specific probabilities
-ncl <- 3
-matplot( imod2, type="o", pch=1:ncl, xlab="Item", ylab="Probability" )
-legend( 1, .3, paste0("Class",1:ncl), lty=1:ncl, col=1:ncl, pch=1:ncl )
-
-# compare models
-AIC(mod1); AIC(mod2)
-}

+doi:10.1016/j.lindif.2010.03.002

+    

+
+    

+    
Examples

+    
if (FALSE) {
+#############################################################################
+# EXAMPLE 1: CCT data, Janssen and Geiser (2010, LID)
+#            Latent class analysis based on data.janssen
+#############################################################################
+
+data(data.janssen)
+dat <- data.janssen
+colnames(dat)
+  ##   [1] "PIS1"  "PIS3"  "PIS4"  "PIS5"  "SCR6"  "SCR9"  "SCR10" "SCR17"
+
+#*********************************************************************
+#*** Model 1: Latent class analysis with two classes
+
+tammodel <- "
+ANALYSIS:
+  TYPE=LCA;
+  NCLASSES(2);
+  NSTARTS(10,20);
+LAVAAN MODEL:
+  # missing item numbers (e.g. PIS2) are ignored in the model
+  F=~ PIS1__PIS5 + SCR6__SCR17
+    "
+mod3 <- TAM::tamaan( tammodel, resp=dat  )
+summary(mod3)
+
+# extract item response functions
+imod2 <- IRT.irfprob(mod3)[,2,]
+# plot class specific probabilities
+ncl <- 2
+matplot( imod2, type="o", pch=1:ncl, xlab="Item", ylab="Probability" )
+legend( 1, .3, paste0("Class",1:ncl), lty=1:ncl, col=1:ncl, pch=1:ncl )
+
+#*********************************************************************
+#*** Model 2: Latent class analysis with three classes
+
+tammodel <- "
+ANALYSIS:
+  TYPE=LCA;
+  NCLASSES(3);
+  NSTARTS(10,20);
+LAVAAN MODEL:
+  F=~ PIS1__PIS5 + SCR6__SCR17
+    "
+mod3 <- TAM::tamaan( tammodel, resp=dat  )
+summary(mod3)
+
+# extract item response functions
+imod2 <- IRT.irfprob(mod3)[,2,]
+# plot class specific probabilities
+ncl <- 3
+matplot( imod2, type="o", pch=1:ncl, xlab="Item", ylab="Probability" )
+legend( 1, .3, paste0("Class",1:ncl), lty=1:ncl, col=1:ncl, pch=1:ncl )
+
+# compare models
+AIC(mod1); AIC(mod2)
+}

+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/reference/data.mc.html b/docs/reference/data.mc.html
index afe27b9..b9db461 100644
--- a/docs/reference/data.mc.html
+++ b/docs/reference/data.mc.html
@@ -1,68 +1,13 @@
-
 
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-Dataset with Raw and Scored Responses from Multiple Choice Items — data.mc • TAM
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Dataset with Raw and Scored Responses from Multiple Choice Items

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Dataset with Raw and Scored Responses from Multiple Choice Items

 on 30 items.

     

 
-    
data(data.mc)

-
-
-    
Format

+    

+    
data(data.mc)

+    

 
+    

+    
Format

     
The dataset is a list with two elements. The entry raw
   contains unscored (raw) item responses and the entry scored
   contains the scored (recoded) item responses. The format is:

-
List of 2 

- $ raw   : chr [1:143, 1:30] "A" "A" "A" "A" ... 

-  ..- attr(*, "dimnames")=List of 2 

-  .. ..$ : NULL 

-  .. ..$ : chr [1:30] "I01" "I02" "I03" "I04" ... 

- $ scored:'data.frame': 

-  ..$ I01: num [1:143] 1 1 1 1 1 1 1 1 1 1 ... 

-  ..$ I02: num [1:143] 1 1 1 0 1 1 1 1 1 1 ... 

-  ..$ I03: num [1:143] 1 1 1 1 1 1 1 1 1 1 ... 

-  [...] 

-  ..$ I29: num [1:143] NA 0 1 0 1 0 0 0 0 0 ... 

-  ..$ I30: num [1:143] NA NA 1 1 1 1 0 1 1 0 ... 

+
List of 2 
 $ raw   : chr [1:143, 1:30] "A" "A" "A" "A" ... 
  ..- attr(*, "dimnames")=List of 2 
  .. ..$ : NULL 
  .. ..$ : chr [1:30] "I01" "I02" "I03" "I04" ... 
 $ scored:'data.frame': 
  ..$ I01: num [1:143] 1 1 1 1 1 1 1 1 1 1 ... 
  ..$ I02: num [1:143] 1 1 1 0 1 1 1 1 1 1 ... 
  ..$ I03: num [1:143] 1 1 1 1 1 1 1 1 1 1 ... 
  [...] 
  ..$ I29: num [1:143] NA 0 1 0 1 0 0 0 0 0 ... 
  ..$ I30: num [1:143] NA NA 1 1 1 1 0 1 1 0 ... 

+    

 
   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
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+  
 
+  
 
diff --git a/docs/reference/data.numeracy.html b/docs/reference/data.numeracy.html
index b3362ac..39116f7 100644
--- a/docs/reference/data.numeracy.html
+++ b/docs/reference/data.numeracy.html
@@ -1,68 +1,13 @@
-
 
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-Dataset Numeracy — data.numeracy • TAM
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-Dataset Numeracy — data.numeracy • TAM
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+      

   

     

     
Dataset Numeracy

@@ -119,125 +51,111 @@ 
Dataset Numeracy

 item responses of 876 persons and 15 items.

     

 
-    
data(data.numeracy)

-
-
-    
Format

+    

+    
data(data.numeracy)

+    

 
+    

+    
Format

     
The format is a list a two entries:

-
List of 2 

- $ raw   :'data.frame': 

-  ..$ I1 : int [1:876] 1 0 1 0 0 0 0 0 1 1 ... 

-  ..$ I2 : int [1:876] 0 1 0 0 1 1 1 1 1 0 ... 

-  ..$ I3 : int [1:876] 4 4 1 3 4 4 4 4 4 4 ... 

-  ..$ I4 : int [1:876] 4 1 2 2 1 1 1 1 1 1 ... 

-  [...]  

-  ..$ I15: int [1:876] 1 1 1 1 0 1 1 1 1 1 ... 

- $ scored:'data.frame': 

-  ..$ I1 : int [1:876] 1 0 1 0 0 0 0 0 1 1 ... 

-  ..$ I2 : int [1:876] 0 1 0 0 1 1 1 1 1 0 ... 

-  ..$ I3 : int [1:876] 1 1 0 0 1 1 1 1 1 1 ... 

-  ..$ I4 : int [1:876] 0 1 0 0 1 1 1 1 1 1 ... 

-  [...]  

-  ..$ I15: int [1:876] 1 1 1 1 0 1 1 1 1 1 ... 

-
-    
Examples

-    
######################################################################
-# (1) Scored numeracy data
-######################################################################
-
-data(data.numeracy)
-dat <- data.numeracy$scored
-
-#Run IRT analysis: Rasch model
-mod1 <- TAM::tam.mml(dat)
-
-#Item difficulties
-mod1$xsi
-ItemDiff <- mod1$xsi$xsi
-ItemDiff
-
-#Ability estimate - Weighted Likelihood Estimate
-Abil <- TAM::tam.wle(mod1)
-Abil
-PersonAbility <- Abil$theta
-PersonAbility
-
-#Descriptive statistics of item and person parameters
-hist(ItemDiff)
-hist(PersonAbility)
-mean(ItemDiff)
-mean(PersonAbility)
-stats::sd(ItemDiff)
-stats::sd(PersonAbility)
-
-if (FALSE) {
-#Extension
-#plot histograms of ability and item parameters in the same graph
-oldpar <- par(no.readonly=TRUE)          # save writable default graphic settings
-windows(width=4.45, height=4.45, pointsize=12)
-layout(matrix(c(1,1,2),3,byrow=TRUE))
-layout.show(2)
-hist(PersonAbility,xlim=c(-3,3),breaks=20)
-hist(ItemDiff,xlim=c(-3,3),breaks=20)
-
-par( oldpar )  # restore default graphic settings
-hist(PersonAbility,xlim=c(-3,3),breaks=20)
-
-######################################################################
-# (2) Raw numeracy data
-######################################################################
-
-raw_resp <- data.numeracy$raw
-
-#score responses
-key <- c(1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1)
-scored <- sapply( seq(1,length(key)),
-            FUN=function(ii){ 1*(raw_resp[,ii]==key[ii]) } )
-
-#run IRT analysis
-mod1 <- TAM::tam.mml(scored)
-
-#Ability estimate - Weighted Likelihood Estimate
-Abil <- TAM::tam.wle(mod1)
-
-#CTT statistics
-ctt1 <- TAM::tam.ctt(raw_resp, Abil$theta)
-write.csv(ctt1,"D1_ctt1.csv")       # write statistics into a file
-        # use maybe write.csv2 if ';' should be the column separator
-
-#Fit statistics
-Fit <- TAM::tam.fit(mod1)
-Fit
-
-# plot expected response curves
-plot( mod1, ask=TRUE )
-}

+
List of 2 
 $ raw   :'data.frame': 
  ..$ I1 : int [1:876] 1 0 1 0 0 0 0 0 1 1 ... 
  ..$ I2 : int [1:876] 0 1 0 0 1 1 1 1 1 0 ... 
  ..$ I3 : int [1:876] 4 4 1 3 4 4 4 4 4 4 ... 
  ..$ I4 : int [1:876] 4 1 2 2 1 1 1 1 1 1 ... 
  [...]  
  ..$ I15: int [1:876] 1 1 1 1 0 1 1 1 1 1 ... 
 $ scored:'data.frame': 
  ..$ I1 : int [1:876] 1 0 1 0 0 0 0 0 1 1 ... 
  ..$ I2 : int [1:876] 0 1 0 0 1 1 1 1 1 0 ... 
  ..$ I3 : int [1:876] 1 1 0 0 1 1 1 1 1 1 ... 
  ..$ I4 : int [1:876] 0 1 0 0 1 1 1 1 1 1 ... 
  [...]  
  ..$ I15: int [1:876] 1 1 1 1 0 1 1 1 1 1 ... 

+    

+
+    

+    
Examples

+    
######################################################################
+# (1) Scored numeracy data
+######################################################################
+
+data(data.numeracy)
+dat <- data.numeracy$scored
+
+#Run IRT analysis: Rasch model
+mod1 <- TAM::tam.mml(dat)
+
+#Item difficulties
+mod1$xsi
+ItemDiff <- mod1$xsi$xsi
+ItemDiff
+
+#Ability estimate - Weighted Likelihood Estimate
+Abil <- TAM::tam.wle(mod1)
+Abil
+PersonAbility <- Abil$theta
+PersonAbility
+
+#Descriptive statistics of item and person parameters
+hist(ItemDiff)
+hist(PersonAbility)
+mean(ItemDiff)
+mean(PersonAbility)
+stats::sd(ItemDiff)
+stats::sd(PersonAbility)
+
+if (FALSE) {
+#Extension
+#plot histograms of ability and item parameters in the same graph
+oldpar <- par(no.readonly=TRUE)          # save writable default graphic settings
+windows(width=4.45, height=4.45, pointsize=12)
+layout(matrix(c(1,1,2),3,byrow=TRUE))
+layout.show(2)
+hist(PersonAbility,xlim=c(-3,3),breaks=20)
+hist(ItemDiff,xlim=c(-3,3),breaks=20)
+
+par( oldpar )  # restore default graphic settings
+hist(PersonAbility,xlim=c(-3,3),breaks=20)
+
+######################################################################
+# (2) Raw numeracy data
+######################################################################
+
+raw_resp <- data.numeracy$raw
+
+#score responses
+key <- c(1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1)
+scored <- sapply( seq(1,length(key)),
+            FUN=function(ii){ 1*(raw_resp[,ii]==key[ii]) } )
+
+#run IRT analysis
+mod1 <- TAM::tam.mml(scored)
+
+#Ability estimate - Weighted Likelihood Estimate
+Abil <- TAM::tam.wle(mod1)
+
+#CTT statistics
+ctt1 <- TAM::tam.ctt(raw_resp, Abil$theta)
+write.csv(ctt1,"D1_ctt1.csv")       # write statistics into a file
+        # use maybe write.csv2 if ';' should be the column separator
+
+#Fit statistics
+Fit <- TAM::tam.fit(mod1)
+Fit
+
+# plot expected response curves
+plot( mod1, ask=TRUE )
+}

+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/reference/data.sim.mfr.html b/docs/reference/data.sim.mfr.html
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Simulated Multifaceted Data

@@ -117,117 +49,110 @@ 
Simulated Multifaceted Data

     
Simulated data from multiple facets.

     

 
-    
data(data.sim.mfr)
- data(data.sim.facets)

-
-
-    
Format

-
-    
The format of data.sim.mfr is: 

- num [1:100, 1:5] 3 2 1 1 0 1 0 1 0 0 ... 

- - attr(*, "dimnames")=List of 2 

-  ..$ : chr [1:100] "V1" "V1.1" "V1.2" "V1.3" ... 

-  ..$ : NULL

-
The format of data.sim.facets is: 

-'data.frame':   100 obs. of  3 variables: 

- $ rater : num  1 2 3 4 5 1 2 3 4 5 ... 

- $ topic : num  3 1 3 1 3 2 3 2 2 1 ... 

- $ female: num  2 2 1 2 1 1 2 1 2 1 ... 

-    
Source

+    

+    
data(data.sim.mfr)
+ data(data.sim.facets)

+    

 
+    

+    
Format

+    
The format of data.sim.mfr is: 
 num [1:100, 1:5] 3 2 1 1 0 1 0 1 0 0 ... 
 - attr(*, "dimnames")=List of 2 
  ..$ : chr [1:100] "V1" "V1.1" "V1.2" "V1.3" ... 
  ..$ : NULL

+
The format of data.sim.facets is: 
'data.frame':   100 obs. of  3 variables: 
 $ rater : num  1 2 3 4 5 1 2 3 4 5 ... 
 $ topic : num  3 1 3 1 3 2 3 2 2 1 ... 
 $ female: num  2 2 1 2 1 1 2 1 2 1 ... 

+    

+    

+    
Source

     
Simulated

+    

 
-    
Examples

-    
#######
-# sim multi faceted Rasch model
-data(data.sim.mfr)
-data(data.sim.facets)
-
-  # 1: A-matrix test_rater
-  test_1_items <- TAM::.A.matrix( data.sim.mfr, formulaA=~rater,
-            facets=data.sim.facets, constraint="items" )
-  test_1_cases <- TAM::.A.matrix( data.sim.mfr, formulaA=~rater,
-            facets=data.sim.facets, constraint="cases" )
-
-  # 2: test_item+rater
-  test_2_cases <- TAM::.A.matrix( data.sim.mfr, formulaA=~item+rater,
-            facets=data.sim.facets, constraint="cases" )
-
-  # 3: test_item+rater+topic+ratertopic
-  test_3_items <- TAM::.A.matrix( data.sim.mfr, formulaA=~item+rater*topic,
-            facets=data.sim.facets, constraint="items" )
-  # conquest uses a different way of ordering the rows
-  # these are the first few rows of the conquest design matrix
-  # test_3_items$A[grep("item1([[:print:]])*topic1", rownames(test_3_items)),]
-
-  # 4: test_item+step
-  test_4_cases <- TAM::.A.matrix( data.sim.mfr, formulaA=~item+step,
-            facets=data.sim.facets, constraint="cases" )
-
-  # 5: test_item+item:step
-  test_5_cases <- TAM::.A.matrix( data.sim.mfr, formulaA=~item+item:step,
-            facets=data.sim.facets, constraint="cases" )
-  test_5_cases$A[, grep("item1", colnames(test_5_cases)) ]
-
-  # 5+x: more
-  #=> 6: is this even well defined in the conquest-design output
-  #          (see test_item+topicstep_cases.cqc / .des)
-  #        regardless of the meaning of such a formula;
-  #        currently .A.matrix throws a warning
-  # test_6_cases <- TAM::.A.matrix( data.sim.mfr, formulaA=~item+topic:step,
-  #                 facets=data.sim.facets, constraint="cases" )
-  test_7_cases <- TAM::.A.matrix( data.sim.mfr, formulaA=~item+topic+topic:step,
-            facets=data.sim.facets, constraint="cases" )
-
-if (FALSE) {
-  #=> 8: same as with 6
-  test_8_cases <- TAM::.A.matrix( data.sim.mfr, formulaA=~item+rater+item:rater:step,
-            facets=data.sim.facets, constraint="cases" )
-## [1] "Can't proceed the estimation: Lower-order term is missing."
-  test_9_cases <- TAM::.A.matrix( data.sim.mfr, formulaA=~item+step+rater+item:step+item:rater,
-            facets=data.sim.facets, constraint="cases" )
-  test_10_cases <- TAM::.A.matrix( data.sim.mfr, formulaA=~item+female+item:female,
-            facets=data.sim.facets, constraint="cases" )
-
-  ### All Design matrices
-  test_1_cases <- TAM::designMatrices.mfr( data.sim.mfr, formulaA=~rater,
-            facets=data.sim.facets, constraint="cases" )
-  test_4_cases <- TAM::designMatrices.mfr( data.sim.mfr, formulaA=~item+item:step,
-            facets=data.sim.facets, constraint="cases" )
-
-  ### TAM
-  test_4_cases <- TAM::tam.mml.mfr( data.sim.mfr, formulaA=~item+item:step )
-  test_tam <- TAM::tam.mml( data.sim.mfr )
-
-  test_1_cases <- TAM::tam.mml.mfr( data.sim.mfr, formulaA=~rater,
-            facets=data.sim.facets, constraint="cases" )
-  test_2_cases <- TAM::tam.mml.mfr( data.sim.mfr, formulaA=~item+rater,
-            facets=data.sim.facets, constraint="cases" )}

+    

+    
Examples

+    
#######
+# sim multi faceted Rasch model
+data(data.sim.mfr)
+data(data.sim.facets)
+
+  # 1: A-matrix test_rater
+  test_1_items <- TAM::.A.matrix( data.sim.mfr, formulaA=~rater,
+            facets=data.sim.facets, constraint="items" )
+  test_1_cases <- TAM::.A.matrix( data.sim.mfr, formulaA=~rater,
+            facets=data.sim.facets, constraint="cases" )
+
+  # 2: test_item+rater
+  test_2_cases <- TAM::.A.matrix( data.sim.mfr, formulaA=~item+rater,
+            facets=data.sim.facets, constraint="cases" )
+
+  # 3: test_item+rater+topic+ratertopic
+  test_3_items <- TAM::.A.matrix( data.sim.mfr, formulaA=~item+rater*topic,
+            facets=data.sim.facets, constraint="items" )
+  # conquest uses a different way of ordering the rows
+  # these are the first few rows of the conquest design matrix
+  # test_3_items$A[grep("item1([[:print:]])*topic1", rownames(test_3_items)),]
+
+  # 4: test_item+step
+  test_4_cases <- TAM::.A.matrix( data.sim.mfr, formulaA=~item+step,
+            facets=data.sim.facets, constraint="cases" )
+
+  # 5: test_item+item:step
+  test_5_cases <- TAM::.A.matrix( data.sim.mfr, formulaA=~item+item:step,
+            facets=data.sim.facets, constraint="cases" )
+  test_5_cases$A[, grep("item1", colnames(test_5_cases)) ]
+
+  # 5+x: more
+  #=> 6: is this even well defined in the conquest-design output
+  #          (see test_item+topicstep_cases.cqc / .des)
+  #        regardless of the meaning of such a formula;
+  #        currently .A.matrix throws a warning
+  # test_6_cases <- TAM::.A.matrix( data.sim.mfr, formulaA=~item+topic:step,
+  #                 facets=data.sim.facets, constraint="cases" )
+  test_7_cases <- TAM::.A.matrix( data.sim.mfr, formulaA=~item+topic+topic:step,
+            facets=data.sim.facets, constraint="cases" )
+
+if (FALSE) {
+  #=> 8: same as with 6
+  test_8_cases <- TAM::.A.matrix( data.sim.mfr, formulaA=~item+rater+item:rater:step,
+            facets=data.sim.facets, constraint="cases" )
+## [1] "Can't proceed the estimation: Lower-order term is missing."
+  test_9_cases <- TAM::.A.matrix( data.sim.mfr, formulaA=~item+step+rater+item:step+item:rater,
+            facets=data.sim.facets, constraint="cases" )
+  test_10_cases <- TAM::.A.matrix( data.sim.mfr, formulaA=~item+female+item:female,
+            facets=data.sim.facets, constraint="cases" )
+
+  ### All Design matrices
+  test_1_cases <- TAM::designMatrices.mfr( data.sim.mfr, formulaA=~rater,
+            facets=data.sim.facets, constraint="cases" )
+  test_4_cases <- TAM::designMatrices.mfr( data.sim.mfr, formulaA=~item+item:step,
+            facets=data.sim.facets, constraint="cases" )
+
+  ### TAM
+  test_4_cases <- TAM::tam.mml.mfr( data.sim.mfr, formulaA=~item+item:step )
+  test_tam <- TAM::tam.mml( data.sim.mfr )
+
+  test_1_cases <- TAM::tam.mml.mfr( data.sim.mfr, formulaA=~rater,
+            facets=data.sim.facets, constraint="cases" )
+  test_2_cases <- TAM::tam.mml.mfr( data.sim.mfr, formulaA=~item+rater,
+            facets=data.sim.facets, constraint="cases" )}

+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/reference/data.sim.rasch.html b/docs/reference/data.sim.rasch.html
index 11402eb..e1d73fc 100644
--- a/docs/reference/data.sim.rasch.html
+++ b/docs/reference/data.sim.rasch.html
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-
 
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-  
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-Simulated Rasch data — data.sim.rasch • TAM
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-Simulated Rasch data — data.sim.rasch • TAM
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Simulated Rasch data

@@ -117,100 +49,90 @@ 
Simulated Rasch data

     
Simulated Rasch data under unidimensional trait distribution

     

 
-    
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- data(data.sim.rasch.pweights)
- data(data.sim.rasch.missing)

-
-
-    
Format

-
-    
The format is: 
 

- num [1:2000, 1:40] 1 0 1 1 1 1 1 1 1 1 ...

-  - attr(*, "dimnames")=List of 2 

-   ..$ : NULL 

-   ..$ : chr [1:40] "I1" "I2" "I3" "I4" ... 

-    
Details

-
-    
N <- 2000      

- # simulate predictors 

- Y <- cbind( stats::rnorm( N, sd=1.5), stats::rnorm(N, sd=.3 ) ) 

- theta <- stats::rnorm( N ) + .4 * Y[,1] + .2 * Y[,2]  # latent regression model 

- # simulate item responses with missing data 

- I <- 40 

- resp[ theta < 0, c(1,seq(I/2+1, I)) ] <- NA 

- # define person weights 

- pweights <- c(  rep(3,N/2), rep( 1, N/2 ) ) 

-    
Source

+    

+    
data(data.sim.rasch)
+ data(data.sim.rasch.pweights)
+ data(data.sim.rasch.missing)

+    

 
+    

+    
Format

+    
The format is: 

num [1:2000, 1:40] 1 0 1 1 1 1 1 1 1 1 ...
 - attr(*, "dimnames")=List of 2 
  ..$ : NULL 
  ..$ : chr [1:40] "I1" "I2" "I3" "I4" ... 

+    

+    

+    
Details

+    
N <- 2000      
 # simulate predictors 
 Y <- cbind( stats::rnorm( N, sd=1.5), stats::rnorm(N, sd=.3 ) ) 
 theta <- stats::rnorm( N ) + .4 * Y[,1] + .2 * Y[,2]  # latent regression model 
 # simulate item responses with missing data 
 I <- 40 
 resp[ theta < 0, c(1,seq(I/2+1, I)) ] <- NA 
 # define person weights 
 pweights <- c(  rep(3,N/2), rep( 1, N/2 ) ) 

+    

+    

+    
Source

     
Simulated data (see Details)

+    

 
-    
Examples

-    
if (FALSE) {
-data(data.sim.rasch)
-N <- 2000
-Y <- cbind( stats::rnorm( N, sd=1.5), stats::rnorm(N, sd=.3 ) )
-
-# Loading Matrix
-# B <- array( 0, dim=c( I, 2, 1 )  )
-# B[1:(nrow(B)), 2, 1] <- 1
-B <- TAM::designMatrices(resp=data.sim.rasch)[["B"]]
-
-# estimate Rasch model
-mod1_1 <- TAM::tam.mml(resp=data.sim.rasch, Y=Y)
-
-# standard errors
-res1 <- TAM::tam.se(mod1_1)
-
-# Compute fit statistics
-tam.fit(mod1_1)
-
-# plausible value imputation
-# PV imputation has to be adpated for multidimensional case!
-pv1 <- TAM::tam.pv( mod1_1, nplausible=7, # 7 plausible values
-               samp.regr=TRUE       # sampling of regression coefficients
-              )
-
-# item parameter constraints
-xsi.fixed <- matrix( c( 1, -2,5, -.22,10, 2 ), nrow=3, ncol=2, byrow=TRUE)
-xsi.fixed
-mod1_4 <- TAM::tam.mml( resp=data.sim.rasch, xsi.fixed=xsi.fixed )
-
-# missing value handling
-data(data.sim.rasch.missing)
-mod1_2 <- TAM::tam.mml(data.sim.rasch.missing, Y=Y)
-
-# handling of sample (person) weights
-data(data.sim.rasch.pweights)
-N <- 1000
-pweights <- c(  rep(3,N/2), rep( 1, N/2 ) )
-mod1_3 <- TAM::tam.mml( data.sim.rasch.pweights, control=list(conv=.001),
-               pweights=pweights )
-  }

+    

+    
Examples

+    
if (FALSE) {
+data(data.sim.rasch)
+N <- 2000
+Y <- cbind( stats::rnorm( N, sd=1.5), stats::rnorm(N, sd=.3 ) )
+
+# Loading Matrix
+# B <- array( 0, dim=c( I, 2, 1 )  )
+# B[1:(nrow(B)), 2, 1] <- 1
+B <- TAM::designMatrices(resp=data.sim.rasch)[["B"]]
+
+# estimate Rasch model
+mod1_1 <- TAM::tam.mml(resp=data.sim.rasch, Y=Y)
+
+# standard errors
+res1 <- TAM::tam.se(mod1_1)
+
+# Compute fit statistics
+tam.fit(mod1_1)
+
+# plausible value imputation
+# PV imputation has to be adpated for multidimensional case!
+pv1 <- TAM::tam.pv( mod1_1, nplausible=7, # 7 plausible values
+               samp.regr=TRUE       # sampling of regression coefficients
+              )
+
+# item parameter constraints
+xsi.fixed <- matrix( c( 1, -2,5, -.22,10, 2 ), nrow=3, ncol=2, byrow=TRUE)
+xsi.fixed
+mod1_4 <- TAM::tam.mml( resp=data.sim.rasch, xsi.fixed=xsi.fixed )
+
+# missing value handling
+data(data.sim.rasch.missing)
+mod1_2 <- TAM::tam.mml(data.sim.rasch.missing, Y=Y)
+
+# handling of sample (person) weights
+data(data.sim.rasch.pweights)
+N <- 1000
+pweights <- c(  rep(3,N/2), rep( 1, N/2 ) )
+mod1_3 <- TAM::tam.mml( data.sim.rasch.pweights, control=list(conv=.001),
+               pweights=pweights )
+  }

+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/reference/data.timssAusTwn.html b/docs/reference/data.timssAusTwn.html
index 9201005..79bc27a 100644
--- a/docs/reference/data.timssAusTwn.html
+++ b/docs/reference/data.timssAusTwn.html
@@ -1,70 +1,15 @@
-
 
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-Dataset TIMSS 2011 of Australian and Taiwanese Students — data.timssAusTwn • TAM
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-Dataset TIMSS 2011 of Australian and Taiwanese Students — data.timssAusTwn • TAM
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Dataset TIMSS 2011 of Australian and Taiwanese Students

@@ -123,140 +55,166 @@ 
Dataset TIMSS 2011 of Australian and Taiwanese Students

 responses.

     

 
-    
data(data.timssAusTwn)
-data(data.timssAusTwn.scored)

-
-
-    
Format

-
-    
A data frame with 1773 observations on the following 14 variables.

-    
M032166
a mathematics item

-    
M032721
a mathematics item

-    
M032757
a mathematics item

-    
M032760A
a mathematics item

-    
M032760B
a mathematics item

-    
M032760C
a mathematics item

-    
M032761
a mathematics item

-    
M032692
a mathematics item

-    
M032626
a mathematics item

-    
M032595
a mathematics item

-    
M032673
a mathematics item

-    
IDCNTRY
Country identifier

-    
ITSEX
Gender

-    
IDBOOK
Booklet identifier

-  
-
-
-    
See also

-
-    
http://www.edmeasurementsurveys.com/TAM/Tutorials/5PartialCredit.htm

-
http://www.edmeasurementsurveys.com/TAM/Tutorials/6Population.htm

+    

+    
data(data.timssAusTwn)
+data(data.timssAusTwn.scored)

+    

 
-    
Examples

-    
data(data.timssAusTwn)
-raw_resp <- data.timssAusTwn
+    

+    
Format

+    
A data frame with 1773 observations on the following 14 variables.
M032166

+
a mathematics item

 
-#Recode data
-resp <- raw_resp[,1:11]
-      #Column 12 is country code. Column 13 is gender code. Column 14 is Book ID.
-all.na <- rowMeans( is.na(resp) )==1
-        #Find records where all responses are missing.
-resp <- resp[!all.na,]              #Delete records with all missing responses
-resp[resp==20 | resp==21] <- 2      #TIMSS double-digit coding: "20" or "21" is a score of 2
-resp[resp==10 | resp==11] <- 1      #TIMSS double-digit coding: "10" or "11" is a score of 1
-resp[resp==70 | resp==79] <- 0      #TIMSS double-digit coding: "70" or "79" is a score of 0
-resp[resp==99] <- 0                 #"99" is omitted responses. Score it as wrong here.
-resp[resp==96 | resp==6] <- NA      #"96" and "6" are not-reached items. Treat these as missing.
+    
M032721

+
a mathematics item

 
-#Score multiple-choice items        #"resp" contains raw responses for MC items.
-Scored <- resp
-Scored[,9] <- (resp[,9]==4)*1       #Key for item 9 is D.
-Scored[,c(1,2)] <- (resp[,c(1,2)]==2)*1  #Key for items 1 and 2 is B.
-Scored[,c(10,11)] <- (resp[,c(10,11)]==3)*1  #Key for items 10 and 11 is C.
+    
M032757

+
a mathematics item

 
-#Run IRT analysis for partial credit model (MML estimation)
-mod1 <- TAM::tam.mml(Scored)
+    
M032760A

+
a mathematics item

 
-#Item parameters
-mod1$xsi
+    
M032760B

+
a mathematics item

 
-#Thurstonian thresholds
-tthresh <- TAM::tam.threshold(mod1)
-tthresh
+    
M032760C

+
a mathematics item

 
-if (FALSE) {
-#Plot Thurstonian thresholds
-windows (width=8, height=7)
-par(ps=9)
-dotchart(t(tthresh), pch=19)
-# plot expected response curves
-plot( mod1, ask=TRUE)
+    
M032761

+
a mathematics item

 
-#Re-run IRT analysis in JML
-mod1.2 <- TAM::tam.jml(Scored)
-stats::var(mod1.2$WLE)
+    
M032692

+
a mathematics item

 
-#Re-run the model with "not-reached" coded as incorrect.
-Scored2 <- Scored
-Scored2[is.na(Scored2)] <- 0
+    
M032626

+
a mathematics item

 
-#Prepare anchor parameter values
-nparam <- length(mod1$xsi$xsi)
-xsi <- mod1$xsi$xsi
-anchor <- matrix(c(seq(1,nparam),xsi), ncol=2)
+    
M032595

+
a mathematics item

 
-#Run IRT with item parameters anchored on mod1 values
-mod2 <- TAM::tam.mml(Scored2, xsi.fixed=anchor)
+    
M032673

+
a mathematics item

 
-#WLE ability estimates
-ability <- TAM::tam.wle(mod2)
-ability
+    
IDCNTRY

+
Country identifier

 
-#CTT statistics
-ctt <- TAM::tam.ctt(resp, ability$theta)
-write.csv(ctt,"TIMSS_CTT.csv")
+    
ITSEX

+
Gender

 
-#plot histograms of ability and item parameters in the same graph
-windows(width=4.45, height=4.45, pointsize=12)
-layout(matrix(c(1,1,2),3,byrow=TRUE))
-layout.show(2)
-hist(ability$theta,xlim=c(-3,3),breaks=20)
-hist(tthresh,xlim=c(-3,3),breaks=20)
+    
IDBOOK

+
Booklet identifier

 
-#Extension
-#Score equivalence table
-dummy <- matrix(0,nrow=16,ncol=11)
-dummy[lower.tri(dummy)] <- 1
-dummy[12:16,c(3,4,7,8)][lower.tri(dummy[12:16,c(3,4,7,8)])]<-2
+  
+

+    
 
-mod3 <- TAM::tam.mml(dummy, xsi.fixed=anchor)
-wle3 <- TAM::tam.wle(mod3)
-}

+    

+    
Examples

+    
data(data.timssAusTwn)
+raw_resp <- data.timssAusTwn
+
+#Recode data
+resp <- raw_resp[,1:11]
+      #Column 12 is country code. Column 13 is gender code. Column 14 is Book ID.
+all.na <- rowMeans( is.na(resp) )==1
+        #Find records where all responses are missing.
+resp <- resp[!all.na,]              #Delete records with all missing responses
+resp[resp==20 | resp==21] <- 2      #TIMSS double-digit coding: "20" or "21" is a score of 2
+resp[resp==10 | resp==11] <- 1      #TIMSS double-digit coding: "10" or "11" is a score of 1
+resp[resp==70 | resp==79] <- 0      #TIMSS double-digit coding: "70" or "79" is a score of 0
+resp[resp==99] <- 0                 #"99" is omitted responses. Score it as wrong here.
+resp[resp==96 | resp==6] <- NA      #"96" and "6" are not-reached items. Treat these as missing.
+
+#Score multiple-choice items        #"resp" contains raw responses for MC items.
+Scored <- resp
+Scored[,9] <- (resp[,9]==4)*1       #Key for item 9 is D.
+Scored[,c(1,2)] <- (resp[,c(1,2)]==2)*1  #Key for items 1 and 2 is B.
+Scored[,c(10,11)] <- (resp[,c(10,11)]==3)*1  #Key for items 10 and 11 is C.
+
+#Run IRT analysis for partial credit model (MML estimation)
+mod1 <- TAM::tam.mml(Scored)
+
+#Item parameters
+mod1$xsi
+
+#Thurstonian thresholds
+tthresh <- TAM::tam.threshold(mod1)
+tthresh
+
+if (FALSE) {
+#Plot Thurstonian thresholds
+windows (width=8, height=7)
+par(ps=9)
+dotchart(t(tthresh), pch=19)
+# plot expected response curves
+plot( mod1, ask=TRUE)
+
+#Re-run IRT analysis in JML
+mod1.2 <- TAM::tam.jml(Scored)
+stats::var(mod1.2$WLE)
+
+#Re-run the model with "not-reached" coded as incorrect.
+Scored2 <- Scored
+Scored2[is.na(Scored2)] <- 0
+
+#Prepare anchor parameter values
+nparam <- length(mod1$xsi$xsi)
+xsi <- mod1$xsi$xsi
+anchor <- matrix(c(seq(1,nparam),xsi), ncol=2)
+
+#Run IRT with item parameters anchored on mod1 values
+mod2 <- TAM::tam.mml(Scored2, xsi.fixed=anchor)
+
+#WLE ability estimates
+ability <- TAM::tam.wle(mod2)
+ability
+
+#CTT statistics
+ctt <- TAM::tam.ctt(resp, ability$theta)
+write.csv(ctt,"TIMSS_CTT.csv")
+
+#plot histograms of ability and item parameters in the same graph
+windows(width=4.45, height=4.45, pointsize=12)
+layout(matrix(c(1,1,2),3,byrow=TRUE))
+layout.show(2)
+hist(ability$theta,xlim=c(-3,3),breaks=20)
+hist(tthresh,xlim=c(-3,3),breaks=20)
+
+#Extension
+#Score equivalence table
+dummy <- matrix(0,nrow=16,ncol=11)
+dummy[lower.tri(dummy)] <- 1
+dummy[12:16,c(3,4,7,8)][lower.tri(dummy[12:16,c(3,4,7,8)])]<-2
+
+mod3 <- TAM::tam.mml(dummy, xsi.fixed=anchor)
+wle3 <- TAM::tam.wle(mod3)
+}

+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/reference/designMatrices.html b/docs/reference/designMatrices.html
index c3e5b9c..964ab19 100644
--- a/docs/reference/designMatrices.html
+++ b/docs/reference/designMatrices.html
@@ -1,67 +1,12 @@
-
 
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-  
-  
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-Generation of Design Matrices — designMatrices • TAM
-
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-Generation of Design Matrices — designMatrices • TAM
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Generation of Design Matrices

@@ -117,163 +49,154 @@ 
Generation of Design Matrices

     
Generate design matrices, and display them at console.

     

 
-    
designMatrices(modeltype=c("PCM", "RSM"), maxKi=NULL, resp=resp,
-    ndim=1, A=NULL, B=NULL, Q=NULL, R=NULL, constraint="cases",...)
+    

+    
designMatrices(modeltype=c("PCM", "RSM"), maxKi=NULL, resp=resp,
+    ndim=1, A=NULL, B=NULL, Q=NULL, R=NULL, constraint="cases",...)
+
+# S3 method for designMatrices
+print(x, ...)
+
+designMatrices.mfr(resp, formulaA=~ item + item:step, facets=NULL,
+    constraint=c("cases", "items"), ndim=1, Q=NULL, A=NULL, B=NULL,
+    progress=FALSE)
+designMatrices.mfr2(resp, formulaA=~ item + item:step, facets=NULL,
+    constraint=c("cases", "items"), ndim=1, Q=NULL, A=NULL, B=NULL,
+    progress=FALSE)
+
+.A.matrix(resp, formulaA=~ item + item*step, facets=NULL,
+    constraint=c("cases", "items"), progress=FALSE, maxKi=NULL)
+rownames.design(X)
+
+.A.PCM2( resp, Kitem=NULL, constraint="cases", Q=NULL)
+   # generates ConQuest parametrization of partial credit model
+
+.A.PCM3( resp, Kitem=NULL ) # parametrization for A matrix in the dispersion model

+    

 
-print.designMatrices(X, ...)
+    

+    
Arguments

+    
modeltype

+
Type of item response model. Until now, the
+     partial credit model (PCM; 'item+item*step') and
+     the rating scale model (RSM; 'item+step') is implemented.

 
-designMatrices.mfr(resp, formulaA=~ item + item:step, facets=NULL,
-    constraint=c("cases", "items"), ndim=1, Q=NULL, A=NULL, B=NULL,
-    progress=FALSE)
-designMatrices.mfr2(resp, formulaA=~ item + item:step, facets=NULL,
-    constraint=c("cases", "items"), ndim=1, Q=NULL, A=NULL, B=NULL,
-    progress=FALSE)
+  
maxKi

+
A vector containing the maximum score per item

 
-.A.matrix(resp, formulaA=~ item + item*step, facets=NULL,
-    constraint=c("cases", "items"), progress=FALSE, maxKi=NULL)
-rownames.design(X)
+  
resp

+
Data frame of item responses

 
-.A.PCM2( resp, Kitem=NULL, constraint="cases", Q=NULL)
-   # generates ConQuest parametrization of partial credit model
+  
ndim

+
Number of dimensions

 
-.A.PCM3( resp, Kitem=NULL ) # parametrization for A matrix in the dispersion model

+  
A

+
The design matrix for linking item category parameters
+     to generalized item parameters \(\xi\).

 
-    
Arguments

-    
-    
-    
-      
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-      
-    
-    
modeltype
Type of item response model. Until now, the
-     partial credit model (PCM; 'item+item*step') and
-     the rating scale model (RSM; 'item+step') is implemented.
maxKi
A vector containing the maximum score per item
resp
Data frame of item responses
ndim
Number of dimensions
A
The design matrix for linking item category parameters
-     to generalized item parameters \(\xi\).
B
The scoring matrix of item categories on \(\theta\)
-     dimensions.
Q
A loading matrix of items on dimensions
+  
B

+
The scoring matrix of item categories on \(\theta\)
+     dimensions.

+
+  
Q

+
A loading matrix of items on dimensions
      with number of rows equal the number
      of items and the number of columns equals the
-     number of dimensions in the item response model.
R
This argument is not used
X
Object generated by designMatrices. This argument is used in
-     print.designMatrices and rownames.design.
formulaA
An R formula object for generating the A design matrix.
-    Variables in formulaA have to be included in facets.
facets
A data frame with observed facets. The number of rows must be equal
-    to the number of rows in resp.
constraint
Constraint in estimation: cases assumes zero means
+     number of dimensions in the item response model.

+
+ 
R

+
This argument is not used

+
+ 
x

+
Object generated by designMatrices. This argument is used in
+     print.designMatrices and rownames.design.

+
+ 
X

+
Object generated by designMatrices. This argument is used in
+     print.designMatrices and rownames.design.

+
+
formulaA

+
An R formula object for generating the A design matrix.
+    Variables in formulaA have to be included in facets.

+
+
facets

+
A data frame with observed facets. The number of rows must be equal
+    to the number of rows in resp.

+
+
constraint

+
Constraint in estimation: cases assumes zero means
     of trait distributions and items a sum constraint of
-    zero of item parameters
Kitem
Maximum number of categories per item
progress
Display progress for creation of design matrices
...
Further arguments

-
-    
Details

+    zero of item parameters

+
+
Kitem

+
Maximum number of categories per item

 
+
progress

+
Display progress for creation of design matrices

+
+  
...

+
Further arguments

+
+

+    

+    
Details

     
The function .A.PCM2 generates the Conquest parametrization
 of the partial credit model.

 
The function .A.PCM3 generates the parametrization for the \(A\)
 design matrix in the dispersion model for ordered data (Andrich, 1982).

-    
References

-
+    

+    

+    
References

     
Andrich, D. (1982). An extension of the Rasch model for ratings providing
 both location and dispersion parameters. Psychometrika, 47(1),
-105-113. doi: 10.1007/BF02293856

-    
Note

-
+105-113. doi:10.1007/BF02293856

+    

+    

+    
Note

     
The function designMatrices.mfr2 handles multi-faceted design for
 items with differing number of response options.

-    
See also

-
-    
See data.sim.mfr for some examples for creating design matrices.
-

-
-    
Examples

-    
###########################################################
-# different parametrizations for ordered data
-data( data.gpcm )
-resp <- data.gpcm
-
-# parametrization for partial credit model
-A1 <- TAM::designMatrices( resp=resp )$A
-# item difficulty and threshold parametrization
-A2 <- TAM::.A.PCM2( resp )
-# dispersion model of Andrich (1982)
-A3 <- TAM::.A.PCM3( resp )
-# rating scale model
-A4 <- TAM::designMatrices( resp=resp, modeltype="RSM" )$A

+    

+    

+    
See also

+    
See data.sim.mfr for some examples for creating design matrices.

+    

+
+    

+    
Examples

+    
###########################################################
+# different parametrizations for ordered data
+data( data.gpcm )
+resp <- data.gpcm
+
+# parametrization for partial credit model
+A1 <- TAM::designMatrices( resp=resp )$A
+# item difficulty and threshold parametrization
+A2 <- TAM::.A.PCM2( resp )
+# dispersion model of Andrich (1982)
+A3 <- TAM::.A.PCM3( resp )
+# rating scale model
+A4 <- TAM::designMatrices( resp=resp, modeltype="RSM" )$A

+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
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+  
Site built with pkgdown 2.0.7.

 

 
-      

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+      

 
   
 
 
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+  
 
+  
 
diff --git a/docs/reference/doparse.html b/docs/reference/doparse.html
index bc038ea..153e703 100644
--- a/docs/reference/doparse.html
+++ b/docs/reference/doparse.html
@@ -1,46 +1,5 @@
-
 
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-Parsing a String with <code>DO</code> Statements — doparse • TAM
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Parsing a String with DO Statements

@@ -133,141 +65,141 @@ 
Parsing a String with DO Statements

 the DO2 statement can be used using %1 and %2
 as indices. See Examples for hints on the specification. The loop in DO2
 must not be explicitly crossed, e.g. in applications for specifying
-covariances or correlations. The formal syntax for 

- for (ii in 1:(K-1)){  for (jj in (ii+1):K) { ... } } 

+covariances or correlations. The formal syntax for 
 for (ii in 1:(K-1)){  for (jj in (ii+1):K) { ... } } 

 can be written as DO2(1,K-1,1,%1,K,1
 ). See Example 2.

     

 
-    
doparse(model)

-
-    
Arguments

-    
-    
-    
-      
-      
-    
-    
model
A string with DO or DO2 statements.

-
-    
Value

-
-    
Parsed string in which DO statements are expanded.

-    
See also

-
-    
This function is also used in lavaanify.IRT and
-tamaanify.

-
-    
Examples

-    
#############################################################################
-# EXAMPLE 1: doparse example
-#############################################################################
+    

+    
doparse(model)

+    

 
-# define model
-model <- "
- # items I1,...,I10 load on G
- DO(1,10,1)
-   G=~ lamg% * I%
- DOEND
- I2 | 0.75*t1
- v10 > 0 ;
- # The first index loops from 1 to 3 and the second index loops from 1 to 2
- DO2(1,3,1,  1,2,1)
-   F%2=~ a%2%1 * A%2%1 ;
- DOEND
- # Loop from 1 to 9 with steps of 2
- DO(1,9,2)
-   HA1=~ I%
-   I% | beta% * t1
- DOEND
- "
+    

+    
Arguments

+    
model

+
A string with DO or DO2 statements.

 
-# process string
-out <- TAM::doparse(model)
-cat(out)
-  ##    # items I1,...,I10 load on G
-  ##       G=~ lamg1 * I1
-  ##       G=~ lamg2 * I2
-  ##       G=~ lamg3 * I3
-  ##       G=~ lamg4 * I4
-  ##       G=~ lamg5 * I5
-  ##       G=~ lamg6 * I6
-  ##       G=~ lamg7 * I7
-  ##       G=~ lamg8 * I8
-  ##       G=~ lamg9 * I9
-  ##       G=~ lamg10 * I10
-  ##     I2 | 0.75*t1
-  ##     v10 > 0
-  ##       F1=~ a11 * A11
-  ##       F2=~ a21 * A21
-  ##       F1=~ a12 * A12
-  ##       F2=~ a22 * A22
-  ##       F1=~ a13 * A13
-  ##       F2=~ a23 * A23
-  ##       HA1=~ I1
-  ##       HA1=~ I3
-  ##       HA1=~ I5
-  ##       HA1=~ I7
-  ##       HA1=~ I9
-  ##       I1 | beta1 * t1
-  ##       I3 | beta3 * t1
-  ##       I5 | beta5 * t1
-  ##       I7 | beta7 * t1
-  ##       I9 | beta9 * t1
+

+    

+    
Value

+    
 
-#############################################################################
-# EXAMPLE 2: doparse with nested loop example
-#############################################################################
+
Parsed string in which DO statements are expanded.

+    

+    

+    
See also

+    
This function is also used in lavaanify.IRT and
+tamaanify.

+    

 
-# define model
-model <- "
- DO(1,4,1)
-   G=~ lamg% * I%
- DOEND
- # specify some correlated residuals
- DO2(1,3,1,%1,4,1)
-   I%1 ~~ I%2
- DOEND
- "
-# process string
-out <- TAM::doparse(model)
-cat(out)
-  ##       G=~ lamg1 * I1
-  ##       G=~ lamg2 * I2
-  ##       G=~ lamg3 * I3
-  ##       G=~ lamg4 * I4
-  ##     # specify some correlated residuals
-  ##       I1 ~~ I2
-  ##       I1 ~~ I3
-  ##       I1 ~~ I4
-  ##       I2 ~~ I3
-  ##       I2 ~~ I4
-  ##       I3 ~~ I4

+    

+    
Examples

+    
#############################################################################
+# EXAMPLE 1: doparse example
+#############################################################################
+
+# define model
+model <- "
+ # items I1,...,I10 load on G
+ DO(1,10,1)
+   G=~ lamg% * I%
+ DOEND
+ I2 | 0.75*t1
+ v10 > 0 ;
+ # The first index loops from 1 to 3 and the second index loops from 1 to 2
+ DO2(1,3,1,  1,2,1)
+   F%2=~ a%2%1 * A%2%1 ;
+ DOEND
+ # Loop from 1 to 9 with steps of 2
+ DO(1,9,2)
+   HA1=~ I%
+   I% | beta% * t1
+ DOEND
+ "
+
+# process string
+out <- TAM::doparse(model)
+cat(out)
+  ##    # items I1,...,I10 load on G
+  ##       G=~ lamg1 * I1
+  ##       G=~ lamg2 * I2
+  ##       G=~ lamg3 * I3
+  ##       G=~ lamg4 * I4
+  ##       G=~ lamg5 * I5
+  ##       G=~ lamg6 * I6
+  ##       G=~ lamg7 * I7
+  ##       G=~ lamg8 * I8
+  ##       G=~ lamg9 * I9
+  ##       G=~ lamg10 * I10
+  ##     I2 | 0.75*t1
+  ##     v10 > 0
+  ##       F1=~ a11 * A11
+  ##       F2=~ a21 * A21
+  ##       F1=~ a12 * A12
+  ##       F2=~ a22 * A22
+  ##       F1=~ a13 * A13
+  ##       F2=~ a23 * A23
+  ##       HA1=~ I1
+  ##       HA1=~ I3
+  ##       HA1=~ I5
+  ##       HA1=~ I7
+  ##       HA1=~ I9
+  ##       I1 | beta1 * t1
+  ##       I3 | beta3 * t1
+  ##       I5 | beta5 * t1
+  ##       I7 | beta7 * t1
+  ##       I9 | beta9 * t1
+
+#############################################################################
+# EXAMPLE 2: doparse with nested loop example
+#############################################################################
+
+# define model
+model <- "
+ DO(1,4,1)
+   G=~ lamg% * I%
+ DOEND
+ # specify some correlated residuals
+ DO2(1,3,1,%1,4,1)
+   I%1 ~~ I%2
+ DOEND
+ "
+# process string
+out <- TAM::doparse(model)
+cat(out)
+  ##       G=~ lamg1 * I1
+  ##       G=~ lamg2 * I2
+  ##       G=~ lamg3 * I3
+  ##       G=~ lamg4 * I4
+  ##     # specify some correlated residuals
+  ##       I1 ~~ I2
+  ##       I1 ~~ I3
+  ##       I1 ~~ I4
+  ##       I2 ~~ I3
+  ##       I2 ~~ I4
+  ##       I3 ~~ I4

+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/reference/index.html b/docs/reference/index.html
index d31ff7e..6ca54c1 100644
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Reference

     

 
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+          
All functions 

           

         

+      

           
anova(<tam>) logLik(<tam>) anova(<tam.mml>) logLik(<tam.mml>) anova(<tam.mml.3pl>) logLik(<tam.mml.3pl>) anova(<tamaan>) logLik(<tamaan>) anova(<tam.latreg>) logLik(<tam.latreg>) anova(<tam.np>) logLik(<tam.np>) 

         		
         
Likelihood Ratio Test for Model Comparisons and Log-Likelihood Value

+      

           
cfa.extract.itempars() 

         		
         
Extracting Item Parameters from a Fitted cfa Object in lavaan

+      

           
data.cqc01 data.cqc02 data.cqc03 data.cqc04 data.cqc05 

         		
         
More Datasets and Examples (Similar to ConQuest Examples)

+      

           
data.ctest1 data.ctest2 

         		
         
Some C-Test Datasets

+      

           
data.ex08 data.ex10 data.ex11 data.ex12 data.ex14 data.ex15 data.exJ03 

         		
         
Datasets data.ex in TAM Package

+      

           
data.fims.Aus.Jpn.raw data.fims.Aus.Jpn.scored 

         		
         
Dataset FIMS Study with Responses of Australian and Japanese Students

+      

           
data.geiser 

         		
         
Dataset from Geiser et al. (2006)

+      

           
data.gpcm 

         		
         
Dataset with Ordered Indicators

+      

           
data.janssen data.janssen2 

         		
         
Dataset from Janssen and Geiser (2010)

+      

           
data.mc 

         		
         
Dataset with Raw and Scored Responses from Multiple Choice Items

+      

           
data.numeracy 

         		
         
Dataset Numeracy

+      

           
data.sim.mfr data.sim.facets 

         		
         
Simulated Multifaceted Data

+      

           
data.sim.rasch data.sim.rasch.pweights data.sim.rasch.missing 

         		
         
Simulated Rasch data

+      

           
data.timssAusTwn data.timssAusTwn.scored 

         		
         
Dataset TIMSS 2011 of Australian and Taiwanese Students

+      

           
DescribeBy() 

         		
         
S3 Method for Descriptive Statistics of Objects

-          
designMatrices() print.designMatrices() designMatrices.mfr() designMatrices.mfr2() .A.matrix() rownames.design() .A.PCM2() .A.PCM3() 

+      

+          
designMatrices() print(<designMatrices>) designMatrices.mfr() designMatrices.mfr2() .A.matrix() rownames.design() .A.PCM2() .A.PCM3() 

         		
         
Generation of Design Matrices

+      

           
doparse() 

         		
         
Parsing a String with DO Statements

+      

           
IRT.cv() 

         		
         
Cross-Validation of a Fitted IRT Model

+      

           
IRT.data(<tam.mml>) IRT.data(<tam.mml.3pl>) IRT.data(<tamaan>) 

         		
         
Extracting Item Response Dataset

+      

           
IRT.drawPV() 

         		
         
Function for Drawing Plausible Values

+      

           
IRT.expectedCounts(<tam>) IRT.expectedCounts(<tam.mml>) IRT.expectedCounts(<tam.mml.3pl>) IRT.expectedCounts(<tamaan>) IRT.expectedCounts(<tam.np>) 

         		
         
Extracting Expected Counts

+      

           
IRT.factor.scores(<tam>) IRT.factor.scores(<tam.mml>) IRT.factor.scores(<tam.mml.3pl>) IRT.factor.scores(<tamaan>) 

         		
         
Extracting Factor Scores in TAM

+      

           
IRT.frequencies(<tam.mml>) IRT.frequencies(<tam.mml.3pl>) IRT.frequencies(<tamaan>) 

         		
         
Observed and Expected Frequencies for Univariate and Bivariate Distributions

+      

           
IRT.informationCurves() plot(<IRT.informationCurves>) 

         		
         
Item and Test Information Curve

+      

           
IRT.irfprob(<tam>) IRT.irfprob(<tam.mml>) IRT.irfprob(<tam.mml.3pl>) IRT.irfprob(<tamaan>) IRT.irfprob(<tam.np>) 

         		
         
Extracting Item Response Functions

+      

           
IRT.itemfit(<tam.mml>) IRT.itemfit(<tam.mml.2pl>) IRT.itemfit(<tam.mml.mfr>) IRT.itemfit(<tam.mml.3pl>) 

         		
         
RMSD Item Fit Statistics for TAM Objects

+      

           
IRT.likelihood(<tam>) IRT.posterior(<tam>) IRT.likelihood(<tam.mml>) IRT.posterior(<tam.mml>) IRT.likelihood(<tam.mml.3pl>) IRT.posterior(<tam.mml.3pl>) IRT.likelihood(<tamaan>) IRT.posterior(<tamaan>) IRT.likelihood(<tam.latreg>) IRT.posterior(<tam.latreg>) IRT.likelihood(<tam.np>) IRT.posterior(<tam.np>) 

         		
         
Extracting Individual Likelihood and Individual Posterior

+      

           
IRT.linearCFA() summary(<IRT.linearCFA>) 

         		
         
Linear Approximation of a Confirmatory Factor Analysis

+      

           
IRT.residuals() residuals(<tam.mml>) residuals(<tam.mml.2pl>) residuals(<tam.mml.mfr>) residuals(<tam.jml>) 

         		
         
Residuals in an IRT Model

+      

           
IRT.simulate() 

         		
         
Simulating Item Response Models

+      

           
IRT.threshold() print(<IRT.threshold>) IRT.WrightMap() 

         		
         
Thurstonian Thresholds and Wright Map for Item Response Models

+      

           
IRT.truescore() 

         		
         
Converts a \(\theta\) Score into a True Score \(\tau ( \theta)\)

+      

+          
IRT.WrightMap(<tam.mml>) IRT.WrightMap(<tamaan>) 

+        
Wright Map for Item Response Models by Using the WrightMap Package

           
IRTLikelihood.cfa() 

         		
         
Individual Likelihood for Confirmatory Factor Analysis

+      

           
IRTLikelihood.ctt() 

         		
         
Computes Individual Likelihood from Classical Test Theory Estimates

+      

           
lavaanify.IRT() 

         		
         
Slight Extension of the lavaan Syntax, with Focus on Item Response Models

+      

           
msq.itemfit() summary(<msq.itemfit>) msq.itemfitWLE() summary(<msq.itemfitWLE>) 

         		
         
Mean Squared Residual Based Item Fit Statistics (Infit, Outfit)

+      

           
plot(<tam>) plot(<tam.mml>) plot(<tam.jml>) 

         		
         
Plot Function for Unidimensional Item Response Models

+      

           
plotDevianceTAM() 

         		
         
Deviance Plot for TAM Objects

+      

           
predict(<tam.mml>) predict(<tam.mml.3pl>) predict(<tamaan>) 

         		
         
Expected Values and Predicted Probabilities for Fitted TAM Models

+      

           
Scale() 

         		
         
S3 Method for Standardizations and Transformations of Variables

+      

           
tam.jml2() 

         		
         
Defunct TAM Functions

-          
TAM-package 

+      

+          
TAM-package TAM 

         		
         
Test Analysis Modules

+      

           
IRT.RISE() tam_model_implied_means() tam_packageinfo() tam_print_call() tam_rsessinfo() tam_args_CALL_search() require_namespace_msg() add.lead() tam_round_data_frame() tam_round_data_frame_print() tam_osink() tam_csink() tam_matrix2() tam_outer() tam_normalize_matrix_rows() tam_normalize_vector() tam_aggregate() tam_interval_index() tam_rowCumsums() tam_dmvnorm() tam_bayesian_bootstrap() tam_cov_wt() tam_cor_wt() tam_ginv() tam_ginv_scaled() tam_remove_missings() tam_AXsi_compute() tam_AXsi_fit() tam_max_abs() tam_max_abs_list() tam_trim_increment() tam_difference_quotient() tam_assign_list_elements() 

         		
         
Utility Functions in TAM

+      

           
tam.ctt() tam.ctt2() tam.ctt3() tam.cb() plotctt() 

         		
         
Classical Test Theory Based Statistics and Plots

+      

           
tam.fa() 

         		
         
Bifactor Model and Exploratory Factor Analysis

+      

           
tam.fit() tam.mml.fit() tam.jml.fit() summary(<tam.fit>) 

         		
         
Item Infit and Outfit Statistic

+      

           
tam.jml() summary(<tam.jml>) logLik(<tam.jml>) 

         		
         
Joint Maximum Likelihood Estimation

+      

           
tam.latreg() summary(<tam.latreg>) print(<tam.latreg>) 

         		
         
Latent Regression Model

+      

           
tam.linking() summary(<tam.linking>) print(<tam.linking>) tam_linking_2studies() summary(<tam_linking_2studies>) print(<tam_linking_2studies>) 

         		
         
Linking of Fitted Unidimensional Item Response Models in TAM

+      

           
tam.mml.3pl() summary(<tam.mml.3pl>) print(<tam.mml.3pl>) 

         		
         
3PL Structured Item Response Model in TAM

+      

           
tam() tam.mml() tam.mml.2pl() tam.mml.mfr() summary(<tam>) summary(<tam.mml>) print(<tam>) print(<tam.mml>) 

         		
         
Test Analysis Modules: Marginal Maximum Likelihood Estimation

+      

           
tam.modelfit() summary(<tam.modelfit>) IRT.modelfit(<tam.mml>) IRT.modelfit(<tam.mml.3pl>) IRT.modelfit(<tamaan>) summary(<IRT.modelfit.tam.mml>) summary(<IRT.modelfit.tam.mml.3pl>) summary(<IRT.modelfit.tamaan>) tam.modelfit.IRT() tam.modelfit.args() tam.Q3() summary(<tam.Q3>) 

         		
         
Model Fit Statistics in TAM

+      

           
tam.np() summary(<tam.np>) IRT.cv(<tam.np>) 

         		
         
Unidimensional Non- and Semiparametric Item Response Model

+      

           
tam.personfit() 

         		
         
Person Outfit and Infit Statistics

+      

           
tam.pv() tam.pv.mcmc() summary(<tam.pv.mcmc>) plot(<tam.pv.mcmc>) 

         		
         
Plausible Value Imputation

+      

           
tam.se() tam_mml_se_quick() tam_latreg_se_quick() 

         		
         
Standard Error Estimation

+      

           
tam.threshold() 

         		
         
Calculation of Thurstonian Thresholds

+      

           
tam.wle() tam.mml.wle() tam.mml.wle2() tam_jml_wle() summary(<tam.wle>) print(<tam.wle>) 

         		
         
Weighted Likelihood Estimation and Maximum Likelihood Estimation of
 Person Parameters

+      

           
tamaan() summary(<tamaan>) print(<tamaan>) 

         		
         
Wrapper Function for TAM Language

+      

           
tamaanify() 

         		
         
Function for Parsing TAM Input

+      

           
tampv2datalist() 

         		
         
Conversion of Plausible Value Object into Datalist

+      

           
tam_downcode() 

         		
         
Downcoding an Item Response Dataset

+      

           
tam_irf_3pl() 

         		
         
Item Response Function for the 3PL Model

+      

           
tam_NA_pattern() tam_01_pattern() 

         		
         
Missing Data Patterns

+      

           
weighted_mean() weighted_var() weighted_sd() weighted_skewness() weighted_kurtosis() weighted_quantile() weighted_table() 

         		
         
Descriptive Statistics for Weighted Data

+      

           
WLErel() EAPrel() 

         		
         
Reliability Estimation in TAM

-  
+      

 
   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/reference/lavaanify.IRT.html b/docs/reference/lavaanify.IRT.html
index c2ea76c..8ff62ca 100644
--- a/docs/reference/lavaanify.IRT.html
+++ b/docs/reference/lavaanify.IRT.html
@@ -1,46 +1,5 @@
-
 
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-Slight Extension of the <code>lavaan</code> Syntax, with Focus on Item Response Models — lavaanify.IRT • TAM
-
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+    
 
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+      

   

     

     
Slight Extension of the lavaan Syntax, with Focus on Item Response Models

@@ -133,7 +65,7 @@ 
Slight Extension of the lavaan Syntax, with Focus on Item Respo
     

     
This functions slightly extends the lavaan
 syntax implemented in the lavaan package
-(see lavaan::lavaanify).

+(see lavaan::lavaanify).

 
Guessing and slipping parameters can be specified
 by using the operators ?=g1 and ?=s1,
 respectively.

@@ -144,286 +76,290 @@ 
Slight Extension of the lavaan Syntax, with Focus on Item Respo
 
Nonlinear terms can also be specified for loadings (=~) and
 regressions (~) (see Example 3).

 
It is also possible to construct the syntax using a loop by making use
-of the DO statement, see doparse for specification.

+of the DO statement, see doparse for specification.

 
The operators MEASERR1 and MEASERR0 can be used for
 model specification for variables which contains known measurement
 error (see Example 6). While MEASERR1 can be used for endogenous
 variables, MEASERR0 provides the specification for exogeneous variables.

     

 
-    
lavaanify.IRT(lavmodel, items=NULL, data=NULL, include.residuals=TRUE,
-    doparse=TRUE)

-
-    
Arguments

-    
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
lavmodel
A model in lavaan syntax plus the additional
-operators ?=g1, ?=s1, __ and nonlinear terms.
items
Optional vector of item names
data
Optional data frame with item responses
include.residuals
Optional logical indicating whether
-       residual variances should be processed such that they
-       are freely estimated.
doparse
Optional logical indicating whether lavmodel
-should be parsed for DO statements.

-
-    
Value

-
-    
A list with following entries

-
lavpartable
A lavaan parameter table

-
lavaan.syntax
Processed syntax for lavaan package

-
nonlin_factors
Data frame with renamed and original nonlinear
-factor specifications

-
nonlin_syntable
Data frame with original and modified
-syntax if nonlinear factors are used.

-
-    
See also

-
-    
lavaan::lavaanify

-
-
See sirt::tam2mirt for
-converting objects of class tam into mirt
-objects.

-
See sirt::lavaan2mirt
-for estimating models in the mirt package using lavaan syntax.

-
See doparse for the DO and DO2 statements.

-
-    
Examples

-    
library(lavaan)
-
-#############################################################################
-# EXAMPLE 1: lavaan syntax with guessing and slipping parameters
-#############################################################################
-
-# define model in lavaan
-lavmodel <- "
-    F=~ A1+c*A2+A3+A4
-    # define slipping parameters for A1 and A2
-    A1 + A2 ?=s1
-    # joint guessing parameter for A1 and A2
-    A1+A2 ?=c1*g1
-    A3 | 0.75*t1
-    # fix guessing parameter to .25 and
-    # slipping parameter to .01 for item A3
-    A3 ?=.25*g1+.01*s1
-    A4 ?=c2*g1
-    A1 | a*t1
-    A2 | b*t1
-      "
-
-# process lavaan syntax
-lavpartable <- TAM::lavaanify.IRT(lavmodel)$lavpartable
-  ##     id lhs op rhs user group free ustart exo label eq.id unco
-  ##  1   1   F=~  A1    1     1    1     NA   0           0    1
-  ##  2   2   F=~  A2    1     1    2     NA   0     c     0    2
-  ##  3   3   F=~  A3    1     1    3     NA   0           0    3
-  ##  4   4   F=~  A4    1     1    4     NA   0           0    4
-  ##  5   5  A3  |  t1    1     1    0   0.75   0           0    0
-  ##  6   6  A1  |  t1    1     1    5     NA   0     a     0    5
-  ##  7   7  A2  |  t1    1     1    6     NA   0     b     0    6
-  ##  8   8  A1 ?=s1    1     1    7     NA   0           0    7
-  ##  9   9  A2 ?=s1    1     1    8     NA   0           0    8
-  ##  10 10  A1 ?=g1    1     1    9     NA   0    c1     1    9
-  ##  11 11  A2 ?=g1    1     1    9     NA   0    c1     1   10
-  ##  12 12  A3 ?=g1    1     1    0   0.25   0           0    0
-  ##  13 13  A3 ?=s1    1     1    0   0.01   0           0    0
-  ##  14 14  A4 ?=g1    1     1   10     NA   0    c2     0   11
-
-if (FALSE) {
-#############################################################################
-# EXAMPLE 2: Usage of "__" and "?=" operators
-#############################################################################
-
-library(sirt)
-data(data.read, package="sirt")
-dat <- data.read
-items <- colnames(dat)
-
-lavmodel <- "
-   F1=~ A1+A2+ A3+lam4*A4
-   # equal item loadings for items B1 to B4
-   F2=~ lam5*B1__B4
-   # different labelled item loadings of items C1 to C4
-   F3=~ lam9__lam12*C1__C4
-   # item intercepts
-   B1__B2 | -0.5*t1
-   B3__C1 | int6*t1
-   # guessing parameters
-   C1__C3 ?=g1
-   C4 + B1__B3 ?=0.2*g1
-   # slipping parameters
-   A1__B1 + B3__C2 ?=slip1*s1
-   # residual variances
-   B1__B3 ~~ errB*B1__B3
-   A2__A4 ~~ erra1__erra3*A2__A4
-    "
-lav2 <- TAM::lavaanify.IRT( lavmodel, data=dat)
-lav2$lavpartable
-cat( lav2$lavaan.syntax )
+    

+    
lavaanify.IRT(lavmodel, items=NULL, data=NULL, include.residuals=TRUE,
+    doparse=TRUE)

+    

 
-#** simplified example
-lavmodel <- "
-   F1=~ A1+lam4*A2+A3+lam4*A4
-   F2=~ lam5__lam8*B1__B4
-   F1 ~~ F2
-   F1 ~~ 1*F1
-   F2 ~~ 1*F2
-    "
-lav3 <- TAM::lavaanify.IRT( lavmodel, data=dat)
-lav3$lavpartable
-cat( lav3$lavaan.syntax )
+    

+    
Arguments

+    
lavmodel

+
A model in lavaan syntax plus the additional
+operators ?=g1, ?=s1, __ and nonlinear terms.

 
-#############################################################################
-# EXAMPLE 3: Nonlinear terms
-#############################################################################
+
items

+
Optional vector of item names

 
-#*** define items
-items <- paste0("I",1:12)
+
data

+
Optional data frame with item responses

 
-#*** define lavaan model
-lavmodel <- "
-   F1=~ I1__I5
-   F2=~ I6__I9
-   F3=~ I10__I12
-   # I3, I4 and I7 load on interaction of F1 and F2
-   I(F1*F2)=~ a*I3+a*I4
-   I(F1*F2)=~ I7
-   # I3 and I5 load on squared factor F1
-   I(F1^2)=~ I3 + I5
-   # I1 regression on B spline version of factor F1
-   I( bs(F1,4) )=~ I1
-   F2 ~ F1 + b*I(F1^2) + I(F1>0)
-   F3 ~ F1 + F2 + 1.4*I(F1*F2) + b*I(F1^2) + I(F2^2 )
-   # F3 ~ F2 + I(F2^2)      # this line is ignored in the lavaan model
-   F1 ~~ 1*F1
-    "
+
include.residuals

+
Optional logical indicating whether
+       residual variances should be processed such that they
+       are freely estimated.

 
-#*** process lavaan syntax
-lav3 <- TAM::lavaanify.IRT( lavmodel, items=items)
+
doparse

+
Optional logical indicating whether lavmodel
+should be parsed for DO statements.

 
-#*** inspect results
-lav3$lavpartable
-cat( lav3$lavaan.syntax )
-lav3$nonlin_syntable
-lav3$nonlin_factors
+

+    

+    
Value

+    
 
-#############################################################################
-# EXAMPLE 4: Using lavaanify.IRT for estimation with lavaan
-#############################################################################
+
A list with following entries

+
lavpartable

+
A lavaan parameter table

 
-data(data.big5, package="sirt")
-# extract first 10 openness items
-items <- which( substring( colnames(data.big5), 1, 1 )=="O"  )[1:10]
-dat <- as.data.frame( data.big5[, items ] )
-  ##   > colnames(dat)
-  ##    [1] "O3"  "O8"  "O13" "O18" "O23" "O28" "O33" "O38" "O43" "O48"
-apply(dat,2,var)  # variances
+
lavaan.syntax

+
Processed syntax for lavaan package

 
-#*** Model 1: Confirmatory factor analysis with one factor
-lavmodel <- "
-   O=~ O3__O48   # convenient syntax for defining the factor for all items
-   O ~~ 1*O
-   "
-# process lavaan syntax
-res <- TAM::lavaanify.IRT( lavmodel, data=dat )
-# estimate lavaan model
-mod1 <- lavaan::lavaan( model=res$lavaan.syntax, data=dat)
-summary(mod1, standardized=TRUE, fit.measures=TRUE, rsquare=TRUE )
-}
+
nonlin_factors

+
Data frame with renamed and original nonlinear
+factor specifications

 
-#############################################################################
-# EXAMPLE 5: lavaanify.IRT with do statements
-#############################################################################
+
nonlin_syntable

+
Data frame with original and modified
+syntax if nonlinear factors are used.

 
-lavmodel <- "
-  DO(1,6,1)
-    F=~ I%
-  DOEND
-  DO(1,5,2)
-    A=~ I%
-  DOEND
-  DO(2,6,2)
-    B=~ I%
-  DOEND
-  F ~~ 1*F
-  A ~~ 1*A
-  B ~~ 1*B
-  F ~~ 0*A
-  F ~~ 0*B
-  A ~~ 0*B
-   "
-res <- TAM::lavaanify.IRT( lavmodel, items=paste("I",1:6) )
-cat(res$lavaan.syntax)
+

+    

+    
See also

+    
lavaan::lavaanify

 
-#############################################################################
-# EXAMPLE 6: Single indicator models with measurement error (MEASERR operator)
-#############################################################################
+
See sirt::tam2mirt for
+converting objects of class tam into mirt
+objects.

+
See sirt::lavaan2mirt
+for estimating models in the mirt package using lavaan syntax.

+
See doparse for the DO and DO2 statements.

+    

 
-# define lavaan model
-lavmodel <- "
-  ytrue ~ xtrue + z
-  # exogeneous variable error-prone y with error variance .20
-  MEASERR1(ytrue,y,.20)
-  # exogeneous variable error-prone x with error variance .35
-  MEASERR0(xtrue,x,.35)
-  ytrue ~~ ytrue
-    "
-# observed items
-items <- c("y","x","z")
-# lavaanify
-res <- TAM::lavaanify.IRT( lavmodel, items )
-cat(res$lavaan.syntax)
-  ##   > cat(res$lavaan.syntax)
-  ##   ytrue~xtrue
-  ##   ytrue~z
-  ##   ytrue=~1*y
-  ##   y~~0.2*y
-  ##   xtrue=~1*x
-  ##   x~~0.35*x
-  ##   xtrue~~xtrue
-  ##   ytrue~~ytrue
-  ##   z~~z

+    

+    
Examples

+    
library(lavaan)
+
+#############################################################################
+# EXAMPLE 1: lavaan syntax with guessing and slipping parameters
+#############################################################################
+
+# define model in lavaan
+lavmodel <- "
+    F=~ A1+c*A2+A3+A4
+    # define slipping parameters for A1 and A2
+    A1 + A2 ?=s1
+    # joint guessing parameter for A1 and A2
+    A1+A2 ?=c1*g1
+    A3 | 0.75*t1
+    # fix guessing parameter to .25 and
+    # slipping parameter to .01 for item A3
+    A3 ?=.25*g1+.01*s1
+    A4 ?=c2*g1
+    A1 | a*t1
+    A2 | b*t1
+      "
+
+# process lavaan syntax
+lavpartable <- TAM::lavaanify.IRT(lavmodel)$lavpartable
+  ##     id lhs op rhs user group free ustart exo label eq.id unco
+  ##  1   1   F=~  A1    1     1    1     NA   0           0    1
+  ##  2   2   F=~  A2    1     1    2     NA   0     c     0    2
+  ##  3   3   F=~  A3    1     1    3     NA   0           0    3
+  ##  4   4   F=~  A4    1     1    4     NA   0           0    4
+  ##  5   5  A3  |  t1    1     1    0   0.75   0           0    0
+  ##  6   6  A1  |  t1    1     1    5     NA   0     a     0    5
+  ##  7   7  A2  |  t1    1     1    6     NA   0     b     0    6
+  ##  8   8  A1 ?=s1    1     1    7     NA   0           0    7
+  ##  9   9  A2 ?=s1    1     1    8     NA   0           0    8
+  ##  10 10  A1 ?=g1    1     1    9     NA   0    c1     1    9
+  ##  11 11  A2 ?=g1    1     1    9     NA   0    c1     1   10
+  ##  12 12  A3 ?=g1    1     1    0   0.25   0           0    0
+  ##  13 13  A3 ?=s1    1     1    0   0.01   0           0    0
+  ##  14 14  A4 ?=g1    1     1   10     NA   0    c2     0   11
+
+if (FALSE) {
+#############################################################################
+# EXAMPLE 2: Usage of "__" and "?=" operators
+#############################################################################
+
+library(sirt)
+data(data.read, package="sirt")
+dat <- data.read
+items <- colnames(dat)
+
+lavmodel <- "
+   F1=~ A1+A2+ A3+lam4*A4
+   # equal item loadings for items B1 to B4
+   F2=~ lam5*B1__B4
+   # different labelled item loadings of items C1 to C4
+   F3=~ lam9__lam12*C1__C4
+   # item intercepts
+   B1__B2 | -0.5*t1
+   B3__C1 | int6*t1
+   # guessing parameters
+   C1__C3 ?=g1
+   C4 + B1__B3 ?=0.2*g1
+   # slipping parameters
+   A1__B1 + B3__C2 ?=slip1*s1
+   # residual variances
+   B1__B3 ~~ errB*B1__B3
+   A2__A4 ~~ erra1__erra3*A2__A4
+    "
+lav2 <- TAM::lavaanify.IRT( lavmodel, data=dat)
+lav2$lavpartable
+cat( lav2$lavaan.syntax )
+
+#** simplified example
+lavmodel <- "
+   F1=~ A1+lam4*A2+A3+lam4*A4
+   F2=~ lam5__lam8*B1__B4
+   F1 ~~ F2
+   F1 ~~ 1*F1
+   F2 ~~ 1*F2
+    "
+lav3 <- TAM::lavaanify.IRT( lavmodel, data=dat)
+lav3$lavpartable
+cat( lav3$lavaan.syntax )
+
+#############################################################################
+# EXAMPLE 3: Nonlinear terms
+#############################################################################
+
+#*** define items
+items <- paste0("I",1:12)
+
+#*** define lavaan model
+lavmodel <- "
+   F1=~ I1__I5
+   F2=~ I6__I9
+   F3=~ I10__I12
+   # I3, I4 and I7 load on interaction of F1 and F2
+   I(F1*F2)=~ a*I3+a*I4
+   I(F1*F2)=~ I7
+   # I3 and I5 load on squared factor F1
+   I(F1^2)=~ I3 + I5
+   # I1 regression on B spline version of factor F1
+   I( bs(F1,4) )=~ I1
+   F2 ~ F1 + b*I(F1^2) + I(F1>0)
+   F3 ~ F1 + F2 + 1.4*I(F1*F2) + b*I(F1^2) + I(F2^2 )
+   # F3 ~ F2 + I(F2^2)      # this line is ignored in the lavaan model
+   F1 ~~ 1*F1
+    "
+
+#*** process lavaan syntax
+lav3 <- TAM::lavaanify.IRT( lavmodel, items=items)
+
+#*** inspect results
+lav3$lavpartable
+cat( lav3$lavaan.syntax )
+lav3$nonlin_syntable
+lav3$nonlin_factors
+
+#############################################################################
+# EXAMPLE 4: Using lavaanify.IRT for estimation with lavaan
+#############################################################################
+
+data(data.big5, package="sirt")
+# extract first 10 openness items
+items <- which( substring( colnames(data.big5), 1, 1 )=="O"  )[1:10]
+dat <- as.data.frame( data.big5[, items ] )
+  ##   > colnames(dat)
+  ##    [1] "O3"  "O8"  "O13" "O18" "O23" "O28" "O33" "O38" "O43" "O48"
+apply(dat,2,var)  # variances
+
+#*** Model 1: Confirmatory factor analysis with one factor
+lavmodel <- "
+   O=~ O3__O48   # convenient syntax for defining the factor for all items
+   O ~~ 1*O
+   "
+# process lavaan syntax
+res <- TAM::lavaanify.IRT( lavmodel, data=dat )
+# estimate lavaan model
+mod1 <- lavaan::lavaan( model=res$lavaan.syntax, data=dat)
+summary(mod1, standardized=TRUE, fit.measures=TRUE, rsquare=TRUE )
+}
+
+#############################################################################
+# EXAMPLE 5: lavaanify.IRT with do statements
+#############################################################################
+
+lavmodel <- "
+  DO(1,6,1)
+    F=~ I%
+  DOEND
+  DO(1,5,2)
+    A=~ I%
+  DOEND
+  DO(2,6,2)
+    B=~ I%
+  DOEND
+  F ~~ 1*F
+  A ~~ 1*A
+  B ~~ 1*B
+  F ~~ 0*A
+  F ~~ 0*B
+  A ~~ 0*B
+   "
+res <- TAM::lavaanify.IRT( lavmodel, items=paste("I",1:6) )
+cat(res$lavaan.syntax)
+
+#############################################################################
+# EXAMPLE 6: Single indicator models with measurement error (MEASERR operator)
+#############################################################################
+
+# define lavaan model
+lavmodel <- "
+  ytrue ~ xtrue + z
+  # exogeneous variable error-prone y with error variance .20
+  MEASERR1(ytrue,y,.20)
+  # exogeneous variable error-prone x with error variance .35
+  MEASERR0(xtrue,x,.35)
+  ytrue ~~ ytrue
+    "
+# observed items
+items <- c("y","x","z")
+# lavaanify
+res <- TAM::lavaanify.IRT( lavmodel, items )
+cat(res$lavaan.syntax)
+  ##   > cat(res$lavaan.syntax)
+  ##   ytrue~xtrue
+  ##   ytrue~z
+  ##   ytrue=~1*y
+  ##   y~~0.2*y
+  ##   xtrue=~1*x
+  ##   x~~0.35*x
+  ##   xtrue~~xtrue
+  ##   ytrue~~ytrue
+  ##   z~~z

+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/reference/msq.itemfit.html b/docs/reference/msq.itemfit.html
index aab8627..1c489e9 100644
--- a/docs/reference/msq.itemfit.html
+++ b/docs/reference/msq.itemfit.html
@@ -1,73 +1,18 @@
-
 
-
-  
-  
-
-
-
-Mean Squared Residual Based Item Fit Statistics (Infit, Outfit) — msq.itemfit • TAM
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
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-
-
-
-
-Mean Squared Residual Based Item Fit Statistics (Infit, Outfit) — msq.itemfit • TAM
-
-
-
-
-
-
-
-
-
-
-
-
-  
+
+    
 
-  
     

-      

-      
 
       
 
-      

-
-

+      

   

     

     
Mean Squared Residual Based Item Fit Statistics (Infit, Outfit)

@@ -121,220 +53,220 @@ 
Mean Squared Residual Based Item Fit Statistics (Infit, Outfit)

 
     

     
The function msq.itemfit computes computed the outfit and infit statistic
-for items or item groups. Contrary to tam.fit, the function
+for items or item groups. Contrary to tam.fit, the function
 msq.itemfit is not based on simulation from individual posterior distributions
 but rather on evaluating the individual posterior.

 
The function msq.itemfit also computes the outfit and infit statistics
 but these are based on weighted likelihood estimates obtained from
-tam.wle.

+tam.wle.

     

 
-    
msq.itemfit( object, fitindices=NULL)
-
-# S3 method for msq.itemfit
-summary(object, file=NULL, ... )
-
-msq.itemfitWLE( tamobj, fitindices=NULL, ... )
-
-# S3 method for msq.itemfitWLE
-summary(object, file=NULL, ... )

-
-    
Arguments

-    
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
object
Object for which the classes IRT.data,
-  IRT.posterior and predict are defined.
fitindices
Vector with parameter labels defining the item groups for
-which the fit should be evaluated.
tamobj
Object of class tam.mml, tam.mml.2pl
-  or tam.mml.mfr.
file
Optional name of a file to which the summary should be written
...
Further arguments to be passed

-
-    
Value

-
-    
List with following entries

-
itemfit
Data frame with outfit and infit statistics.

-
summary_itemfit
Summary statistics of outfit
-and infit

-
-    
See also

-
-    
See also tam.fit for simulation based assessment of item fit.

-
See also eRm::itemfit or mirt::itemfit.

-
-    
Examples

-    
if (FALSE) {
-
-#############################################################################
-# EXAMPLE 1: Simulated data Rasch model
-#############################################################################
-
-#*** simulate data
-library(sirt)
-set.seed(9875)
-N <- 2000
-I <- 20
-b <- sample( seq( -2, 2, length=I ) )
-a <- rep( 1, I )
-# create some misfitting items
-a[c(1,3)] <- c(.5, 1.5 )
-# simulate data
-dat <- sirt::sim.raschtype( rnorm(N), b=b, fixed.a=a )
-#*** estimate Rasch model
-mod1 <- TAM::tam.mml(resp=dat)
-# compute WLEs
-wmod1 <- TAM::tam.wle(mod1)$theta
-
-#--- item fit from "msq.itemfit" function
-fit1 <- TAM::msq.itemfit(mod1)
-summary( fit1 )
-
-#--- item fit using simulation in "tam.fit"
-fit0 <- TAM::tam.fit( mod1 )
-summary(fit0)
-
-#--- item fit based on WLEs
-fit2a <- TAM::msq.itemfitWLE( mod1 )
-summary(fit2a)
-
-#++ fit assessment in mirt package
-library(mirt)
-mod1b <- mirt::mirt( dat, model=1, itemtype="Rasch", verbose=TRUE )
-print(mod1b)
-sirt::mirt.wrapper.coef(mod1b)
-fmod1b <- mirt::itemfit(mod1b, Theta=as.matrix(wmod1,ncol=1),
-                 Zh=TRUE, X2=FALSE, S_X2=FALSE )
-cbind( fit2a$fit_data, fmod1b )
-
-#++ fit assessment in eRm package
-library(eRm)
-mod1c <- eRm::RM( dat )
-summary(mod1c)
-eRm::plotPImap(mod1c)    # person-item map
-pmod1c <- eRm::person.parameter(mod1c)
-fmod1c <- eRm::itemfit(pmod1c)
-print(fmod1c)
-plot(fmod1c)
-
-#--- define some item groups for fit assessment
-
-# bases on evaluating the posterior
-fitindices <- rep( paste0("IG",c(1,2)), each=10)
-fit2 <- TAM::msq.itemfit( mod1, fitindices )
-summary(fit2)
-
-# using WLEs
-fit2b <- TAM::msq.itemfitWLE( mod1, fitindices )
-summary(fit2b)
-
-#############################################################################
-# EXAMPLE 2: data.read | fit statistics assessed for testlets
-#############################################################################
-
-library(sirt)
-data(data.read,package="sirt")
-dat <- data.read
+    

+    
msq.itemfit( object, fitindices=NULL)
+
+# S3 method for msq.itemfit
+summary(object, file=NULL, ... )
+
+msq.itemfitWLE( tamobj, fitindices=NULL, ... )
+
+# S3 method for msq.itemfitWLE
+summary(object, file=NULL, ... )

+    

 
-# fit Rasch model
-mod <- TAM::tam.mml( dat )
+    

+    
Arguments

+    
object

+
Object for which the classes IRT.data,
+  IRT.posterior and predict are defined.

 
-#***** item fit for each item
-# based on posterior
-res1 <- TAM::msq.itemfit( mod  )
-summary(res1)
-# based on WLEs
-res2 <- TAM::msq.itemfitWLE( mod  )
-summary(res2)
+
fitindices

+
Vector with parameter labels defining the item groups for
+which the fit should be evaluated.

 
-#***** item fit for item groups
-# define item groups
-fitindices <- substring( colnames(dat), 1, 1 )
-# based on posterior
-res1 <- TAM::msq.itemfit( mod, fitindices )
-summary(res1)
-# based on WLEs
-res2 <- TAM::msq.itemfitWLE( mod, fitindices )
-summary(res2)
+
tamobj

+
Object of class tam.mml, tam.mml.2pl
+  or tam.mml.mfr.

 
-#############################################################################
-# EXAMPLE 3: Fit statistics for rater models
-#############################################################################
+
file

+
Optional name of a file to which the summary should be written

 
-library(sirt)
-data(data.ratings2, package="sirt")
-dat <- data.ratings2
+
...

+
Further arguments to be passed

 
-# fit rater model "~ item*step + rater"
-mod <- TAM::tam.mml.mfr( resp=dat[, paste0( "k",1:5) ],
-            facets=dat[, "rater", drop=FALSE],
-            pid=dat$pid, formulaA=~ item*step + rater )
+

+    

+    
Value

+    
 
-# fit for parameter with "tam.fit" function
-fmod1a <- TAM::tam.fit( mod )
-fmod1b <- TAM::msq.itemfit( mod )
-summary(fmod1a)
-summary(fmod1b)
+
List with following entries

+
itemfit

+
Data frame with outfit and infit statistics.

 
-# define item groups using pseudo items from object "mod"
-pseudo_items <- colnames(mod$resp)
-pss <- strsplit( pseudo_items, split="-" )
-item_parm <- unlist( lapply( pss, FUN=function(ll){ ll[1] } ) )
-rater_parm <- unlist( lapply( pss, FUN=function(ll){ ll[2] } ) )
+
summary_itemfit

+
Summary statistics of outfit
+and infit

 
-# fit for items with "msq.itemfit" functions
-res2a <- TAM::msq.itemfit( mod, item_parm )
-res2b <- TAM::msq.itemfitWLE( mod, item_parm )
-summary(res2a)
-summary(res2b)
+

+    

+    
See also

+    
See also tam.fit for simulation based assessment of item fit.

+
See also eRm::itemfit or mirt::itemfit.

+    

 
-# fit for raters
-res3a <- TAM::msq.itemfit( mod, rater_parm )
-res3b <- TAM::msq.itemfitWLE( mod, rater_parm )
-summary(res3a)
-summary(res3b)
-}

+    

+    
Examples

+    
if (FALSE) {
+
+#############################################################################
+# EXAMPLE 1: Simulated data Rasch model
+#############################################################################
+
+#*** simulate data
+library(sirt)
+set.seed(9875)
+N <- 2000
+I <- 20
+b <- sample( seq( -2, 2, length=I ) )
+a <- rep( 1, I )
+# create some misfitting items
+a[c(1,3)] <- c(.5, 1.5 )
+# simulate data
+dat <- sirt::sim.raschtype( rnorm(N), b=b, fixed.a=a )
+#*** estimate Rasch model
+mod1 <- TAM::tam.mml(resp=dat)
+# compute WLEs
+wmod1 <- TAM::tam.wle(mod1)$theta
+
+#--- item fit from "msq.itemfit" function
+fit1 <- TAM::msq.itemfit(mod1)
+summary( fit1 )
+
+#--- item fit using simulation in "tam.fit"
+fit0 <- TAM::tam.fit( mod1 )
+summary(fit0)
+
+#--- item fit based on WLEs
+fit2a <- TAM::msq.itemfitWLE( mod1 )
+summary(fit2a)
+
+#++ fit assessment in mirt package
+library(mirt)
+mod1b <- mirt::mirt( dat, model=1, itemtype="Rasch", verbose=TRUE )
+print(mod1b)
+sirt::mirt.wrapper.coef(mod1b)
+fmod1b <- mirt::itemfit(mod1b, Theta=as.matrix(wmod1,ncol=1),
+                 Zh=TRUE, X2=FALSE, S_X2=FALSE )
+cbind( fit2a$fit_data, fmod1b )
+
+#++ fit assessment in eRm package
+library(eRm)
+mod1c <- eRm::RM( dat )
+summary(mod1c)
+eRm::plotPImap(mod1c)    # person-item map
+pmod1c <- eRm::person.parameter(mod1c)
+fmod1c <- eRm::itemfit(pmod1c)
+print(fmod1c)
+plot(fmod1c)
+
+#--- define some item groups for fit assessment
+
+# bases on evaluating the posterior
+fitindices <- rep( paste0("IG",c(1,2)), each=10)
+fit2 <- TAM::msq.itemfit( mod1, fitindices )
+summary(fit2)
+
+# using WLEs
+fit2b <- TAM::msq.itemfitWLE( mod1, fitindices )
+summary(fit2b)
+
+#############################################################################
+# EXAMPLE 2: data.read | fit statistics assessed for testlets
+#############################################################################
+
+library(sirt)
+data(data.read,package="sirt")
+dat <- data.read
+
+# fit Rasch model
+mod <- TAM::tam.mml( dat )
+
+#***** item fit for each item
+# based on posterior
+res1 <- TAM::msq.itemfit( mod  )
+summary(res1)
+# based on WLEs
+res2 <- TAM::msq.itemfitWLE( mod  )
+summary(res2)
+
+#***** item fit for item groups
+# define item groups
+fitindices <- substring( colnames(dat), 1, 1 )
+# based on posterior
+res1 <- TAM::msq.itemfit( mod, fitindices )
+summary(res1)
+# based on WLEs
+res2 <- TAM::msq.itemfitWLE( mod, fitindices )
+summary(res2)
+
+#############################################################################
+# EXAMPLE 3: Fit statistics for rater models
+#############################################################################
+
+library(sirt)
+data(data.ratings2, package="sirt")
+dat <- data.ratings2
+
+# fit rater model "~ item*step + rater"
+mod <- TAM::tam.mml.mfr( resp=dat[, paste0( "k",1:5) ],
+            facets=dat[, "rater", drop=FALSE],
+            pid=dat$pid, formulaA=~ item*step + rater )
+
+# fit for parameter with "tam.fit" function
+fmod1a <- TAM::tam.fit( mod )
+fmod1b <- TAM::msq.itemfit( mod )
+summary(fmod1a)
+summary(fmod1b)
+
+# define item groups using pseudo items from object "mod"
+pseudo_items <- colnames(mod$resp)
+pss <- strsplit( pseudo_items, split="-" )
+item_parm <- unlist( lapply( pss, FUN=function(ll){ ll[1] } ) )
+rater_parm <- unlist( lapply( pss, FUN=function(ll){ ll[2] } ) )
+
+# fit for items with "msq.itemfit" functions
+res2a <- TAM::msq.itemfit( mod, item_parm )
+res2b <- TAM::msq.itemfitWLE( mod, item_parm )
+summary(res2a)
+summary(res2b)
+
+# fit for raters
+res3a <- TAM::msq.itemfit( mod, rater_parm )
+res3b <- TAM::msq.itemfitWLE( mod, rater_parm )
+summary(res3a)
+summary(res3b)
+}

+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/reference/plot.tam.html b/docs/reference/plot.tam.html
index ce4b79b..6822134 100644
--- a/docs/reference/plot.tam.html
+++ b/docs/reference/plot.tam.html
@@ -1,68 +1,13 @@
-
 
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-  
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-Plot Function for Unidimensional Item Response Models — plot.tam • TAM
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-Plot Function for Unidimensional Item Response Models — plot.tam • TAM
-
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-  
+
+    
 
-  
     

-      

-      
 
       
 
-      

-
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+      

   

     

     
Plot Function for Unidimensional Item Response Models

@@ -119,187 +51,176 @@ 
Plot Function for Unidimensional Item Response Models

 or tam.mml.

     

 
-    
# S3 method for tam
-plot(x, items=1:x$nitems, type="expected", low=-3, high=3, ngroups=6,
-                   groups_by_item=FALSE, wle=NULL, export=TRUE, export.type="png",
-                   export.args=list(), observed=TRUE, overlay=FALSE,
-                   ask=FALSE, package="lattice", fix.devices=TRUE, nnodes=100, ...)
-
-# S3 method for tam.mml
-plot(x, items=1:x$nitems, type="expected", low=-3, high=3, ngroups=6,
-                       groups_by_item=FALSE, wle=NULL, export=TRUE, export.type="png",
-                       export.args=list(), observed=TRUE, overlay=FALSE,
-                       ask=FALSE,  package="lattice",  fix.devices=TRUE, nnodes=100, ...)
-
-# S3 method for tam.jml
-plot(x, items=1:x$nitems, type="expected", low=-3, high=3, ngroups=6,
-                       groups_by_item=FALSE, wle=NULL, export=TRUE, export.type="png",
-                       export.args=list(), observed=TRUE, overlay=FALSE,
-                       ask=FALSE,  package="lattice", fix.devices=TRUE, nnodes=100, ...)

-
-    
Arguments

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-    
-    
x
Object of class tam, tam.mml
-or tam.mml.
items
An index vector giving the items to be visualized.
type
Plot type. type="expected" plot the expected item
+    

+    
# S3 method for tam
+plot(x, items=1:x$nitems, type="expected", low=-3, high=3, ngroups=6,
+                   groups_by_item=FALSE, wle=NULL, export=TRUE, export.type="png",
+                   export.args=list(), observed=TRUE, overlay=FALSE,
+                   ask=FALSE, package="lattice", fix.devices=TRUE, nnodes=100, ...)
+
+# S3 method for tam.mml
+plot(x, items=1:x$nitems, type="expected", low=-3, high=3, ngroups=6,
+                       groups_by_item=FALSE, wle=NULL, export=TRUE, export.type="png",
+                       export.args=list(), observed=TRUE, overlay=FALSE,
+                       ask=FALSE,  package="lattice",  fix.devices=TRUE, nnodes=100, ...)
+
+# S3 method for tam.jml
+plot(x, items=1:x$nitems, type="expected", low=-3, high=3, ngroups=6,
+                       groups_by_item=FALSE, wle=NULL, export=TRUE, export.type="png",
+                       export.args=list(), observed=TRUE, overlay=FALSE,
+                       ask=FALSE,  package="lattice", fix.devices=TRUE, nnodes=100, ...)

+    

+
+    

+    
Arguments

+    
x

+
Object of class tam, tam.mml
+or tam.mml.

+
+
items

+
An index vector giving the items to be visualized.

+
+
type

+
Plot type. type="expected" plot the expected item
     response curves while type="items" plots the response
-    curves of all item categories.
low
Lowest \(\theta\) value to be displayed
high
Highest \(\theta\) value to be displayed
ngroups
Number of score groups to be displayed. The default are
-six groups.
groups_by_item
Logical indicating whether grouping of persons
+    curves of all item categories.

+
+  
low

+
Lowest \(\theta\) value to be displayed

+
+  
high

+
Highest \(\theta\) value to be displayed

+
+  
ngroups

+
Number of score groups to be displayed. The default are
+six groups.

+
+
groups_by_item

+
Logical indicating whether grouping of persons
 should be conducted item-wise. The groupings will differ from item to item
-in case of missing item responses.
wle
Use WLE estimate for displaying observed scores.
export
A logical which indicates whether all graphics should be separately
+in case of missing item responses.

+
+  
wle

+
Use WLE estimate for displaying observed scores.

+
+  
export

+
A logical which indicates whether all graphics should be separately
 exported in files of type export.type in a subdirectory 'Plots'
-of the working directory.
export.type
A string which indicates the type of the graphics export. For currently
+of the working directory.

+
+
export.type

+
A string which indicates the type of the graphics export. For currently
   supported file types, see
-grDevices::dev.new.
export.args
A list of arguments that are passed to the export method can be specified.
-  See the respective export device method for supported usage.
observed
A logical which indicates whether observed response curve should
-  be displayed
overlay
A logical indicating whether expected score functions should overlay.
ask
A logical which asks for changing the graphic from item to item.
-  The default is FALSE.
package
Used R package for plot. Can be "lattice" or
-"graphics".
fix.devices
Optional logical indicating whether old graphics devices should
-     be saved.
nnodes
Number of \(\theta\) points at which item response functions
-are evaluated
...
Further arguments to be passed

-
-    
Details

+grDevices::dev.new.

+
+
export.args

+
A list of arguments that are passed to the export method can be specified.
+  See the respective export device method for supported usage.

+
+
observed

+
A logical which indicates whether observed response curve should
+  be displayed

+
+
overlay

+
A logical indicating whether expected score functions should overlay.

 
+
ask

+
A logical which asks for changing the graphic from item to item.
+  The default is FALSE.

+
+
package

+
Used R package for plot. Can be "lattice" or
+"graphics".

+
+
fix.devices

+
Optional logical indicating whether old graphics devices should
+     be saved.

+
+
nnodes

+
Number of \(\theta\) points at which item response functions
+are evaluated

+
+
...

+
Further arguments to be passed

+
+

+    

+    
Details

     
This plot method does not work for multidimensional item response
 models.

-    
Value

-
-    
A plot and list of computed values for plot (if saved as an object)

-    
See also

+    

+    

+    
Value

+    
 
-    
See CDM::IRT.irfprobPlot
+
A plot and list of computed values for plot (if saved as an object)

+    

+    

+    
Author

+    
Margaret Wu, Thomas Kiefer, Alexander Robitzsch, Michal Modzelewski

+    

+    

+    
See also

+    
See CDM::IRT.irfprobPlot
 for a general plot method.

+    

 
-    
Examples

-    
if (FALSE) {
-#############################################################################
-# EXAMPLE 1: Dichotomous data data.sim.rasch
-#############################################################################
-
-data(data.sim.rasch)
-mod <- TAM::tam.mml(data.sim.rasch)
-# expected response curves
-plot(mod, items=1:5, export=FALSE)
-# export computed values
-out <- plot(mod, items=1:5, export=FALSE)
-# item response curves
-plot(mod, items=1:5, type="items", export=FALSE)
-# plot with graphics package
-plot(mod, items=1:5, type="items", export=FALSE, ask=TRUE, package="graphics")
-
-#############################################################################
-# EXAMPLE 2: Polytomous data
-#############################################################################
-
-data(data.Students, package="CDM")
-dat <- data.Students[, c("sc3","sc4", "mj1", "mj2" )]
-dat <- na.omit(dat)
-dat[ dat[,1]==3, 1 ] <- 2   # modify data
-dat[ 1:20, 2 ] <- 4
-
-# estimate model
-mod1 <- TAM::tam.mml( dat )
-# plot item response curves and expected response curves
-plot(mod1, type="items", export=FALSE)
-plot(mod1, type="expected", export=FALSE )
-}

+    

+    
Examples

+    
if (FALSE) {
+#############################################################################
+# EXAMPLE 1: Dichotomous data data.sim.rasch
+#############################################################################
+
+data(data.sim.rasch)
+mod <- TAM::tam.mml(data.sim.rasch)
+# expected response curves
+plot(mod, items=1:5, export=FALSE)
+# export computed values
+out <- plot(mod, items=1:5, export=FALSE)
+# item response curves
+plot(mod, items=1:5, type="items", export=FALSE)
+# plot with graphics package
+plot(mod, items=1:5, type="items", export=FALSE, ask=TRUE, package="graphics")
+
+#############################################################################
+# EXAMPLE 2: Polytomous data
+#############################################################################
+
+data(data.Students, package="CDM")
+dat <- data.Students[, c("sc3","sc4", "mj1", "mj2" )]
+dat <- na.omit(dat)
+dat[ dat[,1]==3, 1 ] <- 2   # modify data
+dat[ 1:20, 2 ] <- 4
+
+# estimate model
+mod1 <- TAM::tam.mml( dat )
+# plot item response curves and expected response curves
+plot(mod1, type="items", export=FALSE)
+plot(mod1, type="expected", export=FALSE )
+}

+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
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+  
 
+  
 
diff --git a/docs/reference/plotDevianceTAM.html b/docs/reference/plotDevianceTAM.html
index 413b447..d44f9ae 100644
--- a/docs/reference/plotDevianceTAM.html
+++ b/docs/reference/plotDevianceTAM.html
@@ -1,67 +1,12 @@
-
 
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-Deviance Plot for <span class="pkg">TAM</span> Objects — plotDevianceTAM • TAM
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-Deviance Plot for TAM Objects — plotDevianceTAM • TAM
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Deviance Plot for TAM Objects

@@ -117,70 +49,68 @@ 
Deviance Plot for TAM Objects

     
Plots the deviance change in every iteration.

     

 
-    
plotDevianceTAM(tam.obj, omitUntil=1, reverse=TRUE, change=TRUE)

-
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Arguments

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tam.obj
Object of class tam.mml, tam.mml.2pl or tam.mml.mfr.
omitUntil
An optional value indicating number of iterations to be omitted for
-plotting.
reverse
A logical indicating whether the deviance change should be
-multiplied by minus 1. The default is TRUE.
change
An optional logical indicating whether deviance change
-or the deviance should be plotted.

-
-
-    
Examples

-    
#############################################################################
-# EXAMPLE 1: deviance plot dichotomous data
-#############################################################################
-data(data.sim.rasch)
-
-# 2PL model
-mod1 <- TAM::tam.mml.2pl(resp=data.sim.rasch )
-# plot deviance change
-plotDevianceTAM( mod1 )
-# plot deviance
-plotDevianceTAM( mod1, change=FALSE)

+    

+    
plotDevianceTAM(tam.obj, omitUntil=1, reverse=TRUE, change=TRUE)

+    

+
+    

+    
Arguments

+    
tam.obj

+
Object of class tam.mml, tam.mml.2pl or tam.mml.mfr.

+
+  
omitUntil

+
An optional value indicating number of iterations to be omitted for
+plotting.

+
+  
reverse

+
A logical indicating whether the deviance change should be
+multiplied by minus 1. The default is TRUE.

+
+
change

+
An optional logical indicating whether deviance change
+or the deviance should be plotted.

+
+

+    

+    
Author

+    
Martin Hecht, Sebastian Weirich, Alexander Robitzsch

+    

+
+    

+    
Examples

+    
#############################################################################
+# EXAMPLE 1: deviance plot dichotomous data
+#############################################################################
+data(data.sim.rasch)
+
+# 2PL model
+mod1 <- TAM::tam.mml.2pl(resp=data.sim.rasch )
+# plot deviance change
+plotDevianceTAM( mod1 )
+# plot deviance
+plotDevianceTAM( mod1, change=FALSE)

+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/reference/predict.html b/docs/reference/predict.html
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-Expected Values and Predicted Probabilities for Fitted <span class="pkg">TAM</span> Models — predict • TAM
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-Expected Values and Predicted Probabilities for Fitted TAM Models — predict • TAM
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+      

   

     

     
Expected Values and Predicted Probabilities for Fitted TAM Models

@@ -123,71 +55,72 @@ 
Expected Values and Predicted Probabilities for Fitted TAM
 for more details.

     

 
-    
# S3 method for tam.mml
-predict(object, ...)
-
-# S3 method for tam.mml.3pl
-predict(object, ...)
+    

+    
# S3 method for tam.mml
+predict(object, ...)
+
+# S3 method for tam.mml.3pl
+predict(object, ...)
+
+# S3 method for tamaan
+predict(object, ...)

+    

 
-# S3 method for tamaan
-predict(object, ...)

+    

+    
Arguments

+    
object

+
Object of class tam, tam.mml,
+tam.mml.3pl or tamaan.

 
-    
Arguments

-    
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
object
Object of class tam, tam.mml,
-tam.mml.3pl or tamaan.
...
Further arguments to be passed

+
...

+
Further arguments to be passed

 
-    
Value

+

+    

+    
Value

+    
 
-    
List with entries for predicted values (expectations and probabilities)
+
List with entries for predicted values (expectations and probabilities)
 for each person and each item.

+
+
 
See predict (CDM).

+    

 
-    
Examples

-    
#############################################################################
-# EXAMPLE 1: Dichotomous data sim.rasch - predict method
-#############################################################################
-
-data(data.sim.rasch)
-# 1PL estimation
-mod1 <- TAM::tam.mml(resp=data.sim.rasch)
-# predict method
-prmod1 <- IRT.predict(mod1, data.sim.rasch)
-str(prmod1)

+    

+    
Examples

+    
#############################################################################
+# EXAMPLE 1: Dichotomous data sim.rasch - predict method
+#############################################################################
+
+data(data.sim.rasch)
+# 1PL estimation
+mod1 <- TAM::tam.mml(resp=data.sim.rasch)
+# predict method
+prmod1 <- IRT.predict(mod1, data.sim.rasch)
+str(prmod1)

+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/reference/tam.ctt.html b/docs/reference/tam.ctt.html
index 8af0570..5ad8a39 100644
--- a/docs/reference/tam.ctt.html
+++ b/docs/reference/tam.ctt.html
@@ -1,68 +1,13 @@
-
 
-
-  
-  
-
-
-
-Classical Test Theory Based Statistics and Plots — tam.ctt • TAM
-
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-
-Classical Test Theory Based Statistics and Plots — tam.ctt • TAM
-
-
-
-  
+
+    
 
-  
     

-      

-      
 
       
 
-      

-
-

+      

   

     

     
Classical Test Theory Based Statistics and Plots

@@ -119,193 +51,208 @@ 
Classical Test Theory Based Statistics and Plots

 theory.

     

 
-    
tam.ctt(resp, wlescore=NULL, pvscores=NULL, group=NULL, progress=TRUE)
-tam.ctt2(resp, wlescore=NULL, group=NULL, allocate=30, progress=TRUE)
-tam.ctt3(resp, wlescore=NULL, group=NULL, allocate=30, progress=TRUE, max_ncat=30,
-          pweights=NULL)
-
-tam.cb( dat, wlescore=NULL, group=NULL, max_ncat=30, progress=TRUE,
-             pweights=NULL, digits_freq=5)
-
-plotctt( resp, theta, Ncuts=NULL, ask=FALSE, col.list=NULL,
-       package="lattice", ... )

-
-    
Arguments

-    
-    
-    
-      
-      
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-      
-      
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-    
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-      
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-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
resp
A data frame with unscored or scored item responses
wlescore
A vector with person parameter estimates, e.g. weighted likelihood
+    

+    
tam.ctt(resp, wlescore=NULL, pvscores=NULL, group=NULL, progress=TRUE)
+tam.ctt2(resp, wlescore=NULL, group=NULL, allocate=30, progress=TRUE)
+tam.ctt3(resp, wlescore=NULL, group=NULL, allocate=30, progress=TRUE, max_ncat=30,
+          pweights=NULL)
+
+tam.cb( dat, wlescore=NULL, group=NULL, max_ncat=30, progress=TRUE,
+             pweights=NULL, digits_freq=5)
+
+plotctt( resp, theta, Ncuts=NULL, ask=FALSE, col.list=NULL,
+       package="lattice", ... )

+    

+
+    

+    
Arguments

+    
resp

+
A data frame with unscored or scored item responses

+
+  
wlescore

+
A vector with person parameter estimates, e.g. weighted likelihood
 estimates obtained from tam.wle. If wlescore=NULL is
 chosen in tam.ctt2, then only a frequency table of all items
-is produced.
pvscores
A matrix with plausible values, e.g. obtained from tam.pv
group
Vector of group identifiers if descriptive statistics shall
-be groupwise calculated
progress
An optional logical indicating whether computation progress
-should be displayed.
allocate
Average number of categories per item. This argument is just
+is produced.

+
+  
pvscores

+
A matrix with plausible values, e.g. obtained from tam.pv

+
+
group

+
Vector of group identifiers if descriptive statistics shall
+be groupwise calculated

+
+  
progress

+
An optional logical indicating whether computation progress
+should be displayed.

+
+
allocate

+
Average number of categories per item. This argument is just
     used for matrix size allocations. If an error is produced, use
-    a sufficiently higher number.
max_ncat
Maximum number of categories of variables for which
-   frequency tables should be computed
pweights
Optional vector of person weights
dat
Data frame
digits_freq
Number of digits for rounding in frequency table
theta
A score to be conditioned
Ncuts
Number of break points for theta
ask
A logical which asks for changing the graphic from item to item.
-  The default is FALSE.
col.list
Optional vector of colors for plotting
package
Package used for plotting. Can be "lattice"
-or "graphics".
...
Further arguments to be passed.

-
-    
Details

+    a sufficiently higher number.

+
+
max_ncat

+
Maximum number of categories of variables for which
+   frequency tables should be computed

+
+
pweights

+
Optional vector of person weights

+
+
dat

+
Data frame

+
+
digits_freq

+
Number of digits for rounding in frequency table

+
+
theta

+
A score to be conditioned

+
+
Ncuts

+
Number of break points for theta

+
+
ask

+
A logical which asks for changing the graphic from item to item.
+  The default is FALSE.

+
+
col.list

+
Optional vector of colors for plotting

 
+
package

+
Package used for plotting. Can be "lattice"
+or "graphics".

+
+
...

+
Further arguments to be passed.

+
+

+    

+    
Details

     
The functions tam.ctt2 and tam.ctt3 use Rcpp code
 and are slightly faster.
 However, only tam.ctt allows the input of wlescore and
 pvscores.

-    
Value

-
-    
A data frame with following columns:

-
index
Index variable in this data frame

-
group
Group identifier

-
itemno
Item number

-
item
Item

-
N
Number of students responding to this item

-
Categ
Category label

-
AbsFreq
Absolute frequency of category

-
RelFreq
Relative frequency of category

-
rpb.WLE
Point biserial correlation of an item category and the WLE

-
M.WLE
Mean of the WLE of students in this item category

-
SD.WLE
Standard deviation of the WLE of students in this item category

-
rpb.PV
Point biserial correlation of an item category and the PV

-
M.PV
Mean of the PV of students in this item category

-
SD.PV
Standard deviation of the PV of students in this item category

-
-    
Note

+    

+    

+    
Value

+    
+
+
A data frame with following columns:

+
index

+
Index variable in this data frame

+
+
group

+
Group identifier

+
+
itemno

+
Item number

+
+
item

+
Item

 
+
N

+
Number of students responding to this item

+
+
Categ

+
Category label

+
+
AbsFreq

+
Absolute frequency of category

+
+
RelFreq

+
Relative frequency of category

+
+
rpb.WLE

+
Point biserial correlation of an item category and the WLE

+
+
M.WLE

+
Mean of the WLE of students in this item category

+
+
SD.WLE

+
Standard deviation of the WLE of students in this item category

+
+
rpb.PV

+
Point biserial correlation of an item category and the PV

+
+
M.PV

+
Mean of the PV of students in this item category

+
+
SD.PV

+
Standard deviation of the PV of students in this item category

+
+

+    

+    
Note

     
For dichotomously scored data, rpb.WLE is the ordinary point biserial
 correlation of an item and a test score (here the WLE).

-    
See also

-
-    
http://www.edmeasurementsurveys.com/TAM/Tutorials/4CTT.htm

-
-    
Examples

-    
if (FALSE) {
-#############################################################################
-# EXAMPLE 1: Multiple choice data data.mc
-#############################################################################
-
-data(data.mc)
-# estimate Rasch model for scored data.mc data
-mod <- TAM::tam.mml( resp=data.mc$scored )
-# estimate WLE
-w1 <- TAM::tam.wle( mod )
-# estimate plausible values
-set.seed(789)
-p1 <- TAM::tam.pv( mod, ntheta=500, normal.approx=TRUE )$pv
-
-# CTT results for raw data
-stat1 <- TAM::tam.ctt( resp=data.mc$raw, wlescore=w1$theta, pvscores=p1[,-1] )
-stat1a <- TAM::tam.ctt2( resp=data.mc$raw, wlescore=w1$theta )  # faster
-stat1b <- TAM::tam.ctt2( resp=data.mc$raw )  # only frequencies
-stat1c <- TAM::tam.ctt3( resp=data.mc$raw, wlescore=w1$theta )  # faster
-
-# plot empirical item response curves
-plotctt( resp=data.mc$raw, theta=w1$theta, Ncuts=5, ask=TRUE)
-# use graphics for plot
-plotctt( resp=data.mc$raw, theta=w1$theta, Ncuts=5, ask=TRUE, package="graphics")
-# change colors
-col.list <- c( "darkred",  "darkslateblue", "springgreen4", "darkorange",
-                "hotpink4", "navy" )
-plotctt( resp=data.mc$raw, theta=w1$theta, Ncuts=5, ask=TRUE,
-        package="graphics", col.list=col.list )
-
-# CTT results for scored data
-stat2 <- TAM::tam.ctt( resp=data.mc$scored, wlescore=w1$theta, pvscores=p1[,-1] )
-
-# descriptive statistics for different groups
-# define group identifier
-group <- c( rep(1,70), rep(2,73) )
-stat3 <- TAM::tam.ctt( resp=data.mc$raw, wlescore=w1$theta, pvscores=p1[,-1], group=group)
-stat3a <- TAM::tam.ctt2( resp=data.mc$raw, wlescore=w1$theta,  group=group)
-}

+    

+    
+
+    

+    
Examples

+    
if (FALSE) {
+#############################################################################
+# EXAMPLE 1: Multiple choice data data.mc
+#############################################################################
+
+data(data.mc)
+# estimate Rasch model for scored data.mc data
+mod <- TAM::tam.mml( resp=data.mc$scored )
+# estimate WLE
+w1 <- TAM::tam.wle( mod )
+# estimate plausible values
+set.seed(789)
+p1 <- TAM::tam.pv( mod, ntheta=500, normal.approx=TRUE )$pv
+
+# CTT results for raw data
+stat1 <- TAM::tam.ctt( resp=data.mc$raw, wlescore=w1$theta, pvscores=p1[,-1] )
+stat1a <- TAM::tam.ctt2( resp=data.mc$raw, wlescore=w1$theta )  # faster
+stat1b <- TAM::tam.ctt2( resp=data.mc$raw )  # only frequencies
+stat1c <- TAM::tam.ctt3( resp=data.mc$raw, wlescore=w1$theta )  # faster
+
+# plot empirical item response curves
+plotctt( resp=data.mc$raw, theta=w1$theta, Ncuts=5, ask=TRUE)
+# use graphics for plot
+plotctt( resp=data.mc$raw, theta=w1$theta, Ncuts=5, ask=TRUE, package="graphics")
+# change colors
+col.list <- c( "darkred",  "darkslateblue", "springgreen4", "darkorange",
+                "hotpink4", "navy" )
+plotctt( resp=data.mc$raw, theta=w1$theta, Ncuts=5, ask=TRUE,
+        package="graphics", col.list=col.list )
+
+# CTT results for scored data
+stat2 <- TAM::tam.ctt( resp=data.mc$scored, wlescore=w1$theta, pvscores=p1[,-1] )
+
+# descriptive statistics for different groups
+# define group identifier
+group <- c( rep(1,70), rep(2,73) )
+stat3 <- TAM::tam.ctt( resp=data.mc$raw, wlescore=w1$theta, pvscores=p1[,-1], group=group)
+stat3a <- TAM::tam.ctt2( resp=data.mc$raw, wlescore=w1$theta,  group=group)
+}

+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/reference/tam.fa.html b/docs/reference/tam.fa.html
index 9522b4e..d6d2d56 100644
--- a/docs/reference/tam.fa.html
+++ b/docs/reference/tam.fa.html
@@ -1,70 +1,15 @@
-
 
-
-  
-  
-
-
-
-Bifactor Model and Exploratory Factor Analysis — tam.fa • TAM
-
-
-
-
-
-
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-Bifactor Model and Exploratory Factor Analysis — tam.fa • TAM
-
-
-
-
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-
-
-  
+
+    
 
-  
     

-      

-      
 
       
 
-      

-
-

+      

   

     

     
Bifactor Model and Exploratory Factor Analysis

@@ -119,72 +51,63 @@ 
Bifactor Model and Exploratory Factor Analysis

     

     
Estimates the bifactor model and exploratory factor analysis with
 marginal maximum likelihood estimation.

-
This function is simply a wrapper to tam.mml or
-tam.mml.2pl.

+
This function is simply a wrapper to tam.mml or
+tam.mml.2pl.

+    

+
+    

+    
tam.fa(resp, irtmodel, dims=NULL, nfactors=NULL, pid=NULL,
+    pweights=NULL, verbose=TRUE, control=list(), ...)

     

 
-    
tam.fa(resp, irtmodel, dims=NULL, nfactors=NULL, pid=NULL,
-    pweights=NULL, verbose=TRUE, control=list(), ...)

+    

+    
Arguments

+    
resp

+
Data frame with polytomous item responses \(k=0,...,K\).
+     Missing responses must be declared as NA.

 
-    
Arguments

-    
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
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-    
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-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
resp
Data frame with polytomous item responses \(k=0,...,K\).
-     Missing responses must be declared as NA.
irtmodel
A string which defines the IRT model to be estimated. Options
+  
irtmodel

+
A string which defines the IRT model to be estimated. Options
 are "efa" (exploratory factor analysis), "bifactor1" (Rasch
 testlet model in case of dichotomous data; Wang & Wilson, 2005;
 for polytomous data it assumes item slopes of 1) and "bifactor2"
 (bifactor model).
-See Details for more information.
dims
A numeric or string vector which only applies in case of
+See Details for more information.

+
+
dims

+
A numeric or string vector which only applies in case of
 irtmodel="bifactor1" or irtmodel="bifactor2".
 Different entries in the vector indicate different dimensions of items
 which should load on the nested factor. If items should only load
-on the general factor, then an NA must be specified.
nfactors
A numerical value which indicates the number of factors in
-exploratory factor analysis.
pid
An optional vector of person identifiers
pweights
An optional vector of person weights
verbose
Logical indicating whether output should
-be printed during iterations. This argument replaces control$progress.
control
See tam.mml for more details. Note that the default is
+on the general factor, then an NA must be specified.

+
+
nfactors

+
A numerical value which indicates the number of factors in
+exploratory factor analysis.

+
+  
pid

+
An optional vector of person identifiers

+
+  
pweights

+
An optional vector of person weights

+
+
verbose

+
Logical indicating whether output should
+be printed during iterations. This argument replaces control$progress.

+
+  
control

+
See tam.mml for more details. Note that the default is
 Quasi Monte Carlo integration with 1500 nodes (snodes=1500,
-QMC=TRUE).
...
Further arguments to be passed. These arguments are used in
-tam.mml and tam.mml.2pl. For example,
-beta.inits or xsi.inits can be supplied.

+QMC=TRUE).

 
-    
Details

+
...

+
Further arguments to be passed. These arguments are used in
+tam.mml and tam.mml.2pl. For example,
+beta.inits or xsi.inits can be supplied.

 
+

+    

+    
Details

     
The exploratory factor analysis (irtmodel="efa"
 is estimated using an echelon form of the loading matrix and uncorrelated factors.
 The obtained standardized loading matrix is rotated using oblimin rotation.
@@ -201,17 +124,27 @@ 
Details
 estimated.

 
For polytomous data, the generalized partial credit model is used. The loading
 structure is defined in the same way as for dichotomous data.

-    
Value

+    

+    

+    
Value

+    
 
-    
The same list entries as in tam.mml but in addition the
+
The same list entries as in tam.mml but in addition the
 following statistics are included:

-
B.stand
Standardized factor loadings of the bifactor model or the
+
B.stand

+
Standardized factor loadings of the bifactor model or the
 exploratory factor analysis.

-
B.SL
In case of exploratory factor analysis (irtmodel="efa"),
+
+
B.SL

+
In case of exploratory factor analysis (irtmodel="efa"),
 loadings form the Schmid-Leimann solution of the psych package.

-
efa.oblimin
Output from oblimin rotation in exploratory
+
+
efa.oblimin

+
Output from oblimin rotation in exploratory
    factor analysis which is produced by the GPArotation package

-
meas
Vector of dimensionality and reliability statistics.
+
+
meas

+
Vector of dimensionality and reliability statistics.
    Included are the ECV measure (explained common variation;
    Reise, Moore & Haviland, 2010; Reise, 2012),
    \(\omega_t\) (Omega Total), \(\omega_a\) (Omega asymptotic)
@@ -220,120 +153,121 @@ 
Value

    the bifactor model for dichotomous item responses is also
    included (Green & Yang, 2009).

 
-    
References

-
+

+    

+    
References

     
Green, S. B., & Yang, Y. (2009). Reliability of summed item
 scores using structural equation modeling: An alternative to
 coefficient alpha. Psychometrika, 74, 155-167.
-doi: 10.1007/s11336-008-9099-3

+doi:10.1007/s11336-008-9099-3

 
Reise, S. P. (2012). The rediscovery of bifactor measurement models.
 Multivariate Behavioral Research, 47(5), 667-696.
-doi: 10.1080/00273171.2012.715555

+doi:10.1080/00273171.2012.715555

 
Reise, S. P., Moore, T. M., & Haviland, M. G.  (2010).
 Bifactor models and rotations: Exploring the extent to which
 multidimensional data yield univocal scale scores.
 Journal of Personality Assessment, 92(6), 544-559.
-doi: 10.1080/00223891.2010.496477

+doi:10.1080/00223891.2010.496477

 
Revelle, W., & Zinbarg, R. E. (2009).
 Coefficients alpha, beta, omega and the glb: Comments on Sijtsma.
 Psychometrika, 74(1), 145-154.
-doi: 10.1007/s11336-008-9102-z

+doi:10.1007/s11336-008-9102-z

 
Wang, W.-C., & Wilson, M. (2005). The Rasch testlet model.
 Applied Psychological Measurement, 29(2), 126-149.
-doi: 10.1177/0146621604271053

-    
See also

-
-    
For more details see tam.mml because tam.fa is just
-a wrapper for tam.mml.2pl and tam.mml.

-
logLik.tam, anova.tam

-
-    
Examples

-    
if (FALSE) {
-#############################################################################
-# EXAMPLE 1: Dataset reading from sirt package
-#############################################################################
-
-data(data.read,package="sirt")
-resp <- data.read
-
-#***
-# Model 1a: Exploratory factor analysis with 2 factors
-mod1a <- TAM::tam.fa( resp=resp, irtmodel="efa", nfactors=2  )
-summary(mod1a)
-# varimax rotation
-stats::varimax(mod1a$B.stand)
-# promax rotation
-stats::promax(mod1a$B.stand)
-# more rotations are included in the GPArotation package
-library(GPArotation)
-# geomin rotation oblique
-GPArotation::geominQ( mod1a$B.stand )
-# quartimin rotation
-GPArotation::quartimin( mod1a$B.stand )
-
-#***
-# Model 1b: Rasch testlet model with 3 testlets
-dims <- substring( colnames(resp),1,1 )     # define dimensions
-mod1b <- TAM::tam.fa( resp=resp, irtmodel="bifactor1", dims=dims )
-summary(mod1b)
-
-#***
-# Model 1c: Bifactor model
-mod1c <- TAM::tam.fa( resp=resp, irtmodel="bifactor2", dims=dims )
-summary(mod1c)
-
-#***
-# Model 1d: reestimate Model 1c but assume that items 3 and 5 do not load on
-#           specific factors
-dims1 <- dims
-dims1[c(3,5)] <- NA
-mod1d <- TAM::tam.fa( resp=resp, irtmodel="bifactor2", dims=dims1 )
-summary(mod1d)
-
-#############################################################################
-# EXAMPLE 2: Polytomous data
-#############################################################################
-
-data(data.timssAusTwn.scored, package="TAM")
-dat <- data.timssAusTwn.scored
-resp <- dat[, grep("M0", colnames(dat))]
-
-#***
-# Model 1a: Rasch testlet model with 2 testlets
-dims <- c( rep(1,5), rep(2,6))
-mod1a <- TAM::tam.fa( resp=resp, irtmodel="bifactor1", dims=dims )
-summary(mod1a)
+doi:10.1177/0146621604271053

+    

+    

+    
See also

+    
For more details see tam.mml because tam.fa is just
+a wrapper for tam.mml.2pl and tam.mml.

+
logLik.tam, anova.tam

+    

 
-#***
-# Model 1b: Bifactor model
-mod1b <- TAM::tam.fa( resp=resp, irtmodel="bifactor2", dims=dims )
-summary(mod1b)
-}
+    

+    
Examples

+    
if (FALSE) {
+#############################################################################
+# EXAMPLE 1: Dataset reading from sirt package
+#############################################################################
+
+data(data.read,package="sirt")
+resp <- data.read
+
+#***
+# Model 1a: Exploratory factor analysis with 2 factors
+mod1a <- TAM::tam.fa( resp=resp, irtmodel="efa", nfactors=2  )
+summary(mod1a)
+# varimax rotation
+stats::varimax(mod1a$B.stand)
+# promax rotation
+stats::promax(mod1a$B.stand)
+# more rotations are included in the GPArotation package
+library(GPArotation)
+# geomin rotation oblique
+GPArotation::geominQ( mod1a$B.stand )
+# quartimin rotation
+GPArotation::quartimin( mod1a$B.stand )
+
+#***
+# Model 1b: Rasch testlet model with 3 testlets
+dims <- substring( colnames(resp),1,1 )     # define dimensions
+mod1b <- TAM::tam.fa( resp=resp, irtmodel="bifactor1", dims=dims )
+summary(mod1b)
+
+#***
+# Model 1c: Bifactor model
+mod1c <- TAM::tam.fa( resp=resp, irtmodel="bifactor2", dims=dims )
+summary(mod1c)
+
+#***
+# Model 1d: reestimate Model 1c but assume that items 3 and 5 do not load on
+#           specific factors
+dims1 <- dims
+dims1[c(3,5)] <- NA
+mod1d <- TAM::tam.fa( resp=resp, irtmodel="bifactor2", dims=dims1 )
+summary(mod1d)
+
+#############################################################################
+# EXAMPLE 2: Polytomous data
+#############################################################################
+
+data(data.timssAusTwn.scored, package="TAM")
+dat <- data.timssAusTwn.scored
+resp <- dat[, grep("M0", colnames(dat))]
+
+#***
+# Model 1a: Rasch testlet model with 2 testlets
+dims <- c( rep(1,5), rep(2,6))
+mod1a <- TAM::tam.fa( resp=resp, irtmodel="bifactor1", dims=dims )
+summary(mod1a)
+
+#***
+# Model 1b: Bifactor model
+mod1b <- TAM::tam.fa( resp=resp, irtmodel="bifactor2", dims=dims )
+summary(mod1b)
+}

+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/reference/tam.fit.html b/docs/reference/tam.fit.html
index 5864efd..2d6d627 100644
--- a/docs/reference/tam.fit.html
+++ b/docs/reference/tam.fit.html
@@ -1,69 +1,14 @@
-
 
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-Item Infit and Outfit Statistic — tam.fit • TAM
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-Item Infit and Outfit Statistic — tam.fit • TAM
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+    
 
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Item Infit and Outfit Statistic

@@ -121,272 +53,281 @@ 
Item Infit and Outfit Statistic

 tam.jml,  respectively.

     

 
-    
tam.fit(tamobj, ...)
-
-tam.mml.fit(tamobj, FitMatrix=NULL, Nsimul=NULL,progress=TRUE,
-   useRcpp=TRUE, seed=NA, fit.facets=TRUE)
-
-tam.jml.fit(tamobj, trim_val=10)
-
-# S3 method for tam.fit
-summary(object, file=NULL, ...)

-
-    
Arguments

-    
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-    
-    
tamobj
An object of class tam, tam.mml or tam.jml
FitMatrix
A fit matrix \(F\) for a specific hypothesis of fit of the linear function
-\(F \xi \) (see Simulated Example 3 and Adams & Wu 2007).
Nsimul
Number of simulations used for fit calculation.
+    

+    
tam.fit(tamobj, ...)
+
+tam.mml.fit(tamobj, FitMatrix=NULL, Nsimul=NULL,progress=TRUE,
+   useRcpp=TRUE, seed=NA, fit.facets=TRUE)
+
+tam.jml.fit(tamobj, trim_val=10)
+
+# S3 method for tam.fit
+summary(object, file=NULL, ...)

+    

+
+    

+    
Arguments

+    
tamobj

+
An object of class tam, tam.mml or tam.jml

+
+ 
FitMatrix

+
A fit matrix \(F\) for a specific hypothesis of fit of the linear function
+\(F \xi \) (see Simulated Example 3 and Adams & Wu 2007).

+
+
Nsimul

+
Number of simulations used for fit calculation.
 The default is 100 (less than 400 students), 40 (less than 1000 students),
-15 (less than 3000 students) and 5 (more than 3000 students)
progress
An optional logical indicating whether computation progress should
-    be displayed at console.
useRcpp
Optional logical indicating whether Rcpp
+15 (less than 3000 students) and 5 (more than 3000 students)

+
+ 
progress

+
An optional logical indicating whether computation progress should
+    be displayed at console.

+
+
useRcpp

+
Optional logical indicating whether Rcpp
     or pure R code should be used for fit calculation.
-The latter is consistent with TAM (<=1.1).
seed
Fixed simulation seed.
fit.facets
An optional logical indicating whether
-fit for all facet parameters should be computed.
trim_val
Optional trimming value. Squared standardized reaisuals
-larger than trim_val are set to trim_val.
object
Object of class tam.fit
file
Optional file name for summary output
...
Further arguments to be passed

-
-    
Value

-
-    
In case of tam.mml.fit a data frame as entry itemfit
-with four columns:

-
Outfit
Item outfit statistic

-
Outfit_t
The \(t\) value for the outfit statistic

-
Outfit_p
Significance \(p\) value for outfit statistic

-
Outfit_pholm
Significance \(p\) value for outfit statistic,
-adjusted for multiple testing according to the Holm procedure

-
Infit
Item infit statistic

-
Infit_t
The \(t\) value for the infit statistic

-
Infit_p
Significance \(p\) value for infit statistic

-
Infit_pholm
Significance \(p\) value for infit statistic,
+The latter is consistent with TAM (<=1.1).

+
+
seed

+
Fixed simulation seed.

+
+
fit.facets

+
An optional logical indicating whether
+fit for all facet parameters should be computed.

+
+
trim_val

+
Optional trimming value. Squared standardized reaisuals
+larger than trim_val are set to trim_val.

+
+
object

+
Object of class tam.fit

+
+
file

+
Optional file name for summary output

+
+
...

+
Further arguments to be passed

+
+

+    

+    
Value

+    
+
+
In case of tam.mml.fit a data frame as entry itemfit

+
+
+
with four columns:

+
Outfit

+
Item outfit statistic

+
+
Outfit_t

+
The \(t\) value for the outfit statistic

+
+
Outfit_p

+
Significance \(p\) value for outfit statistic

+
+
Outfit_pholm

+
Significance \(p\) value for outfit statistic,
 adjusted for multiple testing according to the Holm procedure

 
-    
References

+
Infit

+
Item infit statistic

+
+
Infit_t

+
The \(t\) value for the infit statistic

+
+
Infit_p

+
Significance \(p\) value for infit statistic

+
+
Infit_pholm

+
Significance \(p\) value for infit statistic,
+adjusted for multiple testing according to the Holm procedure

 
+

+    

+    
References

     
Adams, R. J., & Wu, M. L. (2007). The mixed-coefficients multinomial logit model.
 A generalized form of the Rasch model. In M. von Davier & C. H. Carstensen (Eds.),
 Multivariate and mixture distribution Rasch models: Extensions and applications
 (pp. 55-76). New York: Springer.
-doi: 10.1007/978-0-387-49839-3_4

-    
See also

-
-    
Fit statistics can be also calculated by the function msq.itemfit
+doi:10.1007/978-0-387-49839-3_4

+    

+    

+    
See also

+    
Fit statistics can be also calculated by the function msq.itemfit
 which avoids simulations and directly evaluates individual
 posterior distributions.

 
See tam.jml.fit for calculating item fit and person fit statistics
 for models fitted with JML.

-
See tam.personfit for computing person fit statistics.

+
See tam.personfit for computing person fit statistics.

 
Item fit and person fit based on estimated person parameters can also be
-calculated using the sirt::pcm.fit function
+calculated using the sirt::pcm.fit function
 in the sirt package (see Example 1 and Example 2).

+    

 
-    
Examples

-    
#############################################################################
-# EXAMPLE 1: Dichotomous data data.sim.rasch
-#############################################################################
-
-data(data.sim.rasch)
-# estimate Rasch model
-mod1 <- TAM::tam.mml(resp=data.sim.rasch)
-# item fit
-fit1 <- TAM::tam.fit( mod1 )
-summary(fit1)
-  ##   > summary(fit1)
-  ##      parameter Outfit Outfit_t Outfit_p Infit Infit_t Infit_p
-  ##   1         I1  0.966   -0.409    0.171 0.996  -0.087   0.233
-  ##   2         I2  1.044    0.599    0.137 1.029   0.798   0.106
-  ##   3         I3  1.022    0.330    0.185 1.012   0.366   0.179
-  ##   4         I4  1.047    0.720    0.118 1.054   1.650   0.025
-
-if (FALSE) {
-
-#--------
-# infit and oufit based on estimated WLEs
-library(sirt)
-
-# estimate WLE
-wle <- TAM::tam.wle(mod1)
-# extract item parameters
-b1 <- - mod1$AXsi[, -1 ]
-# assess item fit and person fit
-fit1a <- sirt::pcm.fit(b=b1, theta=wle$theta, data.sim.rasch )
-fit1a$item       # item fit statistic
-fit1a$person     # person fit statistic
-
-#############################################################################
-# EXAMPLE 2: Partial credit model data.gpcm
-#############################################################################
-
-data( data.gpcm )
-dat <- data.gpcm
-
-# estimate partial credit model in ConQuest parametrization 'item+item*step'
-mod2 <- TAM::tam.mml( resp=dat, irtmodel="PCM2" )
-summary(mod2)
-# estimate item fit
-fit2 <- TAM::tam.fit(mod2)
-summary(fit2)
-
-#=> The first three rows of the data frame correspond to the fit statistics
-#     of first three items Comfort, Work and Benefit.
-
-#--------
-# infit and oufit based on estimated WLEs
-# compute WLEs
-wle <- TAM::tam.wle(mod2)
-# extract item parameters
-b1 <- - mod2$AXsi[, -1 ]
-# assess fit
-fit1a <- sirt::pcm.fit(b=b1, theta=wle$theta, dat)
-fit1a$item
-
-#############################################################################
-# EXAMPLE 3: Fit statistic testing for local independence
-#############################################################################
-
-# generate data with local dependence and User-defined fit statistics
-set.seed(4888)
-I <- 40        # 40 items
-N <- 1000       # 1000 persons
-
-delta <- seq(-2,2, len=I)
-theta <- stats::rnorm(N, 0, 1)
-# simulate data
-prob <- stats::plogis(outer(theta, delta, "-"))
-rand <- matrix( stats::runif(N*I), nrow=N, ncol=I)
-resp <- 1*(rand < prob)
-colnames(resp) <- paste("I", 1:I, sep="")
-
-#induce some local dependence
-for (item in c(10, 20, 30)){
- #  20
- #are made equal to the previous item
-  row <- round( stats::runif(0.2*N)*N + 0.5)
-  resp[row, item+1] <- resp[row, item]
-}
-
-#run TAM
-mod1 <- TAM::tam.mml(resp)
-
-#User-defined fit design matrix
-F <- array(0, dim=c(dim(mod1$A)[1], dim(mod1$A)[2], 6))
-F[,,1] <- mod1$A[,,10] + mod1$A[,,11]
-F[,,2] <- mod1$A[,,12] + mod1$A[,,13]
-F[,,3] <- mod1$A[,,20] + mod1$A[,,21]
-F[,,4] <- mod1$A[,,22] + mod1$A[,,23]
-F[,,5] <- mod1$A[,,30] + mod1$A[,,31]
-F[,,6] <- mod1$A[,,32] + mod1$A[,,33]
-fit <- TAM::tam.fit(mod1, FitMatrix=F)
-summary(fit)
-
-#############################################################################
-# EXAMPLE 4: Fit statistic testing for items with differing slopes
-#############################################################################
-
-#*** simulate data
-library(sirt)
-set.seed(9875)
-N <- 2000
-I <- 20
-b <- sample( seq( -2, 2, length=I ) )
-a <- rep( 1, I )
-# create some misfitting items
-a[c(1,3)] <- c(.5, 1.5 )
-# simulate data
-dat <- sirt::sim.raschtype( rnorm(N), b=b, fixed.a=a )
-#*** estimate Rasch model
-mod1 <- TAM::tam.mml(resp=dat)
-#*** assess item fit by infit and outfit statistic
-fit1 <- TAM::tam.fit( mod1 )$itemfit
-round( cbind( "b"=mod1$item$AXsi_.Cat1, fit1$itemfit[,-1] )[1:7,], 3 )
-
-#*** compute item fit statistic in mirt package
-library(mirt)
-library(sirt)
-mod1c <- mirt::mirt( dat, model=1, itemtype="Rasch", verbose=TRUE)
-print(mod1c)                      # model summary
-sirt::mirt.wrapper.coef(mod1c)    # estimated parameters
-fit1c <- mirt::itemfit(mod1c, method="EAP")    # model fit in mirt package
-# compare results of TAM and mirt
-dfr <- cbind( "TAM"=fit1, "mirt"=fit1c[,-c(1:2)] )
-
-# S-X2 item fit statistic (see also the output from mirt)
-library(CDM)
-sx2mod1 <- CDM::itemfit.sx2( mod1 )
-summary(sx2mod1)
-
-# compare results of CDM and mirt
-sx2comp <-  cbind( sx2mod1$itemfit.stat[, c("S-X2", "p") ],
-                    dfr[, c("mirt.S_X2", "mirt.p.S_X2") ] )
-round(sx2comp, 3 )
-}

+    

+    
Examples

+    
#############################################################################
+# EXAMPLE 1: Dichotomous data data.sim.rasch
+#############################################################################
+
+data(data.sim.rasch)
+# estimate Rasch model
+mod1 <- TAM::tam.mml(resp=data.sim.rasch)
+# item fit
+fit1 <- TAM::tam.fit( mod1 )
+summary(fit1)
+  ##   > summary(fit1)
+  ##      parameter Outfit Outfit_t Outfit_p Infit Infit_t Infit_p
+  ##   1         I1  0.966   -0.409    0.171 0.996  -0.087   0.233
+  ##   2         I2  1.044    0.599    0.137 1.029   0.798   0.106
+  ##   3         I3  1.022    0.330    0.185 1.012   0.366   0.179
+  ##   4         I4  1.047    0.720    0.118 1.054   1.650   0.025
+
+if (FALSE) {
+
+#--------
+# infit and oufit based on estimated WLEs
+library(sirt)
+
+# estimate WLE
+wle <- TAM::tam.wle(mod1)
+# extract item parameters
+b1 <- - mod1$AXsi[, -1 ]
+# assess item fit and person fit
+fit1a <- sirt::pcm.fit(b=b1, theta=wle$theta, data.sim.rasch )
+fit1a$item       # item fit statistic
+fit1a$person     # person fit statistic
+
+#############################################################################
+# EXAMPLE 2: Partial credit model data.gpcm
+#############################################################################
+
+data( data.gpcm )
+dat <- data.gpcm
+
+# estimate partial credit model in ConQuest parametrization 'item+item*step'
+mod2 <- TAM::tam.mml( resp=dat, irtmodel="PCM2" )
+summary(mod2)
+# estimate item fit
+fit2 <- TAM::tam.fit(mod2)
+summary(fit2)
+
+#=> The first three rows of the data frame correspond to the fit statistics
+#     of first three items Comfort, Work and Benefit.
+
+#--------
+# infit and oufit based on estimated WLEs
+# compute WLEs
+wle <- TAM::tam.wle(mod2)
+# extract item parameters
+b1 <- - mod2$AXsi[, -1 ]
+# assess fit
+fit1a <- sirt::pcm.fit(b=b1, theta=wle$theta, dat)
+fit1a$item
+
+#############################################################################
+# EXAMPLE 3: Fit statistic testing for local independence
+#############################################################################
+
+# generate data with local dependence and User-defined fit statistics
+set.seed(4888)
+I <- 40        # 40 items
+N <- 1000       # 1000 persons
+
+delta <- seq(-2,2, len=I)
+theta <- stats::rnorm(N, 0, 1)
+# simulate data
+prob <- stats::plogis(outer(theta, delta, "-"))
+rand <- matrix( stats::runif(N*I), nrow=N, ncol=I)
+resp <- 1*(rand < prob)
+colnames(resp) <- paste("I", 1:I, sep="")
+
+#induce some local dependence
+for (item in c(10, 20, 30)){
+ #  20
+ #are made equal to the previous item
+  row <- round( stats::runif(0.2*N)*N + 0.5)
+  resp[row, item+1] <- resp[row, item]
+}
+
+#run TAM
+mod1 <- TAM::tam.mml(resp)
+
+#User-defined fit design matrix
+F <- array(0, dim=c(dim(mod1$A)[1], dim(mod1$A)[2], 6))
+F[,,1] <- mod1$A[,,10] + mod1$A[,,11]
+F[,,2] <- mod1$A[,,12] + mod1$A[,,13]
+F[,,3] <- mod1$A[,,20] + mod1$A[,,21]
+F[,,4] <- mod1$A[,,22] + mod1$A[,,23]
+F[,,5] <- mod1$A[,,30] + mod1$A[,,31]
+F[,,6] <- mod1$A[,,32] + mod1$A[,,33]
+fit <- TAM::tam.fit(mod1, FitMatrix=F)
+summary(fit)
+
+#############################################################################
+# EXAMPLE 4: Fit statistic testing for items with differing slopes
+#############################################################################
+
+#*** simulate data
+library(sirt)
+set.seed(9875)
+N <- 2000
+I <- 20
+b <- sample( seq( -2, 2, length=I ) )
+a <- rep( 1, I )
+# create some misfitting items
+a[c(1,3)] <- c(.5, 1.5 )
+# simulate data
+dat <- sirt::sim.raschtype( rnorm(N), b=b, fixed.a=a )
+#*** estimate Rasch model
+mod1 <- TAM::tam.mml(resp=dat)
+#*** assess item fit by infit and outfit statistic
+fit1 <- TAM::tam.fit( mod1 )$itemfit
+round( cbind( "b"=mod1$item$AXsi_.Cat1, fit1$itemfit[,-1] )[1:7,], 3 )
+
+#*** compute item fit statistic in mirt package
+library(mirt)
+library(sirt)
+mod1c <- mirt::mirt( dat, model=1, itemtype="Rasch", verbose=TRUE)
+print(mod1c)                      # model summary
+sirt::mirt.wrapper.coef(mod1c)    # estimated parameters
+fit1c <- mirt::itemfit(mod1c, method="EAP")    # model fit in mirt package
+# compare results of TAM and mirt
+dfr <- cbind( "TAM"=fit1, "mirt"=fit1c[,-c(1:2)] )
+
+# S-X2 item fit statistic (see also the output from mirt)
+library(CDM)
+sx2mod1 <- CDM::itemfit.sx2( mod1 )
+summary(sx2mod1)
+
+# compare results of CDM and mirt
+sx2comp <-  cbind( sx2mod1$itemfit.stat[, c("S-X2", "p") ],
+                    dfr[, c("mirt.S_X2", "mirt.p.S_X2") ] )
+round(sx2comp, 3 )
+}

+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/reference/tam.jml.html b/docs/reference/tam.jml.html
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--- a/docs/reference/tam.jml.html
+++ b/docs/reference/tam.jml.html
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-Joint Maximum Likelihood Estimation — tam.jml • TAM
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Joint Maximum Likelihood Estimation

@@ -121,347 +53,246 @@ 
Joint Maximum Likelihood Estimation

  see e.g. Linacre, 1994).

     

 
-    
tam.jml(resp, group=NULL, adj=.3, disattenuate=FALSE, bias=TRUE,
-    xsi.fixed=NULL, xsi.inits=NULL, theta.fixed=NULL, A=NULL, B=NULL, Q=NULL,
-    ndim=1, pweights=NULL, constraint="cases", verbose=TRUE, control=list(), version=3)
-
-# S3 method for tam.jml
-summary(object, file=NULL, ...)
-
-# S3 method for tam.jml
-logLik(object, ...)

-
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Arguments

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-    
-    
resp
A matrix of item responses. Missing responses must be declared
-     as NA.
group
An optional vector of group identifier
disattenuate
An optional logical indicating whether the person parameters
+    

+    
tam.jml(resp, group=NULL, adj=.3, disattenuate=FALSE, bias=TRUE,
+    xsi.fixed=NULL, xsi.inits=NULL, theta.fixed=NULL, A=NULL, B=NULL, Q=NULL,
+    ndim=1, pweights=NULL, constraint="cases", verbose=TRUE, control=list(), version=3,
+    theta_proc=NULL)
+
+# S3 method for tam.jml
+summary(object, file=NULL, ...)
+
+# S3 method for tam.jml
+logLik(object, ...)

+    

+
+    

+    
Arguments

+    
resp

+
A matrix of item responses. Missing responses must be declared
+     as NA.

+
+  
group

+
An optional vector of group identifier

+
+  
disattenuate

+
An optional logical indicating whether the person parameters
     should be disattenuated due to unreliability?
-    The disattenuation is conducted by applying the Kelley formula.
adj
Adjustment constant which is subtracted or added to extreme
-scores (score of zero or maximum score). The default is a value of 0.3
bias
A logical which indicates if JML bias should be reduced
+    The disattenuation is conducted by applying the Kelley formula.

+
+
adj

+
Adjustment constant which is subtracted or added to extreme
+scores (score of zero or maximum score). The default is a value of 0.3

+
+  
bias

+
A logical which indicates if JML bias should be reduced
      by multiplying item parameters by the adjustment factor
-     of \((I-1)/I\)
xsi.fixed
An optional matrix with two columns for fixing some of the
+     of \((I-1)/I\)

+
+  
xsi.fixed

+
An optional matrix with two columns for fixing some of the
      basis parameters \(\xi\) of item intercepts.
      1st column: Index of \(\xi\) parameter, 2nd column:
-     Fixed value of \(\xi\) parameter
xsi.inits
An optional vector of initial \(\xi\) parameters. Note that
+     Fixed value of \(\xi\) parameter

+
+  
xsi.inits

+
An optional vector of initial \(\xi\) parameters. Note that
      all parameters must be specified and the vector is not of the
-     same format as xsi.fixed.
theta.fixed
Matrix for fixed person parameters \(\theta\). The first
+     same format as xsi.fixed.

+
+
theta.fixed

+
Matrix for fixed person parameters \(\theta\). The first
     column includes the index whereas the second column includes
-the fixed value. This argument can only be applied for version=1.
A
A design array \(A\) for item category intercepts.
+the fixed value. This argument can only be applied for version=1.

+
+  
A

+
A design array \(A\) for item category intercepts.
      For item \(i\) and category \(k\), the threshold is
-     specified as \( \sum _j a_{ikj}   \xi_j\).
B
A design array for scoring item category responses.
+     specified as \( \sum _j a_{ikj}   \xi_j\).

+
+  
B

+
A design array for scoring item category responses.
      Entries in \(B\) represent item loadings on
-     abilities \(\theta\).
Q
A Q-matrix which defines loadings of items on dimensions.
ndim
Number of dimensions in the model. The default is 1.
pweights
An optional vector of person weights.
constraint
Type of constraint for means. Either "cases"
+     abilities \(\theta\).

+
+  
Q

+
A Q-matrix which defines loadings of items on dimensions.

+
+
+  
ndim

+
Number of dimensions in the model. The default is 1.

+
+  
pweights

+
An optional vector of person weights.

+
+
constraint

+
Type of constraint for means. Either "cases"
 (set mean of person parameters to zero)
-or "items" (set mean of item parameters to zero).
verbose
Logical indicating whether output should
-be printed during iterations. This argument replaces control$progress.
control
A list of control arguments. See tam.mml
-     for more details.
version
Version function which should be used. version=2
+or "items" (set mean of item parameters to zero).

+
+
verbose

+
Logical indicating whether output should
+be printed during iterations. This argument replaces control$progress.

+
+  
control

+
A list of control arguments. See tam.mml
+     for more details.

+
+
version

+
Version function which should be used. version=2
 is the former tam.jml2 function in TAM (<2.0).
 The default version=3 allows efficient handling in case of missing
-data.
object
Object of class tam.jml (only for summary.tam
-function)
file
A file name in which the summary output will be written
-(only for summary.tam.jml function)
...
Further arguments to be passed

-
-    
Value

-
-    
A list with following entries

-
item1
Data frame with item parameters

-
xsi
Vector of item parameters \(\xi\)

-
errorP
Standard error of item parameters \(\xi\)

-
theta
MLE in final step

-
errorWLE
Standard error of WLE

-
WLE
WLE in last iteration

-
WLEreliability
WLE reliability

-
PersonScores
Scores for each person (sufficient statistic)

-
ItemScore
Sufficient statistic for each item parameter

-
PersonMax
Maximum person score

-
ItemMax
Maximum item score

-
deviance
Deviance

-
deviance.history
Deviance history in iterations

-
resp
Original data frame

-
resp.ind
Response indicator matrix

-
group
Vector of group identifiers (if provided as an argument)

-
pweights
Vector of person weights

-
A
Design matrix \(A\) of item intercepts

-
B
Loading (or scoring) matrix \(B\)

-
nitems
Number of items

-
maxK
Maximum number of categories

-
nstud
Number of persons in resp

-
resp.ind.list
Like resp.ind, only in the format of a list

-
xsi.fixed
Fixed \(\xi\) item parameters

-
control
Control list

-
item
Extended data frame of item parameters

-
theta_summary
Summary of person parameters

-
...

-
-    
References

+data.

+
+
theta_proc

+
Function for processing theta within iterations. Can only
+be applied for version=1.

+
+  
object

+
Object of class tam.jml (only for summary.tam
+function)

+
+
file

+
A file name in which the summary output will be written
+(only for summary.tam.jml function)

+
+
...

+
Further arguments to be passed

+
+
+

+    

+    
Value

+    
+
+
A list with following entries

+
item1

+
Data frame with item parameters

+
+
xsi

+
Vector of item parameters \(\xi\)

+
+
errorP

+
Standard error of item parameters \(\xi\)

+
+
theta

+
MLE in final step

+
+
errorWLE

+
Standard error of WLE

+
+
WLE

+
WLE in last iteration

+
+
WLEreliability

+
WLE reliability

+
+
PersonScores

+
Scores for each person (sufficient statistic)

+
+
ItemScore

+
Sufficient statistic for each item parameter

+
+
PersonMax

+
Maximum person score

+
+
ItemMax

+
Maximum item score

+
+
deviance

+
Deviance

+
+
deviance.history

+
Deviance history in iterations

+
+
resp

+
Original data frame

+
+
resp.ind

+
Response indicator matrix

 
+
group

+
Vector of group identifiers (if provided as an argument)

+
+
pweights

+
Vector of person weights

+
+
A

+
Design matrix \(A\) of item intercepts

+
+
B

+
Loading (or scoring) matrix \(B\)

+
+
nitems

+
Number of items

+
+
maxK

+
Maximum number of categories

+
+
nstud

+
Number of persons in resp

+
+
resp.ind.list

+
Like resp.ind, only in the format of a list

+
+
xsi.fixed

+
Fixed \(\xi\) item parameters

+
+
control

+
Control list

+
+
item

+
Extended data frame of item parameters

+
+
theta_summary

+
Summary of person parameters

+
+
...

+

+
+

+    

+    
References

     
Linacre, J. M. (1994). Many-Facet Rasch Measurement.
 Chicago: MESA Press.

-    
Note

-
+    

+    

+    
Note

     
This joint maximum likelihood estimation procedure should be
 compatible with Winsteps and Facets software, see also
 http://www.rasch.org/software.htm.

-    
See also

-
-    
For estimating the same class of models with marginal
-maximum likelihood estimation see tam.mml.

-
-    
Examples

-    
#############################################################################
-# EXAMPLE 1: Dichotomous data
-#############################################################################
-data(data.sim.rasch)
-resp <- data.sim.rasch[1:700, seq( 1, 40, len=10)  ]  # subsample
-# estimate the Rasch model with JML (function 'tam.jml')
-mod1a <- TAM::tam.jml(resp=resp)
-summary(mod1a)
-itemfit <- TAM::tam.fit(mod1a)$fit.item
-
-# compare results with Rasch model estimated by MML
-mod1b <- TAM::tam.mml(resp=resp )
-
-# constrain item difficulties to zero
-mod1c <- TAM::tam.jml(resp=resp, constraint="items")
-
-# plot estimated parameters
-plot( mod1a$xsi, mod1b$xsi$xsi, pch=16,
-    xlab=expression( paste( xi[i], " (JML)" )),
-    ylab=expression( paste( xi[i], " (MML)" )),
-    main="Item Parameter Estimate Comparison")
-lines( c(-5,5), c(-5,5), col="gray" )
-
-# Now, the adjustment pf .05 instead of the default .3 is used.
-mod1d <- TAM::tam.jml(resp=resp, adj=.05)
-# compare item parameters
-round( rbind( mod1a$xsi, mod1d$xsi ), 3 )
-  ##          [,1]   [,2]   [,3]   [,4]   [,5]  [,6]  [,7]  [,8]  [,9] [,10]
-  ##   [1,] -2.076 -1.743 -1.217 -0.733 -0.338 0.147 0.593 1.158 1.570 2.091
-  ##   [2,] -2.105 -1.766 -1.233 -0.746 -0.349 0.139 0.587 1.156 1.574 2.108
-
-# person parameters for persons with a score 0, 5 and 10
-pers1 <- data.frame( "score_adj0.3"=mod1a$PersonScore, "theta_adj0.3"=mod1a$theta,
-           "score_adj0.05"=mod1d$PersonScore, "theta_adj0.05"=mod1d$theta  )
-round( pers1[ c(698, 683, 608), ],3  )
-  ##       score_adj0.3 theta_adj0.3 score_adj0.05 theta_adj0.05
-  ##   698          0.3       -4.404          0.05        -6.283
-  ##   683          5.0       -0.070          5.00        -0.081
-  ##   608          9.7        4.315          9.95         6.179
-
-if (FALSE) {
-#*** item fit and person fit statistics
-fmod1a <- TAM::tam.jml.fit(mod1a)
-head(fmod1a$fit.item)
-head(fmod1a$fit.person)
-
-#*** Models in which some item parameters are fixed
-xsi.fixed <- cbind( c(1,3,9,10), c(-2, -1.2, 1.6, 2 ) )
-mod1e <- TAM::tam.jml( resp=resp, xsi.fixed=xsi.fixed )
-summary(mod1e)
-
-#*** Model in which also some person parameters theta are fixed
-# fix theta parameters of persons 2, 3, 4 and 33 to values -2.9, ...
-theta.fixed <- cbind( c(2,3,4,33), c( -2.9, 4, -2.9, -2.9 ) )
-mod1g <- TAM::tam.jml( resp=resp, xsi.fixed=xsi.fixed, theta.fixed=theta.fixed )
-# look at estimated results
-ind.person <- c( 1:5, 30:33 )
-cbind( mod1g$WLE, mod1g$errorWLE )[ind.person,]
-
-#############################################################################
-# EXAMPLE 2: Partial credit model
-#############################################################################
-
-data(data.gpcm, package="TAM")
-dat <- data.gpcm
-
-# JML estimation
-mod2 <- TAM::tam.jml(resp=dat)
-mod2$xsi     # extract item parameters
-summary(mod2)
-TAM::tam.fit(mod2)    # item and person infit/outfit statistic
-
-#* estimate rating scale model
-A <- TAM::designMatrices(resp=dat, modeltype="RSM")$A
-#* estimate model with design matrix A
-mod3 <- TAM::tam.jml(dat, A=A)
-summary(mod3)
-
-#############################################################################
-# EXAMPLE 3: Facet model estimation using joint maximum likelihood
-#            data.ex10; see also Example 10 in ?tam.mml
-#############################################################################
-
-data(data.ex10)
-dat <- data.ex10
-  ## > head(dat)
-  ##  pid rater I0001 I0002 I0003 I0004 I0005
-  ##    1     1     0     1     1     0     0
-  ##    1     2     1     1     1     1     0
-  ##    1     3     1     1     1     0     1
-  ##    2     2     1     1     1     0     1
-  ##    2     3     1     1     0     1     1
-
-facets <- dat[, "rater", drop=FALSE ] # define facet (rater)
-pid <- dat$pid      # define person identifier (a person occurs multiple times)
-resp <- dat[, -c(1:2) ]        # item response data
-formulaA <- ~ item * rater      # formula
-
-# use MML function only to restructure data and input obtained design matrices
-# and processed response data to tam.jml (-> therefore use only 2 iterations)
-mod3a <- TAM::tam.mml.mfr( resp=resp, facets=facets, formulaA=formulaA,
-             pid=dat$pid,  control=list(maxiter=2) )
-
-# use modified response data mod3a$resp and design matrix mod3a$A
-resp1 <- mod3a$resp
-# JML
-mod3b <- TAM::tam.jml( resp=resp1, A=mod3a$A, control=list(maxiter=200) )
-
-#############################################################################
-# EXAMPLE 4: Multi faceted model with some anchored item and person parameters
-#############################################################################
-
-data(data.exJ03)
-resp <- data.exJ03$resp
-X <- data.exJ03$X
-
-#*** (0) preprocess data with TAM::tam.mml.mfr
-mod0 <- TAM::tam.mml.mfr( resp=resp, facets=X, pid=X$rater,
-                formulaA=~ leader + item + step,
-                control=list(maxiter=2) )
-summary(mod0)
-
-#*** (1) estimation with tam.jml (no parameter fixings)
-
-# extract processed data and design matrix from tam.mml.mfr
-resp1 <- mod0$resp
-A1 <- mod0$A
-# estimate model with tam.jml
-mod1 <- TAM::tam.jml( resp=resp1, A=A1, control=list( Msteps=4, maxiter=100 ) )
-summary(mod1)
-
-#*** (2) fix some parameters (persons and items)
-
-# look at indices in mod1$xsi
-mod1$xsi
-# fix step parameters
-xsi.index1 <- cbind( 21:25, c( -2.44, 0.01, -0.15, 0.01,  1.55 ) )
-# fix some item parameters of items 1,2,3,6 and 13
-xsi.index2 <- cbind( c(1,2,3,6,13), c(-2,-1,-1,-1.32, -1 ) )
-xsi.index <- rbind( xsi.index1, xsi.index2 )
-# fix some theta parameters of persons 1, 15 and 20
-theta.fixed <- cbind(  c(1,15,20), c(0.4, 1, 0 ) )
-# estimate model, theta.fixed only works for version=1
-mod2 <- TAM::tam.jml( resp=resp1, A=A1, xsi.fixed=xsi.fixed, theta.fixed=theta.fixed,
-            control=list( Msteps=4, maxiter=100) )
-summary(mod2)
-cbind( mod2$WLE, mod2$errorWLE )
-}

+    

+    

+    
See also

+    
For estimating the same class of models with marginal
+maximum likelihood estimation see tam.mml.

+    

+
+    

+    
Examples

+    
+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/reference/tam.latreg.html b/docs/reference/tam.latreg.html
index 9c074af..872e661 100644
--- a/docs/reference/tam.latreg.html
+++ b/docs/reference/tam.latreg.html
@@ -1,73 +1,18 @@
-
 
-
-  
-  
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-
-Latent Regression Model — tam.latreg • TAM
-
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-Latent Regression Model — tam.latreg • TAM
-
-
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-  
+
+    
 
-  
     

-      

-      
 
       
 
-      

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+      

   

     

     
Latent Regression Model

@@ -124,170 +56,151 @@ 
Latent Regression Model

 \bold{\beta} + \bold{\varepsilon}\).
 Only the individual likelihood evaluated at a
 \(\bold{\theta}\) grid is needed as the input. Like in
-tam.mml a multivariate normal distribution is posed
+tam.mml a multivariate normal distribution is posed
 on the residual distribution. Plausible values can be drawn by subsequent
-application of tam.pv (see Example 1).

+application of tam.pv (see Example 1).

+    

+
+    

+    
tam.latreg(like, theta=NULL, Y=NULL, group=NULL, formulaY=NULL, dataY=NULL,
+   beta.fixed=FALSE, beta.inits=NULL, variance.fixed=NULL,
+   variance.inits=NULL, est.variance=TRUE, pweights=NULL, pid=NULL,
+   userfct.variance=NULL, variance.Npars=NULL, verbose=TRUE, control=list())
+
+# S3 method for tam.latreg
+summary(object,file=NULL,...)
+
+# S3 method for tam.latreg
+print(x,...)

     

 
-    
tam.latreg(like, theta=NULL, Y=NULL, group=NULL, formulaY=NULL, dataY=NULL,
-   beta.fixed=FALSE, beta.inits=NULL, variance.fixed=NULL,
-   variance.inits=NULL, est.variance=TRUE, pweights=NULL, pid=NULL,
-   userfct.variance=NULL, variance.Npars=NULL, verbose=TRUE, control=list())
-
-# S3 method for tam.latreg
-summary(object,file=NULL,...)
-
-# S3 method for tam.latreg
-print(x,...)

-
-    
Arguments

-    
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
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-    
-      
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-      
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-    
-      
-      
-    
-    
-      
-      
-    
-    
like
Individual likelihood. This can be typically extracted from fitted
-item response models by making use of IRT.likelihood.
theta
Used \(\bold{\theta}\) grid in the fitted IRT model. If like
+    

+    
Arguments

+    
like

+
Individual likelihood. This can be typically extracted from fitted
+item response models by making use of IRT.likelihood.

+
+  
theta

+
Used \(\bold{\theta}\) grid in the fitted IRT model. If like
 is generated by the IRT.likelihood function, then theta
-is automatically extracted as an attribute.
Y
A matrix of covariates in latent regression. Note that the
-     intercept is automatically included as the first predictor.
group
An optional vector of group identifiers
formulaY
An R formula for latent regression. Transformations of predictors
+is automatically extracted as an attribute.

+
+  
Y

+
A matrix of covariates in latent regression. Note that the
+     intercept is automatically included as the first predictor.

+
+  
group

+
An optional vector of group identifiers

+
+  
formulaY

+
An R formula for latent regression. Transformations of predictors
      in \(Y\) (included in dataY) can be easily specified,
-     e. g. female*race or I(age^2).
dataY
An optional data frame with possible covariates \(Y\) in latent regression.
+     e. g. female*race or I(age^2).

+
+  
dataY

+
An optional data frame with possible covariates \(Y\) in latent regression.
      This data frame will be used if an R formula in formulaY
-     is specified.
beta.fixed
A matrix with three columns for fixing regression coefficients.
+     is specified.

+
+  
beta.fixed

+
A matrix with three columns for fixing regression coefficients.
      1st column: Index of \(Y\) value, 2nd column: dimension,
-     3rd column: fixed \(\beta\) value. 

+     3rd column: fixed \(\beta\) value. 

      If no constraints should be imposed on \(\beta\), then
      set beta.fixed=FALSE (see Example 2, Model 2_4)
-     which is the default.
beta.inits
A matrix (same format as in beta.fixed)
-     with initial \(\beta\) values
variance.fixed
An optional matrix with three columns for fixing
+     which is the default.

+
+  
beta.inits

+
A matrix (same format as in beta.fixed)
+     with initial \(\beta\) values

+
+  
variance.fixed

+
An optional matrix with three columns for fixing
      entries in covariance matrix:
      1st column: dimension 1, 2nd column: dimension 2,
-     3rd column: fixed value
variance.inits
Initial covariance matrix in estimation. All matrix entries have to be
+     3rd column: fixed value

+
+  
variance.inits

+
Initial covariance matrix in estimation. All matrix entries have to be
      specified and this matrix is NOT in the same format like
-     variance.inits.
est.variance
Should the covariance matrix be estimated? This argument
+     variance.inits.

+
+  
est.variance

+
Should the covariance matrix be estimated? This argument
      applies to estimated item slopes in tam.mml.2pl.
      The default is FALSE which means that latent
-     variables (in the first group) are standardized in 2PL estimation.
pweights
An optional vector of person weights
pid
An optional vector of person identifiers
userfct.variance
Optional user customized function for variance specification
-(See Simulated Example 17).
variance.Npars
Number of estimated parameters of variance matrix
-if a userfct.variance is provided.
verbose
Optional logical indicating whether iteration should be displayed.
control
List of control parameters, see tam.mml fro details.
object
Object of class tam.latreg
file
A file name in which the summary output will be written
x
Object of class tam.latreg
...
Further arguments to be passed

-
-    
Value

-
-    
Subset of values of tam.mml. In addition,
-means (M_post) and standard deviations (SD_post) are computed.

-    
See also

+     variables (in the first group) are standardized in 2PL estimation.

+
+
pweights

+
An optional vector of person weights

+
+  
pid

+
An optional vector of person identifiers

+
+
userfct.variance

+
Optional user customized function for variance specification
+(See Simulated Example 17).

+
+
variance.Npars

+
Number of estimated parameters of variance matrix
+if a userfct.variance is provided.

 
-    
See also tam.pv for plausible value imputation.

+  
verbose

+
Optional logical indicating whether iteration should be displayed.

 
-    
Examples

-    

+
control

+
List of control parameters, see tam.mml fro details.

+
+  
object

+
Object of class tam.latreg

+
+
file

+
A file name in which the summary output will be written

+
+
x

+
Object of class tam.latreg

+
+
...

+
Further arguments to be passed

+
+

+    

+    
Value

+    
+
+
Subset of values of tam.mml. In addition,
+means (M_post) and standard deviations (SD_post) are computed.

+    

+    

+    
See also

+    
See also tam.pv for plausible value imputation.

+    

+
+    

+    
Examples

+    
+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
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-Linking of Fitted Unidimensional Item Response Models in <span class="pkg">TAM</span> — tam.linking • TAM
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-TAM — tam.linking" />
-Linking of Fitted Unidimensional Item Response Models in TAM — tam.linking • TAM
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Linking of Fitted Unidimensional Item Response Models in TAM

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Linking of Fitted Unidimensional Item Response Models in T
 
The linking of two studies is implemented in the tam_linking_2studies function.

     

 
-    
tam.linking(tamobj_list, type="Hae", method="joint", pow_rob_hae=1, eps_rob_hae=1e-4,
-   theta=NULL, wgt=NULL, wgt_sd=2, fix.slope=FALSE, elim_items=NULL,
-   par_init=NULL, verbose=TRUE)
+    

+    
tam.linking(tamobj_list, type="Hae", method="joint", pow_rob_hae=1, eps_rob_hae=1e-4,
+   theta=NULL, wgt=NULL, wgt_sd=2, fix.slope=FALSE, elim_items=NULL,
+   par_init=NULL, verbose=TRUE)
+
+# S3 method for tam.linking
+summary(object, file=NULL, ...)
+
+# S3 method for tam.linking
+print(x, ...)
+
+tam_linking_2studies( B1, AXsi1, guess1, B2, AXsi2, guess2, theta, wgt, type,
+    M1=0, SD1=1, M2=0, SD2=1, fix.slope=FALSE, pow_rob_hae=1)
+
+# S3 method for tam_linking_2studies
+summary(object, file=NULL, ...)
+
+# S3 method for tam_linking_2studies
+print(x, ...)

+    

+
+    

+    
Arguments

+    
tamobj_list

+
List of fitted objects in TAM

+
+  
type

+
Type of linking method: "SL" (Stocking-Lord), "Hae" (Haebara) or
+"RobHae" (robust Haebara). See Details for more information.
+The default is the Haebara linking method.

 
-# S3 method for tam.linking
-summary(object, file=NULL, ...)
+
method

+
Chain linking ("chain") or joint linking ("joint")

 
-# S3 method for tam.linking
-print(x, ...)
+
pow_rob_hae

+
Power for robust Heabara linking

 
-tam_linking_2studies( B1, AXsi1, guess1, B2, AXsi2, guess2, theta, wgt, type,
-    M1=0, SD1=1, M2=0, SD2=1, fix.slope=FALSE, pow_rob_hae=1)
+
eps_rob_hae

+
Value \(\varepsilon\) for numerical approximation of
+loss function \(|x|^p\) in robust Haebara linking

 
-# S3 method for tam_linking_2studies
-summary(object, file=NULL, ...)
+  
theta

+
Grid of \(\theta\) points. The default is seq(-6,6,len=101).

 
-# S3 method for tam_linking_2studies
-print(x, ...)

+  
wgt

+
Weights defined for the theta grid. The default is 
tam_normalize_vector( stats::dnorm( theta, sd=2 )).

 
-    
Arguments

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tamobj_list
List of fitted objects in TAM
type
Type of linking method: "SL" (Stocking-Lord), "Hae" (Haebara) or
-"RobHae" (robust Haebara). See Details for more information.
-The default is the Haebara linking method.
method
Chain linking ("chain") or joint linking ("joint")
pow_rob_hae
Power for robust Heabara linking
eps_rob_hae
Value \(\varepsilon\) for numerical approximation of
-loss function \(|x|^p\) in robust Haebara linking
theta
Grid of \(\theta\) points. The default is seq(-6,6,len=101).
wgt
Weights defined for the theta grid. The default is 

-tam_normalize_vector( stats::dnorm( theta, sd=2 )).
wgt_sd
Standard deviation for \(\theta\) grid used for
-linking function
fix.slope
Logical indicating whether the slope transformation constant is fixed to 1.
elim_items
List of vectors refering to items which should be removed
-from linking (see Model 'lmod2' in Example 1)
par_init
Optional vector with initial parameter values
verbose
Logical indicating progress of linking computation
object
Object of class tam.linking or tam_linking_2studies.
x
Object of class tam.linking or tam_linking_2studies.
file
A file name in which the summary output will be written
...
Further arguments to be passed
B1
Array \(B\) for first study
AXsi1
Matrix \(A \xi\) for first study
guess1
Guessing parameter for first study
B2
Array \(B\) for second study
AXsi2
Matrix \(A \xi\) for second study
guess2
Guessing parameter for second study
M1
Mean of first study
SD1
Standard deviation of first study
M2
Mean of second study
SD2
Standard deviation of second study

-
-    
Details

+
wgt_sd

+
Standard deviation for \(\theta\) grid used for
+linking function

 
+  
fix.slope

+
Logical indicating whether the slope transformation constant is fixed to 1.

+
+
elim_items

+
List of vectors refering to items which should be removed
+from linking (see Model 'lmod2' in Example 1)

+
+
par_init

+
Optional vector with initial parameter values

+
+
verbose

+
Logical indicating progress of linking computation

+
+
object

+
Object of class tam.linking or tam_linking_2studies.

+
+
x

+
Object of class tam.linking or tam_linking_2studies.

+
+
file

+
A file name in which the summary output will be written

+
+
...

+
Further arguments to be passed

+
+
B1

+
Array \(B\) for first study

+
+
AXsi1

+
Matrix \(A \xi\) for first study

+
+
guess1

+
Guessing parameter for first study

+
+
B2

+
Array \(B\) for second study

+
+
AXsi2

+
Matrix \(A \xi\) for second study

+
+
guess2

+
Guessing parameter for second study

+
+
M1

+
Mean of first study

+
+
SD1

+
Standard deviation of first study

+
+
M2

+
Mean of second study

+
+
SD2

+
Standard deviation of second study

+
+

+    

+    
Details

     
The Haebara linking is defined by minimizing the loss function
 $$\sum_i \sum_k \int \left ( P_{ik} ( \theta ) - P_{ik}^\ast ( \theta ) \right )^2  $$
 A robustification of Haebara linking minimizes the loss function
 $$\sum_i \sum_k \int \left ( P_{ik} ( \theta ) - P_{ik}^\ast ( \theta ) \right )^p  $$
 with a power \(p\) (defined in pow_rob_hae) smaller than 2. He, Cui and
 Osterlind (2015) consider \(p=1\).

-    
Value

+    

+    

+    
Value

+    
 
-    
List containing entries

-
parameters_list
List containing transformed item parameters

-
linking_list
List containing results of each linking in the
+
List containing entries

+
parameters_list

+
List containing transformed item parameters

+
+
linking_list

+
List containing results of each linking in the
    linking chain

- 
M_SD
Mean and standard deviation for each study after linking

- 
trafo_items
Transformation constants for item parameters

- 
trafo_persons
Transformation constants for person parameters

 
-    
References

+ 
M_SD

+
Mean and standard deviation for each study after linking

+
+ 
trafo_items

+
Transformation constants for item parameters

 
+ 
trafo_persons

+
Transformation constants for person parameters

+
+

+    

+    
References

     
Battauz, M. (2015). equateIRT: An R package for IRT test equating.
 Journal of Statistical Software, 68(7), 1-22.
-doi: 10.18637/jss.v068.i07

+doi:10.18637/jss.v068.i07

 
Gonzalez, J., & Wiberg, M. (2017).
 Applying test equating methods: Using R. New York, Springer.
-doi: 10.1007/978-3-319-51824-4

+doi:10.1007/978-3-319-51824-4

 
He, Y., Cui, Z., & Osterlind, S. J. (2015). New robust scale transformation methods in the
 presence of outlying common items.
 Applied Psychological Measurement, 39(8), 613-626.
-doi: 10.1177/0146621615587003

+doi:10.1177/0146621615587003

 
Kolen, M. J., & Brennan, R. L. (2014). Test equating, scaling, and linking:
 Methods and practices. New York, Springer.
-doi: 10.1007/978-1-4939-0317-7

+doi:10.1007/978-1-4939-0317-7

 
Weeks, J. P. (2010). plink: An R package for linking mixed-format tests
 using IRT-based methods. Journal of Statistical Software, 35(12), 1-33.
-doi: 10.18637/jss.v035.i12

-    
See also

-
-    
Linking or equating of item response models can be also conducted with plink
+doi:10.18637/jss.v035.i12

+    

+    

+    
See also

+    
Linking or equating of item response models can be also conducted with plink
 (Weeks, 2010), equate, equateIRT (Battauz, 2015), equateMultiple,
 kequate and irteQ packages.

-
See also the sirt::linking.haberman,
-sirt::invariance.alignment and sirt::linking.haebara functions
+
See also the sirt::linking.haberman,
+sirt::invariance.alignment and sirt::linking.haebara functions
 in the sirt package.

+    

 
-    
Examples

-    
if (FALSE) {
-#############################################################################
-# EXAMPLE 1: Linking dichotomous data with the 2PL model
-#############################################################################
-
-data(data.ex16)
-dat <- data.ex16
-items <- colnames(dat)[-c(1,2)]
-
-# fit grade 1
-rdat1 <- TAM::tam_remove_missings( dat[ dat$grade==1, ], items=items )
-mod1 <- TAM::tam.mml.2pl( resp=rdat1$resp[, rdat1$items], pid=rdat1$dat$idstud )
-summary(mod1)
-
-# fit grade 2
-rdat2 <- TAM::tam_remove_missings( dat[ dat$grade==2, ], items=items )
-mod2 <- TAM::tam.mml.2pl( resp=rdat2$resp[, rdat2$items], pid=rdat2$dat$idstud )
-summary(mod2)
-
-# fit grade 3
-rdat3 <- TAM::tam_remove_missings( dat[ dat$grade==3, ], items=items )
-mod3 <- TAM::tam.mml.2pl( resp=rdat3$resp[, rdat3$items], pid=rdat3$dat$idstud )
-summary(mod3)
-
-# define list of fitted models
-tamobj_list <- list( mod1, mod2, mod3 )
-
-#-- link item response models
-lmod <- TAM::tam.linking( tamobj_list)
-summary(lmod)
-
-# estimate WLEs based on transformed item parameters
-parm_list <- lmod$parameters_list
-
-# WLE grade 1
-arglist <- list( resp=mod1$resp, B=parm_list[[1]]$B, AXsi=parm_list[[1]]$AXsi )
-wle1 <- TAM::tam.mml.wle(tamobj=arglist)
-
-# WLE grade 2
-arglist <- list( resp=mod2$resp, B=parm_list[[2]]$B, AXsi=parm_list[[2]]$AXsi )
-wle2 <- TAM::tam.mml.wle(tamobj=arglist)
-
-# WLE grade 3
-arglist <- list( resp=mod3$resp, B=parm_list[[3]]$B, AXsi=parm_list[[3]]$AXsi )
-wle3 <- TAM::tam.mml.wle(tamobj=arglist)
-
-# compare result with chain linking
-lmod1b <- TAM::tam.linking(tamobj_list)
-summary(lmod1b)
-
-#-- linking with some eliminated items
-
-# remove three items from first group and two items from third group
-elim_items <- list( c("A1", "E2","F1"), NULL,  c("F1","F2") )
-lmod2 <- TAM::tam.linking(tamobj_list, elim_items=elim_items)
-summary(lmod2)
-
-#-- Robust Haebara linking with p=1
-lmod3a <- TAM::tam.linking(tamobj_list, type="RobHae", pow_rob_hae=1)
-summary(lmod3a)
-
-#-- Robust Haeabara linking with initial parameters and prespecified epsilon value
-par_init <- lmod3a$par
-lmod3b <- TAM::tam.linking(tamobj_list, type="RobHae", pow_rob_hae=.1,
-                eps_rob_hae=1e-3, par_init=par_init)
-summary(lmod3b)
-
-#############################################################################
-# EXAMPLE 2: Linking polytomous data with the partial credit model
-#############################################################################
-
-data(data.ex17)
-dat <- data.ex17
-
-items <- colnames(dat)[-c(1,2)]
-
-# fit grade 1
-rdat1 <- TAM::tam_remove_missings( dat[ dat$grade==1, ], items=items )
-mod1 <- TAM::tam.mml.2pl( resp=rdat1$resp[, rdat1$items], pid=rdat1$dat$idstud )
-summary(mod1)
-
-# fit grade 2
-rdat2 <- TAM::tam_remove_missings( dat[ dat$grade==2, ], items=items )
-mod2 <- TAM::tam.mml.2pl( resp=rdat2$resp[, rdat2$items], pid=rdat2$dat$idstud )
-summary(mod2)
-
-# fit grade 3
-rdat3 <- TAM::tam_remove_missings( dat[ dat$grade==3, ], items=items )
-mod3 <- TAM::tam.mml.2pl( resp=rdat3$resp[, rdat3$items], pid=rdat3$dat$idstud )
-summary(mod3)
-
-# list of fitted TAM models
-tamobj_list <- list( mod1, mod2, mod3 )
-
-#-- linking: fix slope because partial credit model is fitted
-lmod <- TAM::tam.linking( tamobj_list, fix.slope=TRUE)
-summary(lmod)
-
-# WLEs can be estimated in the same way as in Example 1.
-
-#############################################################################
-# EXAMPLE 3: Linking dichotomous data with the multiple group 2PL models
-#############################################################################
-
-data(data.ex16)
-dat <- data.ex16
-items <- colnames(dat)[-c(1,2)]
-
-# fit grade 1
-rdat1 <- TAM::tam_remove_missings( dat[ dat$grade==1, ], items=items )
-# create some grouping variable
-group <- ( seq( 1, nrow( rdat1$dat ) ) %% 3 ) + 1
-mod1 <- TAM::tam.mml.2pl( resp=rdat1$resp[, rdat1$items], pid=rdat1$dat$idstud, group=group)
-summary(mod1)
-
-# fit grade 2
-rdat2 <- TAM::tam_remove_missings( dat[ dat$grade==2, ], items=items )
-group <- 1*(rdat2$dat$dat$idstud > 500)
-mod2 <- TAM::tam.mml.2pl( resp=rdat2$resp[, rdat2$items], pid=rdat2$dat$dat$idstud, group=group)
-summary(mod2)
-
-# fit grade 3
-rdat3 <- TAM::tam_remove_missings( dat[ dat$grade==3, ], items=items )
-mod3 <- TAM::tam.mml.2pl( resp=rdat3$resp[, rdat3$items], pid=rdat3$dat$idstud )
-summary(mod3)
-
-# define list of fitted models
-tamobj_list <- list( mod1, mod2, mod3 )
-
-#-- link item response models
-lmod <- TAM::tam.linking( tamobj_list)
-
-#############################################################################
-# EXAMPLE 4: Linking simulated dichotomous data with two groups
-#############################################################################
-
-library(sirt)
-
-#*** simulate data
-N <- 3000  # number of persons
-I <- 30    # number of items
-b <- seq(-2,2, length=I)
-# data for group 1
-dat1 <- sirt::sim.raschtype( rnorm(N, mean=0, sd=1), b=b )
-# data for group 2
-dat2 <- sirt::sim.raschtype( rnorm(N, mean=1, sd=.6), b=b )
-
-# fit group 1
-mod1 <- TAM::tam.mml.2pl( resp=dat1 )
-summary(mod1)
-
-# fit group 2
-mod2 <- TAM::tam.mml.2pl( resp=dat2 )
-summary(mod2)
-
-# define list of fitted models
-tamobj_list <- list( mod1, mod2 )
-
-#-- link item response models
-lmod <- TAM::tam.linking( tamobj_list)
-summary(lmod)
-
-# estimate WLEs based on transformed item parameters
-parm_list <- lmod$parameters_list
-
-# WLE grade 1
-arglist <- list( resp=mod1$resp, B=parm_list[[1]]$B, AXsi=parm_list[[1]]$AXsi )
-wle1 <- TAM::tam.mml.wle(tamobj=arglist)
-
-# WLE grade 2
-arglist <- list( resp=mod2$resp, B=parm_list[[2]]$B, AXsi=parm_list[[2]]$AXsi )
-wle2 <- TAM::tam.mml.wle(tamobj=arglist)
-summary(wle1)
-summary(wle2)
-
-# estimation with linked and fixed item parameters for group 2
-B <- parm_list[[2]]$B
-xsi.fixed <- cbind( 1:I, -parm_list[[2]]$AXsi[,2] )
-mod2f <- TAM::tam.mml( resp=dat2, B=B, xsi.fixed=xsi.fixed )
-summary(mod2f)
-}

+    

+    
Examples

+    
if (FALSE) {
+#############################################################################
+# EXAMPLE 1: Linking dichotomous data with the 2PL model
+#############################################################################
+
+data(data.ex16)
+dat <- data.ex16
+items <- colnames(dat)[-c(1,2)]
+
+# fit grade 1
+rdat1 <- TAM::tam_remove_missings( dat[ dat$grade==1, ], items=items )
+mod1 <- TAM::tam.mml.2pl( resp=rdat1$resp[, rdat1$items], pid=rdat1$dat$idstud )
+summary(mod1)
+
+# fit grade 2
+rdat2 <- TAM::tam_remove_missings( dat[ dat$grade==2, ], items=items )
+mod2 <- TAM::tam.mml.2pl( resp=rdat2$resp[, rdat2$items], pid=rdat2$dat$idstud )
+summary(mod2)
+
+# fit grade 3
+rdat3 <- TAM::tam_remove_missings( dat[ dat$grade==3, ], items=items )
+mod3 <- TAM::tam.mml.2pl( resp=rdat3$resp[, rdat3$items], pid=rdat3$dat$idstud )
+summary(mod3)
+
+# define list of fitted models
+tamobj_list <- list( mod1, mod2, mod3 )
+
+#-- link item response models
+lmod <- TAM::tam.linking( tamobj_list)
+summary(lmod)
+
+# estimate WLEs based on transformed item parameters
+parm_list <- lmod$parameters_list
+
+# WLE grade 1
+arglist <- list( resp=mod1$resp, B=parm_list[[1]]$B, AXsi=parm_list[[1]]$AXsi )
+wle1 <- TAM::tam.mml.wle(tamobj=arglist)
+
+# WLE grade 2
+arglist <- list( resp=mod2$resp, B=parm_list[[2]]$B, AXsi=parm_list[[2]]$AXsi )
+wle2 <- TAM::tam.mml.wle(tamobj=arglist)
+
+# WLE grade 3
+arglist <- list( resp=mod3$resp, B=parm_list[[3]]$B, AXsi=parm_list[[3]]$AXsi )
+wle3 <- TAM::tam.mml.wle(tamobj=arglist)
+
+# compare result with chain linking
+lmod1b <- TAM::tam.linking(tamobj_list)
+summary(lmod1b)
+
+#-- linking with some eliminated items
+
+# remove three items from first group and two items from third group
+elim_items <- list( c("A1", "E2","F1"), NULL,  c("F1","F2") )
+lmod2 <- TAM::tam.linking(tamobj_list, elim_items=elim_items)
+summary(lmod2)
+
+#-- Robust Haebara linking with p=1
+lmod3a <- TAM::tam.linking(tamobj_list, type="RobHae", pow_rob_hae=1)
+summary(lmod3a)
+
+#-- Robust Haeabara linking with initial parameters and prespecified epsilon value
+par_init <- lmod3a$par
+lmod3b <- TAM::tam.linking(tamobj_list, type="RobHae", pow_rob_hae=.1,
+                eps_rob_hae=1e-3, par_init=par_init)
+summary(lmod3b)
+
+#############################################################################
+# EXAMPLE 2: Linking polytomous data with the partial credit model
+#############################################################################
+
+data(data.ex17)
+dat <- data.ex17
+
+items <- colnames(dat)[-c(1,2)]
+
+# fit grade 1
+rdat1 <- TAM::tam_remove_missings( dat[ dat$grade==1, ], items=items )
+mod1 <- TAM::tam.mml.2pl( resp=rdat1$resp[, rdat1$items], pid=rdat1$dat$idstud )
+summary(mod1)
+
+# fit grade 2
+rdat2 <- TAM::tam_remove_missings( dat[ dat$grade==2, ], items=items )
+mod2 <- TAM::tam.mml.2pl( resp=rdat2$resp[, rdat2$items], pid=rdat2$dat$idstud )
+summary(mod2)
+
+# fit grade 3
+rdat3 <- TAM::tam_remove_missings( dat[ dat$grade==3, ], items=items )
+mod3 <- TAM::tam.mml.2pl( resp=rdat3$resp[, rdat3$items], pid=rdat3$dat$idstud )
+summary(mod3)
+
+# list of fitted TAM models
+tamobj_list <- list( mod1, mod2, mod3 )
+
+#-- linking: fix slope because partial credit model is fitted
+lmod <- TAM::tam.linking( tamobj_list, fix.slope=TRUE)
+summary(lmod)
+
+# WLEs can be estimated in the same way as in Example 1.
+
+#############################################################################
+# EXAMPLE 3: Linking dichotomous data with the multiple group 2PL models
+#############################################################################
+
+data(data.ex16)
+dat <- data.ex16
+items <- colnames(dat)[-c(1,2)]
+
+# fit grade 1
+rdat1 <- TAM::tam_remove_missings( dat[ dat$grade==1, ], items=items )
+# create some grouping variable
+group <- ( seq( 1, nrow( rdat1$dat ) ) %% 3 ) + 1
+mod1 <- TAM::tam.mml.2pl( resp=rdat1$resp[, rdat1$items], pid=rdat1$dat$idstud, group=group)
+summary(mod1)
+
+# fit grade 2
+rdat2 <- TAM::tam_remove_missings( dat[ dat$grade==2, ], items=items )
+group <- 1*(rdat2$dat$dat$idstud > 500)
+mod2 <- TAM::tam.mml.2pl( resp=rdat2$resp[, rdat2$items], pid=rdat2$dat$dat$idstud, group=group)
+summary(mod2)
+
+# fit grade 3
+rdat3 <- TAM::tam_remove_missings( dat[ dat$grade==3, ], items=items )
+mod3 <- TAM::tam.mml.2pl( resp=rdat3$resp[, rdat3$items], pid=rdat3$dat$idstud )
+summary(mod3)
+
+# define list of fitted models
+tamobj_list <- list( mod1, mod2, mod3 )
+
+#-- link item response models
+lmod <- TAM::tam.linking( tamobj_list)
+
+#############################################################################
+# EXAMPLE 4: Linking simulated dichotomous data with two groups
+#############################################################################
+
+library(sirt)
+
+#*** simulate data
+N <- 3000  # number of persons
+I <- 30    # number of items
+b <- seq(-2,2, length=I)
+# data for group 1
+dat1 <- sirt::sim.raschtype( rnorm(N, mean=0, sd=1), b=b )
+# data for group 2
+dat2 <- sirt::sim.raschtype( rnorm(N, mean=1, sd=.6), b=b )
+
+# fit group 1
+mod1 <- TAM::tam.mml.2pl( resp=dat1 )
+summary(mod1)
+
+# fit group 2
+mod2 <- TAM::tam.mml.2pl( resp=dat2 )
+summary(mod2)
+
+# define list of fitted models
+tamobj_list <- list( mod1, mod2 )
+
+#-- link item response models
+lmod <- TAM::tam.linking( tamobj_list)
+summary(lmod)
+
+# estimate WLEs based on transformed item parameters
+parm_list <- lmod$parameters_list
+
+# WLE grade 1
+arglist <- list( resp=mod1$resp, B=parm_list[[1]]$B, AXsi=parm_list[[1]]$AXsi )
+wle1 <- TAM::tam.mml.wle(tamobj=arglist)
+
+# WLE grade 2
+arglist <- list( resp=mod2$resp, B=parm_list[[2]]$B, AXsi=parm_list[[2]]$AXsi )
+wle2 <- TAM::tam.mml.wle(tamobj=arglist)
+summary(wle1)
+summary(wle2)
+
+# estimation with linked and fixed item parameters for group 2
+B <- parm_list[[2]]$B
+xsi.fixed <- cbind( 1:I, -parm_list[[2]]$AXsi[,2] )
+mod2f <- TAM::tam.mml( resp=dat2, B=B, xsi.fixed=xsi.fixed )
+summary(mod2f)
+}

+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/reference/tam.mml.3pl.html b/docs/reference/tam.mml.3pl.html
index 8b3c728..4f94d82 100644
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+++ b/docs/reference/tam.mml.3pl.html
@@ -1,69 +1,14 @@
-
 
-
-  
-  
-
-
-
-3PL Structured Item Response Model in <span class="pkg">TAM</span> — tam.mml.3pl • TAM
-
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-TAM — tam.mml.3pl" />
-3PL Structured Item Response Model in TAM — tam.mml.3pl • TAM
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+    
 
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3PL Structured Item Response Model in TAM

@@ -121,294 +53,245 @@ 
3PL Structured Item Response Model in TAM

 allowed which can be log-linearly smoothed.

     

 
-    
tam.mml.3pl(resp, Y=NULL, group=NULL, formulaY=NULL, dataY=NULL, ndim=1,
-  pid=NULL, xsi.fixed=NULL, xsi.inits=NULL, xsi.prior=NULL,
-  beta.fixed=NULL, beta.inits=NULL, variance.fixed=NULL, variance.inits=NULL,
-  est.variance=TRUE, A=NULL, notA=FALSE, Q=NULL, Q.fixed=NULL, E=NULL,
-  gammaslope.des="2PL", gammaslope=NULL, gammaslope.fixed=NULL,
-  est.some.slopes=TRUE, gammaslope.max=9.99, gammaslope.constr.V=NULL,
-  gammaslope.constr.c=NULL, gammaslope.center.index=NULL,  gammaslope.center.value=NULL,
-  gammaslope.prior=NULL, userfct.gammaslope=NULL, gammaslope.constr.Npars=0,
-  est.guess=NULL, guess=rep(0, ncol(resp)),
-  guess.prior=NULL, max.guess=0.5, skillspace="normal", theta.k=NULL,
-  delta.designmatrix=NULL, delta.fixed=NULL, delta.inits=NULL, pweights=NULL,
-  item.elim=TRUE, verbose=TRUE, control=list(), Edes=NULL )
-
-# S3 method for tam.mml.3pl
-summary(object,file=NULL,...)
-
-# S3 method for tam.mml.3pl
-print(x,...)

-
-    
Arguments

-    
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resp
Data frame with polytomous item responses \(k=0,...,K\).
-     Missing responses must be declared as NA.
Y
A matrix of covariates in latent regression. Note that the
-     intercept is automatically included as the first predictor.
group
An optional vector of group identifiers
formulaY
An R formula for latent regression. Transformations of predictors
+    

+    
tam.mml.3pl(resp, Y=NULL, group=NULL, formulaY=NULL, dataY=NULL, ndim=1,
+  pid=NULL, xsi.fixed=NULL, xsi.inits=NULL, xsi.prior=NULL,
+  beta.fixed=NULL, beta.inits=NULL, variance.fixed=NULL, variance.inits=NULL,
+  est.variance=TRUE, A=NULL, notA=FALSE, Q=NULL, Q.fixed=NULL, E=NULL,
+  gammaslope.des="2PL", gammaslope=NULL, gammaslope.fixed=NULL,
+  est.some.slopes=TRUE, gammaslope.max=9.99, gammaslope.constr.V=NULL,
+  gammaslope.constr.c=NULL, gammaslope.center.index=NULL,  gammaslope.center.value=NULL,
+  gammaslope.prior=NULL, userfct.gammaslope=NULL, gammaslope.constr.Npars=0,
+  est.guess=NULL, guess=rep(0, ncol(resp)),
+  guess.prior=NULL, max.guess=0.5, skillspace="normal", theta.k=NULL,
+  delta.designmatrix=NULL, delta.fixed=NULL, delta.inits=NULL, pweights=NULL,
+  item.elim=TRUE, verbose=TRUE, control=list(), Edes=NULL )
+
+# S3 method for tam.mml.3pl
+summary(object,file=NULL,...)
+
+# S3 method for tam.mml.3pl
+print(x,...)

+    

+
+    

+    
Arguments

+    
resp

+
Data frame with polytomous item responses \(k=0,...,K\).
+     Missing responses must be declared as NA.

+
+  
Y

+
A matrix of covariates in latent regression. Note that the
+     intercept is automatically included as the first predictor.

+
+  
group

+
An optional vector of group identifiers

+
+  
formulaY

+
An R formula for latent regression. Transformations of predictors
      in \(Y\) (included in dataY) can be easily specified,
-     e. g. female*race or I(age^2).
dataY
An optional data frame with possible covariates \(Y\) in latent regression.
+     e. g. female*race or I(age^2).

+
+  
dataY

+
An optional data frame with possible covariates \(Y\) in latent regression.
      This data frame will be used if an R formula in formulaY
-     is specified.
ndim
Number of dimensions (is not needed to determined by the user)
pid
An optional vector of person identifiers
xsi.fixed
A matrix with two columns for fixing \(\xi\) parameters.
-     1st column: index of \(\xi\) parameter, 2nd column: fixed value
xsi.inits
A matrix with two columns (in the same way defined as in
-     xsi.fixed with initial value for \(\xi\).
xsi.prior
Item-specific prior distribution for \(\xi\) parameters. It is
+     is specified.

+
+  
ndim

+
Number of dimensions (is not needed to determined by the user)

+
+  
pid

+
An optional vector of person identifiers

+
+  
xsi.fixed

+
A matrix with two columns for fixing \(\xi\) parameters.
+     1st column: index of \(\xi\) parameter, 2nd column: fixed value

+
+  
xsi.inits

+
A matrix with two columns (in the same way defined as in
+     xsi.fixed with initial value for \(\xi\).

+
+  
xsi.prior

+
Item-specific prior distribution for \(\xi\) parameters. It is
      assumed that \(\xi_k \sim N( \mu_k, \sigma_k^2 )\). The first column
-     in xsi.prior is \(\mu_k\), the second is \(\sigma_k\).
beta.fixed
A matrix with three columns for fixing regression coefficients.
+     in xsi.prior is \(\mu_k\), the second is \(\sigma_k\).

+
+  
beta.fixed

+
A matrix with three columns for fixing regression coefficients.
      1st column: Index of \(Y\) value, 2nd column: dimension,
-     3rd column: fixed \(\beta\) value. 

+     3rd column: fixed \(\beta\) value. 

      If no constraints should be imposed on \(\beta\), then
-     set beta.fixed=FALSE (see Example 2, Model 2_4).
beta.inits
A matrix (same format as in beta.fixed)
-     with initial \(\beta\) values
variance.fixed
An optional matrix. In case of a single group it is a matrix with three columns for fixing
+     set beta.fixed=FALSE (see Example 2, Model 2_4).

+
+  
beta.inits

+
A matrix (same format as in beta.fixed)
+     with initial \(\beta\) values

+
+  
variance.fixed

+
An optional matrix. In case of a single group it is a matrix with three columns for fixing
      entries in covariance matrix:
      1st column: dimension 1, 2nd column: dimension 2,
      3rd column: fixed value of covariance/variance.
      In case of multiple groups, it is a matrix with four columns
      1st column: group index (from \(1,\ldots,G\), 2nd column: dimension 1,
-     3rd column: dimension 2, 4th column: fixed value of covariance
variance.inits
Initial covariance matrix in estimation. All matrix entries have to be
+     3rd column: dimension 2, 4th column: fixed value of covariance

+
+  
variance.inits

+
Initial covariance matrix in estimation. All matrix entries have to be
      specified and this matrix is NOT in the same format like
-     variance.fixed.
est.variance
Should the covariance matrix be estimated? This argument
+     variance.fixed.

+
+  
est.variance

+
Should the covariance matrix be estimated? This argument
      applies to estimated item slopes in tam.mml.2pl.
      The default is FALSE which means that latent
-     variables (in the first group) are standardized in 2PL estimation.
A
An optional array of dimension \( I \times (K+1) \times N_\xi\).
+     variables (in the first group) are standardized in 2PL estimation.

+
+  
A

+
An optional array of dimension \( I \times (K+1) \times N_\xi\).
      Only \(\xi\) parameters are estimated, entries in \(A\)
-     only correspond to the design.
notA
An optional logical indicating whether all entries in
+     only correspond to the design.

+
+
notA

+
An optional logical indicating whether all entries in
     the \(A\) matrix are set to zero and no item intercept
-    \(\xi\) should be estimated.
Q
An optional \(I \times D\) matrix (the Q-matrix) which specifies the
-  loading structure of items on dimensions.
Q.fixed
Optional \(I \times D\) matrix of the same dimensions
+    \(\xi\) should be estimated.

+
+  
Q

+
An optional \(I \times D\) matrix (the Q-matrix) which specifies the
+  loading structure of items on dimensions.

+
+
Q.fixed

+
Optional \(I \times D\) matrix of the same dimensions
     like Q. Non NA entries contain values at which
-item loadings should be fixed to.
E
Optional design array for item slopes \(\gamma\). It is a four
+item loadings should be fixed to.

+
+  
E

+
Optional design array for item slopes \(\gamma\). It is a four
 dimensional array of size \(I \times (K+1) \times D \times N_\gamma\)
-containing items, categories, dimensions, \(\gamma\) parameter.
gammaslope.des
Optional string indicating type of item slope parameter to be estimated.
+containing items, categories, dimensions, \(\gamma\) parameter.

+
+
gammaslope.des

+
Optional string indicating type of item slope parameter to be estimated.
 gammaslope.des="2PL" estimates a slope parameter for an item,
-gammaslope.des="2PLcat" for an item and a
gammaslope
Initial or fixed vector of \(\gamma\) parameters
gammaslope.fixed
An optional matrix containing fixed values in the \(\gamma\) vector.
-First column: parameter index; second colunmn: fixed value.
est.some.slopes
An optional logical indicating whether some item slopes should be estimated.
gammaslope.max
Value for absolute entries in \(\gamma\) vector
gammaslope.constr.V
An optional constraint matrix \(V\) for item slope parameters \(\gamma\)
gammaslope.constr.c
An optional constraint vector \(c\) for item slope parameters \(\gamma\)
gammaslope.center.index
Indices of gammaslope parameters which should be fixed to
-sum specified in gammaslope.center.value (see Example 7).
gammaslope.center.value
Specified values of sum of
-subset of gammaslope parameters.
gammaslope.prior
Item-specific prior distribution for \(\gamma\) parameters. It is
+gammaslope.des="2PLcat" for an item and a

+
+  
gammaslope

+
Initial or fixed vector of \(\gamma\) parameters

+
+  
gammaslope.fixed

+
An optional matrix containing fixed values in the \(\gamma\) vector.
+First column: parameter index; second colunmn: fixed value.

+
+  
est.some.slopes

+
An optional logical indicating whether some item slopes should be estimated.

+
+
gammaslope.max

+
Value for absolute entries in \(\gamma\) vector

+
+  
gammaslope.constr.V

+
An optional constraint matrix \(V\) for item slope parameters \(\gamma\)

+
+  
gammaslope.constr.c

+
An optional constraint vector \(c\) for item slope parameters \(\gamma\)

+
+
gammaslope.center.index

+
Indices of gammaslope parameters which should be fixed to
+sum specified in gammaslope.center.value (see Example 7).

+
+
gammaslope.center.value

+
Specified values of sum of
+subset of gammaslope parameters.

+
+  
gammaslope.prior

+
Item-specific prior distribution for \(\gamma\) parameters. It is
      assumed that \(\gamma_k \sim N( \mu_k, \sigma_k^2 )\). The first column
-     in gammaslope.prior is \(\mu_k\), the second is \(\sigma_k\).
userfct.gammaslope
A user specified function for
+     in gammaslope.prior is \(\mu_k\), the second is \(\sigma_k\).

+
+
userfct.gammaslope

+
A user specified function for
     constraints or transformations of the \(\gamma\) parameters
-within the algorithm. See Example 17 in tam.mml.
gammaslope.constr.Npars
Number of constrained
-    \(\gamma\) parameters in userfct.gammaslope
est.guess
An optional vector of integers indicating for which items a guessing
+within the algorithm. See Example 17 in tam.mml.

+
+
gammaslope.constr.Npars

+
Number of constrained
+    \(\gamma\) parameters in userfct.gammaslope

+
+
+  
est.guess

+
An optional vector of integers indicating for which items a guessing
 parameter should be estimated. Same integers correspond to same estimated
 guessing parameters. A value of 0 denotes an item for which no guessing
-parameter is estimated.
guess
Fixed or initial guessing parameters
guess.prior
Item-specific prior distribution for guessing parameters \(c_i\). It is
+parameter is estimated.

+
+  
guess

+
Fixed or initial guessing parameters

+
+  
guess.prior

+
Item-specific prior distribution for guessing parameters \(c_i\). It is
      assumed that \(c_i \sim Beta(a_i, b_i)\). The first column
-     in gammaslope.prior is \(a_i\), the second is \(b_i\).
max.guess
Upper bound for guessing parameters
skillspace
Skill space: normal distribution ("normal") or discrete
-distribution ("discrete").
theta.k
A matrix of the \(\bold{\theta}\) skill space in case of a discrete
-distribution (skillspace="discrete").
delta.designmatrix
A design matrix of the log-linear model for the skill space in case of a discrete
-distribution (skillspace="discrete").
delta.fixed
Fixed \(\delta\) values of the log-linear skill space.
+     in gammaslope.prior is \(a_i\), the second is \(b_i\).

+
+
max.guess

+
Upper bound for guessing parameters

+
+  
skillspace

+
Skill space: normal distribution ("normal") or discrete
+distribution ("discrete").

+
+  
theta.k

+
A matrix of the \(\bold{\theta}\) skill space in case of a discrete
+distribution (skillspace="discrete").

+
+  
delta.designmatrix

+
A design matrix of the log-linear model for the skill space in case of a discrete
+distribution (skillspace="discrete").

+
+  
delta.fixed

+
Fixed \(\delta\) values of the log-linear skill space.
 delta.fixed must be a matrix with three columns. First column:
 \(\delta\) parameter index, Second column: Group index,
-Third column: Fixed \(\delta\) parameter value.
delta.inits
Optional initial matrix of \(\delta\)
-parameters.
pweights
Optional vector of person weights.
item.elim
Optional logical indicating whether an item with has
+Third column: Fixed \(\delta\) parameter value.

+
+
delta.inits

+
Optional initial matrix of \(\delta\)
+parameters.

+
+  
pweights

+
Optional vector of person weights.

+
+
item.elim

+
Optional logical indicating whether an item with has
     only zero entries should be removed from the analysis. The default
-    is TRUE.
verbose
Logical indicating whether output should
-be printed during iterations. This argument replaces control$progress.
control
See tam.mml for more details.
Edes
Compact form of design matrix. This argument is only
+    is TRUE.

+
+
verbose

+
Logical indicating whether output should
+be printed during iterations. This argument replaces control$progress.

+
+  
control

+
See tam.mml for more details.

+
+
Edes

+
Compact form of design matrix. This argument is only
     defined for convenience for models with random starting
-    values to avoid recalculations.
object
Object of class tam.mml.3pl
file
A file name in which the summary output will be written
x
Object of class tam.mml.3pl
...
Further arguments to be passed

-
-    
Details

+    values to avoid recalculations.

+
+  
object

+
Object of class tam.mml.3pl

+
+
file

+
A file name in which the summary output will be written

 
+
x

+
Object of class tam.mml.3pl

+
+
...

+
Further arguments to be passed

+
+

+    

+    
Details

     
The item response model for item \(i\) and category \(h\) and no guessing
 parameters can be written as
 $$ P( X_{i}=h | \bold{\theta} ) \propto \exp( \sum_d b_{ihd} \theta_d +
@@ -424,7 +307,7 @@ 
Details
 class model see Formann (1992). Linear constraints on \(\gamma\)
 can be specified by equations \(V \gamma=c\) and using the arguments
 gammaslope.constr.V and gammaslope.constr.c.

-
Like in tam.mml, a multivariate linear regression
+
Like in tam.mml, a multivariate linear regression
 $$ \bold{\theta}=Y \beta + \bold{\epsilon}$$
 assuming a multivariate normal distribution on the residuals \(\bold{\epsilon}\)
 can be specified (skillspace="normal").

@@ -434,69 +317,87 @@ 
Details
 von Davier (2008). The design matrix \(D_{\delta}\) can be specified in
 delta.designmatrix. The theta grid \(\bold{\theta}\) of the skill space
 can be defined in theta.k.

-    
Value

+    

+    

+    
Value

+    
+
+
The same output as in tam.mml and additional entries

+
delta

+
Parameter vector \(\delta\)

+
+ 
gammaslope

+
Estimated \(\gamma\) item slope parameters

 
-    
The same output as in tam.mml and additional entries

-
delta
Parameter vector \(\delta\)

- 
gammaslope
Estimated \(\gamma\) item slope parameters

- 
se.gammaslope
Standard errors \(\gamma\) item slope parameters

- 
E
Used design matrix \(E\)

- 
Edes
Used design matrix \(E\) in compact form

- 
guess
Estimated \(c\) guessing parameters

- 
se.guess
Standard errors \(c\) guessing parameters

+ 
se.gammaslope

+
Standard errors \(\gamma\) item slope parameters

 
+ 
E

+
Used design matrix \(E\)

 
-    
References

+ 
Edes

+
Used design matrix \(E\) in compact form

 
+ 
guess

+
Estimated \(c\) guessing parameters

+
+ 
se.guess

+
Standard errors \(c\) guessing parameters

+
+
+

+    

+    
References

     
Formann, A. K. (1992). Linear logistic latent class analysis for polytomous data.
 Journal of the American Statistical Association, 87, 476-486.
-doi: 10.2307/2290280

+doi:10.2307/2290280

 
Formann, A. K. (2007). (Almost) Equivalence between conditional and mixture maximum
 likelihood estimates for some models of the Rasch type. In M. von Davier & C. H. Carstensen
 (Eds.), Multivariate and mixture distribution Rasch models (pp. 177-189).
 New York: Springer.
-doi: 10.1007/978-0-387-49839-3_11

+doi:10.1007/978-0-387-49839-3_11

 
Xu, X., & von Davier, M. (2008). Fitting the structured general diagnostic
 model to NAEP data. ETS Research Report ETS RR-08-27. Princeton, ETS.
-doi: 10.1002/j.2333-8504.2008.tb02113.x

-    
Note

-
+doi:10.1002/j.2333-8504.2008.tb02113.x

+    

+    

+    
Note

     
The implementation of the model builds on pieces work of Anton Formann.
-See http://www.antonformann.at/ for more information.

-    
See also

-
-    
See also tam.mml.

-
See the CDM::slca function in the CDM package
+See http://www.antonformann.at/ for more information.

+    

+    

+    
See also

+    
See also tam.mml.

+
See the CDM::slca function in the CDM package
 for a similar method.

-
logLik.tam, anova.tam

+
logLik.tam, anova.tam

+    

 
-    
Examples

-    

+    

+    
Examples

+    
+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
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diff --git a/docs/reference/tam.mml.html b/docs/reference/tam.mml.html
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--- a/docs/reference/tam.mml.html
+++ b/docs/reference/tam.mml.html
@@ -1,74 +1,19 @@
-
 
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-Test Analysis Modules: Marginal Maximum Likelihood Estimation — tam.mml • TAM
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-Test Analysis Modules: Marginal Maximum Likelihood Estimation — tam.mml • TAM
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Test Analysis Modules: Marginal Maximum Likelihood Estimation

@@ -131,68 +63,65 @@ 
Test Analysis Modules: Marginal Maximum Likelihood Estimation

   estimation of ability.

     

 
-    
tam(resp, irtmodel="1PL", formulaA=NULL, ...)
-
-tam.mml(resp, Y=NULL, group=NULL, irtmodel="1PL", formulaY=NULL,
-    dataY=NULL, ndim=1,  pid=NULL, xsi.fixed=NULL, xsi.inits=NULL,
-    beta.fixed=NULL, beta.inits=NULL, variance.fixed=NULL,
-    variance.inits=NULL, est.variance=TRUE, constraint="cases", A=NULL,
-    B=NULL, B.fixed=NULL,  Q=NULL,  est.slopegroups=NULL, E=NULL,
-    pweights=NULL, userfct.variance=NULL,
-    variance.Npars=NULL, item.elim=TRUE, verbose=TRUE, control=list() )
-
-tam.mml.2pl(resp, Y=NULL, group=NULL, irtmodel="2PL", formulaY=NULL,
-    dataY=NULL, ndim=1, pid=NULL, xsi.fixed=NULL, xsi.inits=NULL,
-    beta.fixed=NULL, beta.inits=NULL, variance.fixed=NULL,
-    variance.inits=NULL, est.variance=FALSE, A=NULL, B=NULL,
-    B.fixed=NULL, Q=NULL, est.slopegroups=NULL, E=NULL, gamma.init=NULL,
-    pweights=NULL, userfct.variance=NULL, variance.Npars=NULL,
-    item.elim=TRUE, verbose=TRUE, control=list() )
-
-tam.mml.mfr(resp, Y=NULL, group=NULL, irtmodel="1PL", formulaY=NULL,
-    dataY=NULL, ndim=1, pid=NULL, xsi.fixed=NULL, xsi.setnull=NULL,
-    xsi.inits=NULL, beta.fixed=NULL, beta.inits=NULL, variance.fixed=NULL,
-    variance.inits=NULL, est.variance=TRUE, formulaA=~item+item:step,
-    constraint="cases", A=NULL, B=NULL,  B.fixed=NULL, Q=NULL,
-    facets=NULL, est.slopegroups=NULL, E=NULL,
-    pweights=NULL, verbose=TRUE, control=list(), delete.red.items=TRUE )
-
-# S3 method for tam
-summary(object, file=NULL, ...)
-
-# S3 method for tam.mml
-summary(object, file=NULL, ...)
-
-# S3 method for tam
-print(x, ...)
-
-# S3 method for tam.mml
-print(x, ...)

-
-    
Arguments

-    
-    
-    
-      
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-      
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-      
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-    
-    
-      
-      
-    
-    
resp
Data frame with polytomous item responses \(k=0,...,K\).
-     Missing responses must be declared as NA.
Y
A matrix of covariates in latent regression. Note that the
-     intercept is automatically included as the first predictor.
group
An optional vector of group identifiers
irtmodel
For fixed item slopes (in tam.mml)
+    

+    
tam(resp, irtmodel="1PL", formulaA=NULL, ...)
+
+tam.mml(resp, Y=NULL, group=NULL, irtmodel="1PL", formulaY=NULL,
+    dataY=NULL, ndim=1,  pid=NULL, xsi.fixed=NULL, xsi.inits=NULL,
+    beta.fixed=NULL, beta.inits=NULL, variance.fixed=NULL,
+    variance.inits=NULL, est.variance=TRUE, constraint="cases", A=NULL,
+    B=NULL, B.fixed=NULL,  Q=NULL,  est.slopegroups=NULL, E=NULL,
+    pweights=NULL, userfct.variance=NULL,
+    variance.Npars=NULL, item.elim=TRUE, verbose=TRUE, control=list() )
+
+tam.mml.2pl(resp, Y=NULL, group=NULL, irtmodel="2PL", formulaY=NULL,
+    dataY=NULL, ndim=1, pid=NULL, xsi.fixed=NULL, xsi.inits=NULL,
+    beta.fixed=NULL, beta.inits=NULL, variance.fixed=NULL,
+    variance.inits=NULL, est.variance=FALSE, A=NULL, B=NULL,
+    B.fixed=NULL, Q=NULL, est.slopegroups=NULL, E=NULL, gamma.init=NULL,
+    pweights=NULL, userfct.variance=NULL, variance.Npars=NULL,
+    item.elim=TRUE, verbose=TRUE, control=list() )
+
+tam.mml.mfr(resp, Y=NULL, group=NULL, irtmodel="1PL", formulaY=NULL,
+    dataY=NULL, ndim=1, pid=NULL, xsi.fixed=NULL, xsi.setnull=NULL,
+    xsi.inits=NULL, beta.fixed=NULL, beta.inits=NULL, variance.fixed=NULL,
+    variance.inits=NULL, est.variance=TRUE, formulaA=~item+item:step,
+    constraint="cases", A=NULL, B=NULL,  B.fixed=NULL, Q=NULL,
+    facets=NULL, est.slopegroups=NULL, E=NULL,
+    pweights=NULL, verbose=TRUE, control=list(), delete.red.items=TRUE )
+
+# S3 method for tam
+summary(object, file=NULL, ...)
+
+# S3 method for tam.mml
+summary(object, file=NULL, ...)
+
+# S3 method for tam
+print(x, ...)
+
+# S3 method for tam.mml
+print(x, ...)

+    

+
+    

+    
Arguments

+    
resp

+
Data frame with polytomous item responses \(k=0,...,K\).
+     Missing responses must be declared as NA.

+
+  
Y

+
A matrix of covariates in latent regression. Note that the
+     intercept is automatically included as the first predictor.

+
+  
group

+
An optional vector of group identifiers

+
+  
irtmodel

+
For fixed item slopes (in tam.mml)
      options include PCM (partial credit model), PCM2
      (partial credit model with ConQuest parametrization
      'item+item*step' and RSM (rating scale model;
-     the ConQuest parametrization 'item+step'). 

+     the ConQuest parametrization 'item+step'). 

      For estimated item slopes (only available in tam.mml.2pl)
      options are 2PL (all slopes of item categories
      are estimated; Nominal Item Response Model),
@@ -206,168 +135,134 @@ 
Arg
      Note that item slopes can not be estimated with faceted
      designs using the function tam.mml.mfr. However,
      it is easy to use pre-specified design matrices and apply
-     some restrictions to tam.mml.2pl (see Example 14, Model 3).
formulaY
An R formula for latent regression. Transformations of predictors
+     some restrictions to tam.mml.2pl (see Example 14, Model 3).

+
+  
formulaY

+
An R formula for latent regression. Transformations of predictors
      in \(Y\) (included in dataY) can be easily specified,
-     e. g. female*race or I(age^2).
dataY
An optional data frame with possible covariates \(Y\) in latent regression.
+     e. g. female*race or I(age^2).

+
+  
dataY

+
An optional data frame with possible covariates \(Y\) in latent regression.
      This data frame is used if an R formula in formulaY
-     is specified.
ndim
Number of dimensions (is not needed to determined by the user)
pid
An optional vector of person identifiers
xsi.fixed
A matrix with two columns for fixing \(\xi\) parameters.
-     1st column: index of \(\xi\) parameter, 2nd column: fixed value
xsi.setnull
A vector of strings indicating which \(\xi\)
+     is specified.

+
+  
ndim

+
Number of dimensions (is not needed to determined by the user)

+
+  
pid

+
An optional vector of person identifiers

+
+  
xsi.fixed

+
A matrix with two columns for fixing \(\xi\) parameters.
+     1st column: index of \(\xi\) parameter, 2nd column: fixed value

+
+
xsi.setnull

+
A vector of strings indicating which \(\xi\)
     elements should be set to zero which do have entries in
-    xsi.setnull in their labels (see Example 10a).
xsi.inits
A matrix with two columns (in the same way defined as in
-     xsi.fixed with initial value for \(\xi\).
beta.fixed
A matrix with three columns for fixing regression coefficients.
+    xsi.setnull in their labels (see Example 10a).

+
+  
xsi.inits

+
A matrix with two columns (in the same way defined as in
+     xsi.fixed with initial value for \(\xi\).

+
+  
beta.fixed

+
A matrix with three columns for fixing regression coefficients.
      1st column: Index of \(Y\) value, 2nd column: dimension,
-     3rd column: fixed \(\beta\) value. 

+     3rd column: fixed \(\beta\) value. 

      If no constraints should be imposed on \(\beta\), then
-     set beta.fixed=FALSE (see Example 2, Model 2_4).
beta.inits
A matrix (same format as in beta.fixed)
-     with initial \(\beta\) values
variance.fixed
An optional matrix with three columns for fixing
+     set beta.fixed=FALSE (see Example 2, Model 2_4).

+
+  
beta.inits

+
A matrix (same format as in beta.fixed)
+     with initial \(\beta\) values

+
+  
variance.fixed

+
An optional matrix with three columns for fixing
      entries in covariance matrix:
      1st column: dimension 1, 2nd column: dimension 2,
-     3rd column: fixed value
variance.inits
Initial covariance matrix in estimation. All matrix entries have to be
+     3rd column: fixed value

+
+  
variance.inits

+
Initial covariance matrix in estimation. All matrix entries have to be
      specified and this matrix is NOT in the same format like
-     variance.fixed.
est.variance
Should the covariance matrix be estimated? This argument
+     variance.fixed.

+
+  
est.variance

+
Should the covariance matrix be estimated? This argument
      applies to estimated item slopes in tam.mml.2pl.
      The default is FALSE which means that latent
-     variables (in the first group) are standardized in 2PL estimation.
constraint
Set sum constraint for parameter identification
+     variables (in the first group) are standardized in 2PL estimation.

+
+
constraint

+
Set sum constraint for parameter identification
     for items or cases (applies to
-    tam.mml and tam.mml.mfr)
A
An optional array of dimension \( I \times (K+1) \times N_\xi\).
+    tam.mml and tam.mml.mfr)

+
+  
A

+
An optional array of dimension \( I \times (K+1) \times N_\xi\).
      Only \(\xi\) parameters are estimated, entries in \(A\)
-     only correspond to the design.
B
An optional array of dimension \( I \times (K+1) \times D\).
+     only correspond to the design.

+
+  
B

+
An optional array of dimension \( I \times (K+1) \times D\).
      In case of tam.mml.2pl entries of the \(B\) matrix can be
-     estimated.
B.fixed
An optional matrix with four columns for fixing \(B\) matrix entries in 2PL estimation.
+     estimated.

+
+  
B.fixed

+
An optional matrix with four columns for fixing \(B\) matrix entries in 2PL estimation.
   1st column: item index, 2nd column: category, 3rd column: dimension,
-  4th column: fixed value.
Q
An optional \(I \times D\) matrix (the Q-matrix) which specifies the
-  loading structure of items on dimensions.
est.slopegroups
A vector of integers of length \(I\) for estimating item slope
+  4th column: fixed value.

+
+  
Q

+
An optional \(I \times D\) matrix (the Q-matrix) which specifies the
+  loading structure of items on dimensions.

+
+  
est.slopegroups

+
A vector of integers of length \(I\) for estimating item slope
   parameters of item groups. This function only applies to
-  the generalized partial credit model 
 (irtmodel="2PL.groups").
E
An optional design matrix for estimating item slopes
-  in the generalized partial credit model (irtmodel="GPCM.design")
gamma.init
Optional initial \(gamma\) parameter vector
-(irtmodel="GPCM.design").
pweights
An optional vector of person weights
formulaA
Design formula (only applies to tam.mml.mfr).
+  the generalized partial credit model 
 (irtmodel="2PL.groups").

+
+
E

+
An optional design matrix for estimating item slopes
+  in the generalized partial credit model (irtmodel="GPCM.design")

+
+
gamma.init

+
Optional initial \(gamma\) parameter vector
+(irtmodel="GPCM.design").

+
+
pweights

+
An optional vector of person weights

+
+
formulaA

+
Design formula (only applies to tam.mml.mfr).
     See Example 8. It is also to possible to set all effects
-  of a facet to zero, e.g. item*step + 0*rater (see Example 10a).
facets
A data frame with facet entries (only applies to
-    tam.mml.mfr)
userfct.variance
Optional user customized function for variance specification
-(See Simulated Example 17).
variance.Npars
Number of estimated parameters of variance matrix
-if a userfct.variance is provided.
item.elim
Optional logical indicating whether an item with has
+  of a facet to zero, e.g. item*step + 0*rater (see Example 10a).

+
+
+
facets

+
A data frame with facet entries (only applies to
+    tam.mml.mfr)

+
+
userfct.variance

+
Optional user customized function for variance specification
+(See Simulated Example 17).

+
+
variance.Npars

+
Number of estimated parameters of variance matrix
+if a userfct.variance is provided.

+
+
item.elim

+
Optional logical indicating whether an item with has
     only zero entries should be removed from the analysis. The default
-    is TRUE.
verbose
Logical indicating whether output should
-be printed during iterations. This argument replaces control$progress.
control
A list of control arguments for the algorithm: 


-   list( nodes=seq(-6,6,len=21), snodes=0, QMC=TRUE,

-            convD=.001,conv=.0001, convM=.0001, Msteps=4,   

-            maxiter=1000, max.increment=1, 

-            min.variance=.001, progress=TRUE, ridge=0,    

-            seed=NULL, xsi.start0=0, increment.factor=1,  

-            fac.oldxsi=0, acceleration="none", dev_crit="absolute" )  

-            trim_increment="half" )  

+    is TRUE.

+
+
verbose

+
Logical indicating whether output should
+be printed during iterations. This argument replaces control$progress.

+
+
control

+
A list of control arguments for the algorithm: 

 list( nodes=seq(-6,6,len=21), snodes=0, QMC=TRUE,
        convD=.001,conv=.0001, convM=.0001, Msteps=4,   
        maxiter=1000, max.increment=1, 
        min.variance=.001, progress=TRUE, ridge=0,    
        seed=NULL, xsi.start0=0, increment.factor=1,  
        fac.oldxsi=0, acceleration="none", dev_crit="absolute",  
        trim_increment="half" )  

 
nodes: the discretized \(\theta\) nodes for numerical integration

 
snodes: number of simulated \(\theta\) nodes for stochastic integration.
     If snodes=0, numerical integration is used.

@@ -427,37 +322,31 @@ 
Arg
 dev_crit="relative" refers to relative differences.

 
trim_increment: Type of method for trimming parameter increments in
 algorithm. Possible types are "half" or ""cut".
-

-
-
delete.red.items
An optional logical indicating whether redundant
-    generalized items (with no observations) should be eliminated.
object
Object of class tam or tam.mml (only for summary.tam
-functions)
file
A file name in which the summary output should be written
-(only for summary.tam functions)
...
Further arguments to be passed
x
Object of class tam or tam.mml

-
-    
Details

+

+
+
+
+
delete.red.items

+
An optional logical indicating whether redundant
+    generalized items (with no observations) should be eliminated.

+
+  
object

+
Object of class tam or tam.mml (only for summary.tam
+functions)

+
+
file

+
A file name in which the summary output should be written
+(only for summary.tam functions)

 
+
...

+
Further arguments to be passed

+
+
x

+
Object of class tam or tam.mml

+
+

+    

+    
Details

     
The multidimensional item response model in TAM is
 described in Adams, Wilson and Wu (1997) or Adams and Wu (2007).

 
The data frame resp contains item responses of \(N\) persons (in rows)
@@ -506,119 +395,231 @@ 
Details
 (because control$QMC=TRUE is set by default). If
 control$QMC=FALSE is specified, then stochastic (Monte Carlo) integration
 is employed with control$snodes stochastic nodes.

-    
Value

+    

+    

+    
Value

+    
 
-    
A list with following entries:

-
xsi
Vector of \(\xi\) parameter estimates and their
+
A list with following entries:

+
xsi

+
Vector of \(\xi\) parameter estimates and their
 corresponding standard errors

-
xsi.facets
Data frame of \(\xi\) parameters and corresponding
+
+
xsi.facets

+
Data frame of \(\xi\) parameters and corresponding
 constraints for multifacet models

-
beta
Matrix of \(\beta\) regression coefficient estimates

-
variance
Covariance matrix. In case of multiple groups,
+
+
beta

+
Matrix of \(\beta\) regression coefficient estimates

+
+
variance

+
Covariance matrix. In case of multiple groups,
     it is a vector indicating heteroscedastic variances

-
item
Data frame with item parameters. The column xsi.item
+
+
item

+
Data frame with item parameters. The column xsi.item
 denotes the item difficulty of polytomous items in the parametrization
 irtmodel="PCM2".

-
item_irt
IRT parameterization of item parameters

-
person
Matrix with person parameter estimates.
+
+
item_irt

+
IRT parameterization of item parameters

+
+
person

+
Matrix with person parameter estimates.
     EAP is the mean of the posterior distribution and SD.EAP
     the corresponding standard deviation

-
pid
Vector of person identifiers

-
EAP.rel
EAP reliability

-
post
Posterior distribution for item response pattern

-
rprobs
A three-dimensional array with estimated response probabilities
+
+
pid

+
Vector of person identifiers

+
+
EAP.rel

+
EAP reliability

+
+
post

+
Posterior distribution for item response pattern

+
+
rprobs

+
A three-dimensional array with estimated response probabilities
         (dimensions are items \(\times\) categories \(\times\)
       theta length)

-
itemweight
Matrix of item weights

-
theta
Theta grid

-
n.ik
Array of expected counts: theta class \(\times\)
+
+
itemweight

+
Matrix of item weights

+
+
theta

+
Theta grid

+
+
n.ik

+
Array of expected counts: theta class \(\times\)
 item \(\times\) category \(\times\) group

-
pi.k
Marginal trait distribution at grid theta

-
Y
Matrix of covariates

-
resp
Original data frame

-
resp.ind
Response indicator matrix

-
group
Group identifier

-
G
Number of groups

-
formulaY
Formula for latent regression

-
dataY
Data frame for latent regression

-
pweights
Person weights

-
time
Computation time

-
A
Design matrix \(A\) for \(\xi\) parameters

-
B
Fixed or estimated loading matrix

-
se.B
Standard errors of \(B\) parameters

-
nitems
Number of items

-
maxK
Maximum number of categories

-
AXsi
Estimated item intercepts \( a_{ik} \xi\)

-
AXsi_
Estimated item intercepts -\( a_{ik} \xi\).
+
+
pi.k

+
Marginal trait distribution at grid theta

+
+
Y

+
Matrix of covariates

+
+
resp

+
Original data frame

+
+
resp.ind

+
Response indicator matrix

+
+
group

+
Group identifier

+
+
G

+
Number of groups

+
+
formulaY

+
Formula for latent regression

+
+
dataY

+
Data frame for latent regression

+
+
pweights

+
Person weights

+
+
time

+
Computation time

+
+
A

+
Design matrix \(A\) for \(\xi\) parameters

+
+
B

+
Fixed or estimated loading matrix

+
+
se.B

+
Standard errors of \(B\) parameters

+
+
nitems

+
Number of items

+
+
maxK

+
Maximum number of categories

+
+
AXsi

+
Estimated item intercepts \( a_{ik} \xi\)

+
+
AXsi_

+
Estimated item intercepts -\( a_{ik} \xi\).
 Note that in summary.tam, the parameters AXsi_
 are displayed.

-
se.AXsi
Standard errors of \(a_{ik} \xi\) parameters

-
nstud
Number of persons

-
resp.ind.list
List of response indicator vectors

-
hwt
Individual posterior distribution

-
like
Individual likelihood

-
ndim
Number of dimensions

-
xsi.fixed
Fixed \(\xi\) parameters

-
xsi.fixed.estimated
Matrix of estimated \(\xi\) parameters
+
+
se.AXsi

+
Standard errors of \(a_{ik} \xi\) parameters

+
+
nstud

+
Number of persons

+
+
resp.ind.list

+
List of response indicator vectors

+
+
hwt

+
Individual posterior distribution

+
+
like

+
Individual likelihood

+
+
ndim

+
Number of dimensions

+
+
xsi.fixed

+
Fixed \(\xi\) parameters

+
+
xsi.fixed.estimated

+
Matrix of estimated \(\xi\) parameters
     in form of xsi.fixed which can
     be used for parameter fixing in subsequent estimations.

-
B.fixed
Fixed loading parameters (only applies to tam.mml.2pl)

-
B.fixed.estimated
Matrix of estimated \(B\) parameters
+
+
B.fixed

+
Fixed loading parameters (only applies to tam.mml.2pl)

+
+
B.fixed.estimated

+
Matrix of estimated \(B\) parameters
    in the same format as B.fixed.

-
est.slopegroups
An index vector of item groups of common slope
+
+
est.slopegroups

+
An index vector of item groups of common slope
 parameters (only applies to tam.mml.2pl)

-
E
Design matrix for estimated item slopes in the generalized partial
+
+
E

+
Design matrix for estimated item slopes in the generalized partial
 credit model (only applies to tam.mml.2pl in case of
 irtmodel="GPCM.design")

-
basispar
Vector of \(\gamma\) parameters of the linear combination
+
+
basispar

+
Vector of \(\gamma\) parameters of the linear combination
 \(a_i=( E \gamma)_i \) for item slopes (only applies to
 tam.mml.2pl in case of irtmodel='GPCM.design')

-
formulaA
Design formula (only applies to tam.mml.mfr)

-
facets
Data frame with facet entries (only applies to
+
+
formulaA

+
Design formula (only applies to tam.mml.mfr)

+
+
facets

+
Data frame with facet entries (only applies to
   tam.mml.mfr)

-
variance.fixed
Fixed covariance matrix

-
nnodes
Number of theta nodes

-
deviance
Final deviance

-
ic
Vector with information criteria

-
deviance.history
Deviance history in iterations

-
control
List of control arguments

-
latreg_stand
List containing standardized regression coefficients

-
...
Further values

 
-    
References

+
variance.fixed

+
Fixed covariance matrix

 
+
nnodes

+
Number of theta nodes

+
+
deviance

+
Final deviance

+
+
ic

+
Vector with information criteria

+
+
deviance.history

+
Deviance history in iterations

+
+
control

+
List of control arguments

+
+
latreg_stand

+
List containing standardized regression coefficients

+
+
...

+
Further values

+
+

+    

+    
References

     
Adams, R. J., Wilson, M., & Wu, M. (1997).
 Multilevel item response models: An approach to errors in
 variables regression. Journal of Educational and Behavioral
 Statistics, 22, 47-76.
-doi: 10.3102/10769986022001047

+doi:10.3102/10769986022001047

 
Adams, R. J., & Wu, M. L. (2007). The mixed-coefficients multinomial logit model.
 A generalized form of the Rasch model. In M. von Davier & C. H. Carstensen (Eds.),
 Multivariate and mixture distribution Rasch models: Extensions and applications
 (pp. 55-76). New York: Springer.
-doi: 10.1007/978-0-387-49839-3_4

+doi:10.1007/978-0-387-49839-3_4

 
Embretson, S. E. (1999). Generating items during testing:
 Psychometric issues and models. Psychometrika, 64, 407-433.
-doi: 10.1007/BF02294564

+doi:10.1007/BF02294564

 
Gonzalez, J., Tuerlinckx, F., De Boeck, P., & Cools, R. (2006).
 Numerical integration in logistic-normal models.
 Computational Statistics & Data Analysis, 51, 1535-1548.
-doi: 10.1016/j.csda.2006.05.003

+doi:10.1016/j.csda.2006.05.003

 
Pan, J., & Thompson, R. (2007). Quasi-Monte Carlo estimation in
 generalized linear mixed models. Computational Statistics &
 Data Analysis, 51, 5765-5775.
-doi: 10.1016/j.csda.2006.10.003

+doi:10.1016/j.csda.2006.10.003

 
Ramsay, J. O. (1975). Solving implicit equations in psychometric data analysis.
 Psychometrika, 40(3), 337-360.
-doi: 10.1007/BF02291762

+doi:10.1007/BF02291762

 
Yu, Y. (2012). Monotonically overrelaxed EM algorithms.
 Journal of Computational and Graphical Statistics, 21(2), 518-537.
-doi: 10.1080/10618600.2012.672115

+doi:10.1080/10618600.2012.672115

 
Wu, M. L., Adams, R. J., Wilson, M. R. & Haldane, S. (2007).
 ACER ConQuest Version 2.0. Mulgrave.
 https://shop.acer.edu.au/acer-shop/group/CON3.

-    
Note

-
+    

+    

+    
Note

     
For more than three dimensions, quasi-Monte Carlo or stochastic integration
 is recommended because otherwise problems in memory allocation and large
 computation time will result. Choose in control a suitable value of
@@ -634,1737 +635,1737 @@ 
Note

 Third, change in estimated parameters can be stabilized by fac.oldxsi for
 which a value of 0 (the default) and a value of 1 can be chosen. We recommend
 values between .5 and .8 if your model does not converge.

-    
See also

-
-    
See data.cqc01 for more examples which is are similar to the ones
+    

+    

+    
See also

+    
See data.cqc01 for more examples which is are similar to the ones
 in the ConQuest manual (Wu, Adams, Wilson & Haldane, 2007).

-
See tam.jml for joint maximum likelihood estimation.

+
See tam.jml for joint maximum likelihood estimation.

 
Standard errors are estimated by a rather crude (but quick) approximation.
-Use tam.se for improved standard errors.

-
For model comparisons see anova.tam.

-
See sirt::tam2mirt for converting
+Use tam.se for improved standard errors.

+
For model comparisons see anova.tam.

+
See sirt::tam2mirt for converting
 tam objects into objects of class
-mirt::mirt in the mirt package.

-
-    
Examples

-    
#############################################################################
-# EXAMPLE 1: dichotomous data
-# data.sim.rasch: 2000 persons, 40 items
-#############################################################################
-data(data.sim.rasch)
-
-#************************************************************
-# Model 1: Rasch model (MML estimation)
-mod1 <- TAM::tam.mml(resp=data.sim.rasch)
-# extract item parameters
-mod1$item    # item difficulties
-
-if (FALSE) {
-# WLE estimation
-wle1 <- TAM::tam.wle( mod1 )
-# item fit
-fit1 <- TAM::tam.fit(mod1)
-# plausible value imputation
-pv1 <- TAM::tam.pv(mod1, normal.approx=TRUE, ntheta=300)
-# standard errors
-se1 <- TAM::tam.se( mod1 )
-# summary
-summary(mod1)
-
-#-- specification with tamaan
-tammodel <- "
- LAVAAN MODEL:
-   F=~ I1__I40;
-   F ~~ F
- ITEM TYPE:
-   ALL(Rasch)
-   "
-mod1t <- TAM::tamaan( tammodel, data.sim.rasch)
-summary(mod1t)
-
-#************************************************************
-# Model 1a: Rasch model with fixed item difficulties from 'mod1'
-xsi0 <- mod1$xsi$xsi
-xsi.fixed <- cbind( 1:(length(xsi0)), xsi0 )
-        # define vector with fixed item difficulties
-mod1a <- TAM::tam.mml( resp=data.sim.rasch, xsi.fixed=xsi.fixed )
-summary(mod1a)
-
-# Usage of the output value mod1$xsi.fixed.estimated has the right format
-# as the input of xsi.fixed
-mod1aa <- TAM::tam.mml( resp=data.sim.rasch, xsi.fixed=mod1$xsi.fixed.estimated )
-summary(mod1b)
-
-#************************************************************
-# Model 1b: Rasch model with initial xsi parameters for items 2 (item difficulty b=-1.8),
-# item 4 (b=-1.6) and item 40 (b=2)
-xsi.inits <- cbind( c(2,4,40), c(-1.8,-1.6,2))
-mod1b <- TAM::tam.mml( resp=data.sim.rasch, xsi.inits=xsi.inits )
-
-#-- tamaan specification
-tammodel <- "
- LAVAAN MODEL:
-   F=~ I1__I40
-   F ~~ F
-   # Fix item difficulties. Note that item intercepts instead of difficulties
-   # must be specified.
-   I2 | 1.8*t1
-   I4 | 1.6*t1
- ITEM TYPE:
-   ALL(Rasch)
-   "
-mod1bt <- TAM::tamaan( tammodel, data.sim.rasch)
-summary(mod1bt)
-
-#************************************************************
-# Model 1c: 1PL estimation with sum constraint on item difficulties
-dat <- data.sim.rasch
-# modify A design matrix to include the sum constraint
-des <- TAM::designMatrices(resp=dat)
-A1 <- des$A[,, - ncol(dat) ]
-A1[ ncol(dat),2, ] <- 1
-A1[,2,]
-# estimate model
-mod1c <- TAM::tam.mml( resp=dat, A=A1, beta.fixed=FALSE,
-           control=list(fac.oldxsi=.1) )
-summary(mod1c)
-
-#************************************************************
-# Model 1d: estimate constraint='items' using tam.mml.mfr
-formulaA=~ 0 + item
-mod1d <- TAM::tam.mml.mfr( resp=dat, formulaA=formulaA,
-                     control=list(fac.oldxsi=.1), constraint="items")
-summary(mod1d)
-
-#************************************************************
-# Model 1e: This sum constraint can also be obtained by using the argument
-# constraint="items" in tam.mml
-mod1e <- TAM::tam.mml( resp=data.sim.rasch, constraint="items" )
-summary(mod1e)
-
-#************************************************************
-# Model 1d2: estimate constraint='items' using tam.mml.mfr
-# long format response data
-resp.long <- c(dat)
-
-# pid and item facet specifications are necessary
-#     Note, that we recommend the facet labels to be sortable in the same order that the
-#     results are desired.
-#     compare to: facets <- data.frame( "item"=rep(colnames(dat), each=nrow(dat)) )
-pid <- rep(1:nrow(dat), ncol(dat))
-itemnames <- paste0("I", sprintf(paste('%0', max(nchar(1:ncol(dat))), 'i', sep='' ),
-                    c(1:ncol(dat)) ) )
-facets   <- data.frame( "item_"=rep(itemnames, each=nrow(dat)) )
-formulaA=~ 0 + item_
-
-mod1d2 <- TAM::tam.mml.mfr( resp=resp.long, formulaA=formulaA, control=list(fac.oldxsi=.1),
-                       constraint="items", facets=facets, pid=pid)
-stopifnot( all(mod1d$xsi.facets$xsi==mod1d2$xsi.facets$xsi) )
-}
-
-
-#************************************************************
-# Model 2: 2PL model
-mod2 <- TAM::tam.mml.2pl(resp=data.sim.rasch,irtmodel="2PL")
-
-# extract item parameters
-mod2$xsi    # item difficulties
-mod2$B      # item slopes
-
-#--- tamaan specification
-tammodel <- "
- LAVAAN MODEL:
-   F=~ I1__I40
-   F ~~ 1*F
-   # item type of 2PL is the default for dichotomous data
-   "
-# estimate model
-mod2t <- TAM::tamaan( tammodel, data.sim.rasch)
-summary(mod2t)
-
-if (FALSE) {
-#************************************************************
-# Model 2a: 2PL with fixed item difficulties and slopes from 'mod2'
-xsi0 <- mod2$xsi$xsi
-xsi.fixed <- cbind( 1:(length(xsi0)), xsi0 )
-        # define vector with fixed item difficulties
-mod2a <- TAM::tam.mml( resp=data.sim.rasch, xsi.fixed=xsi.fixed,
-                 B=mod2$B # fix slopes
-            )
-summary(mod2a)
-mod2a$B     # inspect used slope matrix
-
-#************************************************************
-# Model 3: constrained 2PL estimation
-# estimate item parameters in different slope groups
-# items 1-10, 21-30 group 1
-# items 11-20 group 2 and items 31-40 group 3
-est.slope <- rep(1,40)
-est.slope[ 11:20 ] <- 2
-est.slope[ 31:40 ] <- 3
-mod3 <- TAM::tam.mml.2pl( resp=data.sim.rasch, irtmodel="2PL.groups",
-               est.slopegroups=est.slope )
-mod3$B
-summary(mod3)
-
-#--- tamaan specification (A)
-tammodel <- "
- LAVAAN MODEL:
-   F=~ lam1*I1__I10 + lam2*I11__I20 + lam1*I21__I30 + lam3*I31__I40;
-   F ~~ 1*F
-   "
-# estimate model
-mod3tA <- TAM::tamaan( tammodel, data.sim.rasch)
-summary(mod3tA)
-
-#--- tamaan specification (alternative B)
-tammodel <- "
- LAVAAN MODEL:
-   F=~ a1__a40*I1__I40;
-   F ~~ 1*F
- MODEL CONSTRAINT:
-   a1__a10==lam1
-   a11__a20==lam2
-   a21__a30==lam1
-   a31__a40==lam3
-   "
-mod3tB <- TAM::tamaan( tammodel, data.sim.rasch)
-summary(mod3tB)
-
-#--- tamaan specification (alternative C using DO operator)
-tammodel <- "
- LAVAAN MODEL:
- DO(1,10,1)
-   F=~ lam1*I%
- DOEND
- DO(11,20,1)
-   F=~ lam2*I%
- DOEND
- DO(21,30,1)
-   F=~ lam1*I%
- DOEND
- DO(31,40,1)
-   F=~ lam3*I%
- DOEND
-   F ~~ 1*F
-   "
-# estimate model
-mod3tC <- TAM::tamaan( tammodel, data.sim.rasch)
-summary(mod3tC)
-
-#############################################################################
-# EXAMPLE 2: Unidimensional calibration with latent regressors
-#############################################################################
-
-# (1) simulate data
-set.seed(6778)     # set simulation seed
-N <- 2000          # number of persons
-# latent regressors Y
-Y <- cbind( stats::rnorm( N, sd=1.5), stats::rnorm(N, sd=.3 ) )
-# simulate theta
-theta <- stats::rnorm( N ) + .4 * Y[,1] + .2 * Y[,2]  # latent regression model
-# number of items
-I <- 40
-p1 <- stats::plogis( outer( theta, seq( -2, 2, len=I ), "-" ) )
-# simulate response matrix
-resp <- 1 * ( p1 > matrix( stats::runif( N*I ), nrow=N, ncol=I ) )
-colnames(resp) <- paste("I", 1:I, sep="")
-
-# (2) estimate model
-mod2_1 <- TAM::tam.mml(resp=resp, Y=Y)
-summary(mod2_1)
-
-# (3) setting initial values for beta coefficients
-#   beta_2=.20, beta_3=.35 for dimension 1
-beta.inits <- cbind( c(2,3), 1, c(.2, .35 ) )
-mod2_2 <- TAM::tam.mml(resp=resp, Y=Y, beta.inits=beta.inits)
-
-# (4) fix intercept to zero and third coefficient to .3
-beta.fixed <- cbind( c(1,3), 1, c(0, .3 ) )
-mod2_3 <- TAM::tam.mml(resp=resp, Y=Y, beta.fixed=beta.fixed )
-
-# (5) same model but with R regression formula for Y
-dataY <- data.frame(Y)
-colnames(dataY) <- c("Y1","Y2")
-mod2_4 <- TAM::tam.mml(resp=resp, dataY=dataY, formulaY=~ Y1+Y2 )
-summary(mod2_4)
-
-# (6) model with interaction of regressors
-mod2_5 <- TAM::tam.mml(resp=resp, dataY=dataY, formulaY=~ Y1*Y2 )
-summary(mod2_5)
-
-# (7) no constraint on regressors (removing constraint from intercept)
-mod2_6 <- TAM::tam.mml(resp=resp, Y=Y, beta.fixed=FALSE )
-
-#############################################################################
-# EXAMPLE 3: Multiple group estimation
-#############################################################################
-
-# (1) simulate data
-set.seed(6778)
-N <- 3000
-theta <- c( stats::rnorm(N/2,mean=0,sd=1.5), stats::rnorm(N/2,mean=.5,sd=1)  )
-I <- 20
-p1 <- stats::plogis( outer( theta, seq( -2, 2, len=I ), "-" ) )
-resp <- 1 * ( p1 > matrix( stats::runif( N*I ), nrow=N, ncol=I ) )
-colnames(resp) <- paste("I", 1:I, sep="")
-group <- rep(1:2, each=N/2 )
-
-# (2) estimate model
-mod3_1 <- TAM::tam.mml( resp,  group=group )
-summary(mod3_1)
-
-#############################################################################
-# EXAMPLE 4: Multidimensional estimation
-# with two dimensional theta's - simulate some bivariate data,
-# and regressors
-# 40 items: first 20 items load on dimension 1,
-#           second 20 items load on dimension 2
-#############################################################################
-
-# (1) simulate some data
-set.seed(6778)
-library(mvtnorm)
-N <- 1000
-Y <- cbind( stats::rnorm( N ), stats::rnorm(N) )
-theta <- mvtnorm::rmvnorm( N,mean=c(0,0), sigma=matrix( c(1,.5,.5,1), 2, 2 ))
-theta[,1] <- theta[,1] + .4 * Y[,1] + .2 * Y[,2]  # latent regression model
-theta[,2] <- theta[,2] + .8 * Y[,1] + .5 * Y[,2]  # latent regression model
-I <- 20
-p1 <- stats::plogis( outer( theta[,1], seq( -2, 2, len=I ), "-" ) )
-resp1 <- 1 * ( p1 > matrix( stats::runif( N*I ), nrow=N, ncol=I ) )
-p1 <- stats::plogis( outer( theta[,2], seq( -2, 2, len=I ), "-" ) )
-resp2 <- 1 * ( p1 > matrix( stats::runif( N*I ), nrow=N, ncol=I ) )
-resp <- cbind(resp1,resp2)
-colnames(resp) <- paste("I", 1:(2*I), sep="")
-
-# (2) define loading Matrix
-Q <- array( 0, dim=c( 2*I, 2 ))
-Q[cbind(1:(2*I), c( rep(1,I), rep(2,I) ))] <- 1
-
-# (3) estimate models
-
-#************************************************************
-# Model 4.1: Rasch model: without regressors
-mod4_1 <- TAM::tam.mml( resp=resp, Q=Q )
-
-#--- tamaan specification
-tammodel <- "
-  LAVAAN MODEL:
-    F1=~ 1*I1__I20
-    F2=~ 1*I21__I40
-    # Alternatively to the factor 1 one can use the item type Rasch
-    F1 ~~ F1
-    F2 ~~ F2
-    F1 ~~ F2
-    "
-mod4_1t <- TAM::tamaan( tammodel, resp, control=list(maxiter=100))
-summary(mod4_1t)
-
-#************************************************************
-# Model 4.1b: estimate model with sum constraint of items for each dimension
-mod4_1b <- TAM::tam.mml( resp=resp, Q=Q,constraint="items")
-
-#************************************************************
-# Model 4.2: Rasch model: set covariance between dimensions to zero
-variance_fixed <- cbind( 1, 2, 0 )
-mod4_2 <- TAM::tam.mml( resp=resp, Q=Q, variance.fixed=variance_fixed )
-summary(mod4_2)
-
-#--- tamaan specification
-tammodel <- "
-  LAVAAN MODEL:
-    F1=~ I1__I20
-    F2=~ I21__I40
-    F1 ~~ F1
-    F2 ~~ F2
-    F1 ~~ 0*F2
-  ITEM TYPE:
-    ALL(Rasch)
-    "
-mod4_2t <- TAM::tamaan( tammodel, resp)
-summary(mod4_2t)
-
-#************************************************************
-# Model 4.3: 2PL model
-mod4_3 <- TAM::tam.mml.2pl( resp=resp, Q=Q, irtmodel="2PL" )
-
-#--- tamaan specification
-tammodel <- "
-  LAVAAN MODEL:
-    F1=~ I1__I20
-    F2=~ I21__I40
-    F1 ~~ F1
-    F2 ~~ F2
-    F1 ~~ F2
-    "
-mod4_3t <- TAM::tamaan( tammodel, resp )
-summary(mod4_3t)
-
-#************************************************************
-# Model 4.4: Rasch model with 2000 quasi monte carlo nodes
-# -> nodes are useful for more than 3 or 4 dimensions
-mod4_4 <- TAM::tam.mml( resp=resp, Q=Q, control=list(snodes=2000) )
-
-#************************************************************
-# Model 4.5: Rasch model with 2000 stochastic nodes
-mod4_5 <- TAM::tam.mml( resp=resp, Q=Q,control=list(snodes=2000,QMC=FALSE))
-
-#************************************************************
-# Model 4.6: estimate two dimensional Rasch model with regressors
-mod4_6 <- TAM::tam.mml( resp=resp, Y=Y, Q=Q )
-
-#--- tamaan specification
-tammodel <- "
-  LAVAAN MODEL:
-    F1=~ I1__I20
-    F2=~ I21__I40
-    F1 ~~ F1
-    F2 ~~ F2
-    F1 ~~ F2
-  ITEM TYPE:
-    ALL(Rasch)
-    "
-mod4_6t <- TAM::tamaan( tammodel, resp, Y=Y )
-summary(mod4_6t)
-
-#############################################################################
-# EXAMPLE 5: 2-dimensional estimation with within item dimensionality
-#############################################################################
-library(mvtnorm)
-# (1) simulate data
-set.seed(4762)
-N <- 2000 # 2000 persons
-Y <- stats::rnorm( N )
-theta <- mvtnorm::rmvnorm( N,mean=c(0,0), sigma=matrix( c(1,.5,.5,1), 2, 2 ))
-I <- 10
-# 10 items load on the first dimension
-p1 <- stats::plogis( outer( theta[,1], seq( -2, 2, len=I ), "-" ) )
-resp1 <- 1 * ( p1 > matrix( stats::runif( N*I ), nrow=N, ncol=I ) )
-# 10 items load on the second dimension
-p1 <- stats::plogis( outer( theta[,2], seq( -2, 2, len=I ), "-" ) )
-resp2 <- 1 * ( p1 > matrix( stats::runif( N*I ), nrow=N, ncol=I ) )
-# 20 items load on both dimensions
-p1 <- stats::plogis( outer( 0.5*theta[,1] + 1.5*theta[,2], seq(-2,2,len=2*I ), "-" ))
-resp3 <- 1 * ( p1 > matrix( stats::runif( N*2*I ), nrow=N, ncol=2*I ) )
-#Combine the two sets of items into one response matrix
-resp <- cbind(resp1, resp2, resp3 )
-colnames(resp) <- paste("I", 1:(4*I), sep="")
-
-# (2) define loading matrix
-Q <- cbind(c(rep(1,10),rep(0,10),rep(1,20)), c(rep(0,10),rep(1,10),rep(1,20)))
-
-# (3) model: within item dimensionality and 2PL estimation
-mod5 <- TAM::tam.mml.2pl(resp, Q=Q, irtmodel="2PL" )
-summary(mod5)
-
-# item difficulties
-mod5$item
-# item loadings
-mod5$B
-
-#--- tamaan specification
-tammodel <- "
-  LAVAAN MODEL:
-    F1=~ I1__I10 + I21__I40
-    F2=~ I11__I20 + I21__I40
-    F1 ~~ 1*F1
-    F1 ~~ F2
-    F2 ~~ 1*F2
-    "
-mod5t <- TAM::tamaan( tammodel, resp,  control=list(maxiter=10))
-summary(mod5t)
-
-#############################################################################
-# EXAMPLE 6: ordered data - Generalized partial credit model
-#############################################################################
-data(data.gpcm, package="TAM")
-
-#************************************************************
-# Ex6.1: Nominal response model (irtmodel="2PL")
-mod6_1 <- TAM::tam.mml.2pl( resp=data.gpcm, irtmodel="2PL", control=list(maxiter=200) )
-mod6_1$item # item intercepts
-mod6_1$B    # for every category a separate slope parameter is estimated
-
-# reestimate the model with fixed item parameters
-mod6_1a <- TAM::tam.mml.2pl( resp=data.gpcm, irtmodel="2PL",
-       xsi.fixed=mod6_1$xsi.fixed.estimated,  B.fixed=mod6_1$B.fixed.estimated,
-       est.variance=TRUE )
-
-# estimate the model with initial item parameters from mod6_1
-mod6_1b <- TAM::tam.mml.2pl( resp=data.gpcm, irtmodel="2PL",
-       xsi.inits=mod6_1$xsi.fixed.estimated,  B=mod6_1$B )
-
-#************************************************************
-# Ex6.2: Generalized partial credit model
-mod6_2 <- TAM::tam.mml.2pl( resp=data.gpcm, irtmodel="GPCM", control=list(maxiter=200))
-mod6_2$B[,2,]    # joint slope parameter for all categories
-
-#************************************************************
-# Ex6.3: some fixed entries of slope matrix B
-# B: nitems x maxK x ndim
-#   ( number of items x maximum number of categories x number of dimensions)
-# set two constraints
-B.fixed <- matrix( 0, 2, 4 )
-# set second item, score of 2 (category 3), at first dimension to 2.3
-B.fixed[1,] <- c(2,3,1,2.3)
-# set third item, score of 1 (category 2), at first dimension to 1.4
-B.fixed[2,] <- c(3,2,1,1.4)
-
-# estimate item parameter with variance fixed (by default)
-mod6_3 <- TAM::tam.mml.2pl( resp=data.gpcm, irtmodel="2PL", B.fixed=B.fixed,
-                 control=list( maxiter=200) )
-mod6_3$B
-
-#************************************************************
-# Ex 6.4: estimate the same model, but estimate variance
-mod6_4 <- TAM::tam.mml.2pl( resp=data.gpcm, irtmodel="2PL", B.fixed=B.fixed,
-               est.variance=TRUE, control=list( maxiter=350) )
-mod6_4$B
-
-#************************************************************
-# Ex 6.5: partial credit model
-mod6_5 <- TAM::tam.mml( resp=data.gpcm,control=list( maxiter=200) )
-mod6_5$B
-
-#************************************************************
-# Ex 6.6: partial credit model: Conquest parametrization 'item+item*step'
-mod6_6 <- TAM::tam.mml( resp=data.gpcm, irtmodel="PCM2" )
-summary(mod6_6)
-
-# estimate mod6_6 applying the sum constraint of item difficulties
-# modify design matrix of xsi paramters
-A1 <- TAM::.A.PCM2(resp=data.gpcm )
-A1[3,2:4,"Comfort"] <- 1:3
-A1[3,2:4,"Work"] <- 1:3
-A1 <- A1[,, -3] # remove Benefit xsi item parameter
-# estimate model
-mod6_6b <- TAM::tam.mml( resp=data.gpcm, A=A1, beta.fixed=FALSE )
-summary(mod6_6b)
-
-# estimate model with argument constraint="items"
-mod6_6c <- TAM::tam.mml( resp=data.gpcm, irtmodel="PCM2", constraint="items")
-
-# estimate mod6_6 using tam.mml.mfr
-mod6_6d <- TAM::tam.mml.mfr( resp=data.gpcm, formulaA=~ 0 + item + item:step,
-    control=list(fac.oldxsi=.1), constraint="items" )
-summary(mod6_6d)
-
-#************************************************************
-# Ex 6.7: Rating scale model: Conquest parametrization 'item+step'
-mod6_7 <- TAM::tam.mml( resp=data.gpcm, irtmodel="RSM" )
-summary(mod6_7)
-
-#************************************************************
-# Ex 6.8: sum constraint on item difficulties
-#         partial credit model: ConQuest parametrization 'item+item*step'
-#         polytomous scored TIMMS data
-#         compare to Example 16
-#
-
-data(data.timssAusTwn.scored)
-dat <- data.timssAusTwn.scored[,1:11]
-
-## > tail(sort(names(dat)),1) # constrained item
-## [1] "M032761"
-
-# modify design matrix of xsi paramters
-A1 <- TAM::.A.PCM2( resp=dat )
-# constrained item loads on every other main item parameter
-# with opposing margin it had been loaded on its own main item parameter
-A1["M032761",,setdiff(colnames(dat), "M032761")] <- -A1["M032761",,"M032761"]
-# remove main item parameter for constrained item
-A1 <- A1[,, setdiff(dimnames(A1)[[3]],"M032761")]
-
-# estimate model
-mod6_8a <- TAM::tam.mml( resp=dat, A=A1, beta.fixed=FALSE )
-summary(mod6_8a)
-# extract fixed item parameter for item M032761
-## - sum(mod6_8a$xsi[setdiff(colnames(dat), "M032761"),"xsi"])
-
-# estimate mod6_8a using tam.mml.mfr
-## fixed a bug in 'tam.mml.mfr' for differing number of categories
-## per item -> now a xsi vector with parameter fixings to values
-## of 99 is used
-mod6_8b <- TAM::tam.mml.mfr( resp=dat, formulaA=~ 0 + item + item:step,
-                        control=list(fac.oldxsi=.1), constraint="items" )
-summary(mod6_8b)
-
-#************************************************************
-# Ex 6.9: sum constraint on item difficulties for irtmodel="PCM"
-
-data(data.timssAusTwn.scored)
-dat <- data.timssAusTwn.scored[,2:11]
-dat[ dat==9 ] <- NA
-
-# obtain the design matrix for the PCM parametrization and
-# the number of categories for each item
-maxKi <- apply(dat, 2, max, na.rm=TRUE)
-des <- TAM::designMatrices(resp=dat)
-A1 <- des$A
-
-# define the constrained item category and remove the respective parameter
-(par <- unlist( strsplit(dimnames(A1)[[3]][dim(A1)[3]], split="_") ))
-A1 <- A1[,,-dim(A1)[3]]
-
-# the item category loads on every other item category parameter with
-# opposing margin, balancing the number of categories for each item
-item.id <- which(colnames(dat)==par[1])
-cat.id <- maxKi[par[1]]+1
-loading <- 1/rep(maxKi, maxKi)
-loading <- loading [-which(names(loading)==par[1])[1]]
-A1[item.id, cat.id, ] <- loading
-A1[item.id,,]
-
-# estimate model
-mod6_9 <- TAM::tam.mml( resp=dat, A=A1, beta.fixed=FALSE )
-summary(mod6_9)
-
-## extract fixed item category parameter
-# calculate mean for each item
-ind.item.cat.pars <- sapply(colnames(dat), grep, rownames(mod6_8$xsi))
-item.means <- lapply(ind.item.cat.pars, function(ii) mean(mod6_8$xsi$xsi[ii]))
-
-# these sum up to the negative of the fixed parameter
-fix.par <- -sum( unlist(item.means), na.rm=TRUE)
-
-#************************************************************
-# Ex 6.10: Generalized partial credit model with equality constraints
-#          on item discriminations
-
-data(data.gpcm)
-dat <- data.gpcm
-
-# Ex 6.10a: set all slopes of three items equal to each other
-E <- matrix( 1, nrow=3, ncol=1 )
-mod6_10a <- TAM::tam.mml.2pl( dat, irtmodel="GPCM.design", E=E  )
-summary(mod6_10a)
-mod6_10a$B[,,]
-
-# Ex 6.10b: equal slope for first and third item
-E <- matrix( 0, nrow=3, ncol=2 )
-E[c(1,3),1] <- 1
-E[ 2, 2 ] <- 1
-mod6_10b <- TAM::tam.mml.2pl( dat, irtmodel="GPCM.design", E=E  )
-summary(mod6_10b)
-mod6_10b$B[,,]
-
-#############################################################################
-# EXAMPLE 7: design matrix for slopes for the generalized partial credit model
-#############################################################################
-
-# (1) simulate data from a model with a (item slope) design matrix E
-set.seed(789)
-I <- 42
-b <- seq( -2, 2, len=I)
-# create design matrix for loadings
-E <- matrix( 0, I, 5 )
-E[ seq(1,I,3), 1 ] <- 1
-E[ seq(2,I,3), 2 ] <- 1
-E[ seq(3,I,3), 3 ] <- 1
-ind <- seq( 1, I, 2 ) ; E[ ind, 4 ] <- rep( c( .3, -.2 ), I )[ 1:length(ind) ]
-ind <- seq( 2, I, 4 ) ; E[ ind, 5 ] <- rep( .15, I )[ 1:length(ind) ]
-E
-
-# true basis slope parameters
-lambda <- c( 1, 1.2, 0.8, 1, 1.1 )
-# calculate item slopes
-a <- E %*% lambda
-
-# simulate
-N <- 4000
-theta <- stats::rnorm( N )
-aM <- outer( rep(1,N), a[,1] )
-bM <- outer( rep(1,N), b )
-pM <- stats::plogis( aM * ( matrix( theta, nrow=N, ncol=I  ) - bM ) )
-dat <- 1 * ( pM > stats::runif( N*I ) )
-colnames(dat) <- paste("I", 1:I, sep="")
-
-# estimate model
-mod7 <- TAM::tam.mml.2pl( resp=dat, irtmodel="GPCM.design", E=E )
-mod7$B
-
-# recalculate estimated basis parameters
-stats::lm( mod7$B[,2,1] ~ 0+ as.matrix(E ) )
-  ##   Call:
-  ##   lm(formula=mod7$B[, 2, 1] ~ 0 + as.matrix(E))
-  ##   Coefficients:
-  ##   as.matrix(E)1  as.matrix(E)2  as.matrix(E)3  as.matrix(E)4  as.matrix(E)5
-  ##          0.9904         1.1896         0.7817         0.9601         1.2132
-
-#############################################################################
-# EXAMPLE 8: Differential item functioning                                  #
-#  A first example of a Multifaceted Rasch Model                            #
-#  Facet is only female; 10 items are studied                               #
-#############################################################################
-data(data.ex08)
-
-formulaA <- ~ item+female+item*female
-# this formula is in R equivalent to 'item*female'
-resp <- data.ex08[["resp"]]
-facets <- as.data.frame( data.ex08[["facets"]] )
-
-#***
-# Model 8a: investigate gender DIF on all items
-mod8a <- TAM::tam.mml.mfr( resp=resp, facets=facets, formulaA=formulaA )
-summary(mod8a)
-
-#***
-# Model 8a 2: specification with long format response data
-resp.long <- c( data.ex08[["resp"]] )
-pid <- rep( 1:nrow(data.ex08[["resp"]]), ncol(data.ex08[["resp"]]) )
-
-itemnames <- rep(colnames(data.ex08[["resp"]]), each=nrow(data.ex08[["resp"]]))
-facets.long <- cbind( data.frame( "item"=itemnames ),
-                 data.ex08[["facets"]][pid,,drop=F] )
-
-mod8a_2 <- TAM::tam.mml.mfr( resp=resp.long, facets=facets.long,
-                      formulaA=formulaA, pid=pid)
-stopifnot( all(mod8a$xsi.facets$xsi==mod8a_2$xsi.facets$xsi) )
-
-#***
-# Model 8b: Differential bundle functioning (DBF)
-#   - investigate differential item functioning in item groups
-
-# modify pre-specified design matrix to define 'appropriate' DBF effects
-formulaA <- ~ item*female
-des <- TAM::designMatrices.mfr( resp=resp, facets=facets, formulaA=formulaA)
-A1 <- des$A$A.3d
-# item group A: items 1-5
-# item group B: items 6-8
-# item group C: items 9-10
-A1 <- A1[,,1:13]
-dimnames(A1)[[3]][ c(12,13) ] <- c("A:female1", "B:female1")
-# item group A
-A1[,2,12] <- 0
-A1[c(1,5,7,9,11),2,12] <- -1
-A1[c(1,5,7,9,11)+1,2,12] <- 1
-# item group B
-A1[,2,13] <- 0
-A1[c(13,15,17),2,13] <- -1
-A1[c(13,15,17)+1,2,13] <- 1
-# item group C (define effect(A)+effect(B)+effect(C)=0)
-A1[c(19,3),2,c(12,13)] <- 1
-A1[c(19,3)+1,2,c(12,13)] <- -1
-#   A1[,2,]   # look at modified design matrix
-# estimate model
-mod8b <- TAM::tam.mml( resp=des$gresp$gresp.noStep, A=A1 )
-summary(mod8b)
-
-#############################################################################
-# EXAMPLE 9: Multifaceted Rasch Model
-#############################################################################
-
-data(data.sim.mfr)
-data(data.sim.facets)
-
-# two way interaction item and rater
-formulaA <- ~item+item:step + item*rater
-mod9a <- TAM::tam.mml.mfr( resp=data.sim.mfr, facets=data.sim.facets, formulaA=formulaA)
-mod9a$xsi.facets
-summary(mod9a)
-
-# three way interaction item, female and rater
-formulaA <- ~item+item:step + female*rater + female*item*step
-mod9b <- TAM::tam.mml.mfr( resp=data.sim.mfr, facets=data.sim.facets, formulaA=formulaA)
-summary(mod9b)
-
-#############################################################################
-# EXAMPLE 10: Model with raters.
-#   Persons are arranged in multiple rows which is indicated
-#   by multiple person identifiers.
-#############################################################################
-data(data.ex10)
-dat <- data.ex10
-head(dat)
-  ##     pid rater I0001 I0002 I0003 I0004 I0005
-  ## 1     1     1     0     1     1     0     0
-  ## 451   1     2     1     1     1     1     0
-  ## 901   1     3     1     1     1     0     1
-  ## 452   2     2     1     1     1     0     1
-  ## 902   2     3     1     1     0     1     1
-
-facets <- dat[, "rater", drop=FALSE ] # define facet (rater)
-pid <- dat$pid      # define person identifier (a person occurs multiple times)
-resp <- dat[, -c(1:2) ]        # item response data
-formulaA <- ~ item * rater      # formula
-
-mod10 <- TAM::tam.mml.mfr( resp=resp, facets=facets, formulaA=formulaA, pid=dat$pid )
-summary(mod10)
-
-# estimate person parameter with WLE
-wmod10 <- TAM::tam.wle( mod10 )
-
-#--- Example 10a
-# compare model containing only item
-formulaA <- ~ item + rater      # pseudo formula for item
-xsi.setnull <- "rater"          # set all rater effects to zero
-mod10a <- TAM::tam.mml.mfr( resp=resp, facets=facets, formulaA=formulaA,
-            xsi.setnull=xsi.setnull, pid=dat$pid, beta.fixed=cbind(1,1,0))
-summary(mod10a)
-
-# A shorter way for specifying this example is
-formulaA <- ~ item + 0*rater        # set all rater effects to zero
-mod10a1 <- TAM::tam.mml.mfr( resp=resp, facets=facets, formulaA=formulaA, pid=dat$pid )
-summary(mod10a1)
-
-# tam.mml.mfr also appropriately extends the facets data frame with pseudo facets
-# if necessary
-formulaA <- ~ item     # omitting the rater term
-mod10a2 <- TAM::tam.mml.mfr( resp=resp, facets=facets, formulaA=formulaA, pid=dat$pid )
-  ##   Item Parameters Xsi
-  ##              xsi se.xsi
-  ##   I0001   -1.931  0.111
-  ##   I0002   -1.023  0.095
-  ##   I0003   -0.089  0.089
-  ##   I0004    1.015  0.094
-  ##   I0005    1.918  0.110
-  ##   psfPF11  0.000  0.000
-  ##   psfPF12  0.000  0.000
-
-#***
-# Model 10_2: specification with long format response data
-resp.long <- c(unlist( dat[, -c(1:2) ] ))
-
-pid <- rep( dat$pid, ncol(dat[, -c(1:2) ]) )
-itemnames <- rep(colnames(dat[, -c(1:2) ]), each=nrow(dat[, -c(1:2) ]))
-
-# quick note: the 'trick' to use pid as the row index of the facet  (cf., used in Ex 8a_2)
-# is not working here, since pid already occures multiple times in the original response data
-facets <- cbind( data.frame("item"=itemnames),
-                 dat[ rep(1:nrow(dat), ncol(dat[,-c(1:2)])), "rater",drop=F]
-)
-
-mod10_2 <- TAM::tam.mml.mfr( resp=resp.long, facets=facets, formulaA=formulaA, pid=pid)
-
-stopifnot( all(mod10$xsi.facets$xsi==mod10_2$xsi.facets$xsi) )
-
-#############################################################################
-# EXAMPLE 11: Dichotomous data with missing and omitted responses
-#############################################################################
-data(data.ex11) ; dat <- data.ex11
-
-#***
-# Model 11a: Calibration (item parameter estimating) in which omitted
-#            responses (code 9) are set to missing
-dat1 <- dat[,-1]
-dat1[ dat1==9 ] <- NA
-# estimate Rasch model
-mod11a <- TAM::tam.mml( resp=dat1 )
-summary(mod11a)
-# compute person parameters
-wmod11a <- TAM::tam.wle( mod11a )
-
-#***
-# Model 11b: Scaling persons (WLE estimation) setting omitted
-#            responses as incorrect and using fixed
-#            item parameters form Model 11a
-
-# set matrix with fixed item difficulties as the input
-xsi1 <- mod11a$xsi    # xsi output from Model 11a
-xsi.fixed <- cbind( seq(1,nrow(xsi1) ), xsi1$xsi )
-# recode 9 to 0
-dat2 <- dat[,-1]
-dat2[ dat2==9 ] <- 0
-# run Rasch model with fixed item difficulties
-mod11b <- TAM::tam.mml( resp=dat2, xsi.fixed=xsi.fixed )
-summary(mod11b)
-# WLE estimation
-wmod11b <- TAM::tam.wle( mod11b )
-
-#############################################################################
-# EXAMPLE 12: Avoiding nonconvergence using the argument increment.factor
-#############################################################################
-data(data.ex12)
-dat <- data.ex12
-
-# non-convergence without increment.factor
-mod1 <- TAM::tam.mml.2pl( resp=data.ex12, control=list( maxiter=1000) )
-
-# avoiding non-convergence with increment.factor=1.02
-mod2 <- TAM::tam.mml.2pl( resp=data.ex12,
-            control=list( maxiter=1000, increment.factor=1.02) )
-summary(mod1)
-summary(mod2)
-
-#############################################################################
-# EXAMPLE 13: Longitudinal data 'data.long' from sirt package
-#############################################################################
-library(sirt)
-data(data.long, package="sirt")
-dat <- data.long
-  ##   > colnames(dat)
-  ##    [1] "idstud" "I1T1"   "I2T1"   "I3T1"   "I4T1"   "I5T1"   "I6T1"
-  ##    [8] "I3T2"   "I4T2"   "I5T2"   "I6T2"   "I7T2"   "I8T2"
-
-## item 1 to 6 administered at T1 and items 3 to 8 at T2
-## items 3 to 6 are anchor items
-
-#***
-# Model 13a: 2-dimensional Rasch model assuming invariant item difficulties
-
-# define matrix loadings
-Q <- matrix(0,12,2)
-colnames(Q) <- c("T1","T2")
-Q[1:6,1] <- 1       # items at T1
-Q[7:12,2] <- 1      # items at T2
-
-# assume equal item difficulty of I3T1 and I3T2, I4T1 and I4T2, ...
-# create draft design matrix and modify it
-A <- TAM::designMatrices(resp=data.long[,-1])$A
-dimnames(A)[[1]] <- colnames(data.long)[-1]
-  ##   > str(A)
-  ##    num [1:12, 1:2, 1:12] 0 0 0 0 0 0 0 0 0 0 ...
-  ##    - attr(*, "dimnames")=List of 3
-  ##     ..$ : chr [1:12] "Item01" "Item02" "Item03" "Item04" ...
-  ##     ..$ : chr [1:2] "Category0" "Category1"
-  ##     ..$ : chr [1:12] "I1T1" "I2T1" "I3T1" "I4T1" ...
-A1 <- A[,, c(1:6, 11:12 ) ]
-dimnames(A1)[[3]] <- substring( dimnames(A1)[[3]],1,2)
-A1[7,2,3] <- -1     # difficulty(I3T1)=difficulty(I3T2)
-A1[8,2,4] <- -1     # I4T1=I4T2
-A1[9,2,5] <- A1[10,2,6] <- -1
-  ##   > A1[,2,]
-  ##        I1 I2 I3 I4 I5 I6 I7 I8
-  ##   I1T1 -1  0  0  0  0  0  0  0
-  ##   I2T1  0 -1  0  0  0  0  0  0
-  ##   I3T1  0  0 -1  0  0  0  0  0
-  ##   I4T1  0  0  0 -1  0  0  0  0
-  ##   I5T1  0  0  0  0 -1  0  0  0
-  ##   I6T1  0  0  0  0  0 -1  0  0
-  ##   I3T2  0  0 -1  0  0  0  0  0
-  ##   I4T2  0  0  0 -1  0  0  0  0
-  ##   I5T2  0  0  0  0 -1  0  0  0
-  ##   I6T2  0  0  0  0  0 -1  0  0
-  ##   I7T2  0  0  0  0  0  0 -1  0
-  ##   I8T2  0  0  0  0  0  0  0 -1
-
-# estimate model
-# set intercept of second dimension (T2) to zero
-beta.fixed <- cbind( 1, 2, 0 )
-mod13a <- TAM::tam.mml( resp=data.long[,-1], Q=Q, A=A1, beta.fixed=beta.fixed)
-summary(mod13a)
-
-#--- tamaan specification
-tammodel <- "
-  LAVAAN MODEL:
-    T1=~ 1*I1T1__I6T1
-    T2=~ 1*I3T2__I8T2
-    T1 ~~ T1
-    T2 ~~ T2
-    T1 ~~ T2
-    # constraint on item difficulties
-    I3T1 + I3T2 | b3*t1
-    I4T1 + I4T2 | b4*t1
-    I5T1 + I5T2 | b5*t1
-    I6T1 + I6T2 | b6*t1
-    "
-# The constraint on item difficulties can be more efficiently written as
-  ##       DO(3,6,1)
-  ##         I%T1 + I%T2 | b%*t1
-  ##       DOEND
-# estimate model
-mod13at <- TAM::tamaan( tammodel, resp=data.long,  beta.fixed=beta.fixed )
-summary(mod13at)
-
-#***
-# Model 13b: invariant item difficulties with zero mean item difficulty
-#           of anchor items
-
-A <- TAM::designMatrices(resp=data.long[,-1])$A
-dimnames(A)[[1]] <- colnames(data.long)[-1]
-A1 <- A[,, c(1:5, 11:12 ) ]
-dimnames(A1)[[3]] <- substring( dimnames(A1)[[3]],1,2)
-A1[7,2,3] <- -1     # difficulty(I3T1)=difficulty(I3T2)
-A1[8,2,4] <- -1     # I4T1=I4T2
-A1[9,2,5] <- -1
-A1[6,2,3] <- A1[6,2,4] <- A1[6,2,5] <- 1     # I6T1=-(I3T1+I4T1+I5T1)
-A1[10,2,3] <- A1[10,2,4] <- A1[10,2,5] <- 1  # I6T2=-(I3T2+I4T2+I5T2)
-A1[,2,]
-  ##      I1 I2 I3 I4 I5 I7 I8
-  ## I1T1 -1  0  0  0  0  0  0
-  ## I2T1  0 -1  0  0  0  0  0
-  ## I3T1  0  0 -1  0  0  0  0
-  ## I4T1  0  0  0 -1  0  0  0
-  ## I5T1  0  0  0  0 -1  0  0
-  ## I6T1  0  0  1  1  1  0  0
-  ## I3T2  0  0 -1  0  0  0  0
-  ## I4T2  0  0  0 -1  0  0  0
-  ## I5T2  0  0  0  0 -1  0  0
-  ## I6T2  0  0  1  1  1  0  0
-  ## I7T2  0  0  0  0  0 -1  0
-  ## I8T2  0  0  0  0  0  0 -1
-
-mod13b <- TAM::tam.mml( resp=data.long[,-1], Q=Q, A=A1, beta.fixed=FALSE)
-summary(mod13b)
-
-#***
-# Model 13c: longitudinal polytomous data
-#
-
-# modifiy Items I1T1, I4T1, I4T2 in order to be trichotomous (codes: 0,1,2)
-set.seed(42)
-dat <- data.long
-dat[(1:50),2] <- sample(c(0,1,2), 50, replace=TRUE)
-dat[(1:50),5] <- sample(c(0,1,2), 50, replace=TRUE)
-dat[(1:50),9] <- sample(c(0,1,2), 50, replace=TRUE)
-  ##   > colnames(dat)
-  ##    [1] "idstud" "I1T1"   "I2T1"   "I3T1"   "I4T1"   "I5T1"   "I6T1"
-  ##    [8] "I3T2"   "I4T2"   "I5T2"   "I6T2"   "I7T2"   "I8T2"
-
-## item 1 to 6 administered at T1, items 3 to 8 at T2
-## items 3 to 6 are anchor items
-
-# (1) define matrix loadings
-Q <- matrix(0,12,2)
-colnames(Q) <- c("T1","T2")
-Q[1:6,1] <- 1       # items at T1
-Q[7:12,2] <- 1      # items at T2
-
-# (2) assume equal item difficulty of anchor items
-#     create draft design matrix and modify it
-A <- TAM::designMatrices(resp=dat[,-1])$A
-dimnames(A)[[1]] <- colnames(dat)[-1]
-  ## > str(A)
-  ## num [1:12, 1:3, 1:15] 0 0 0 0 0 0 0 0 0 0 ...
-  ## - attr(*, "dimnames")=List of 3
-  ## ..$ : chr [1:12] "I1T1" "I2T1" "I3T1" "I4T1" ...
-  ## ..$ : chr [1:3] "Category0" "Category1" "Category2"
-  ## ..$ : chr [1:15] "I1T1_Cat1" "I1T1_Cat2" "I2T1_Cat1" "I3T1_Cat1" ...
-
-# define matrix A
-# Items 1 to 3 administered at T1, Items 3 to 6 are anchor items
-# Item 7 to 8 administered at T2
-# Item I1T1, I4T1, I4T2 are trichotomous (codes: 0,1,2)
-A1 <- A[,, c(1:8, 14:15) ]
-dimnames(A1)[[3]] <- gsub("T1|T2", "",  dimnames(A1)[[3]])
-
-# Modifications are shortened compared to Model 13 a, but are still valid
-A1[7,,] <- A1[3,,]  # item 7, i.e. I3T2, loads on same parameters as
-                    # item 3, I3T1
-A1[8,,] <- A1[4,,]  # same for item 8 and item 4
-A1[9,,] <- A1[5,,]  # same for item 9 and item 5
-A1[10,,] <- A1[6,,] # same for item 10 and item 6
-  ## > A1[8,,]
-  ##           I1_Cat1 I1_Cat2 I2_Cat1 I3_Cat1 I4_Cat1 I4_Cat2 I5_Cat1 ...
-  ## Category0       0       0       0       0       0       0       0
-  ## Category1       0       0       0       0      -1       0       0
-  ## Category2       0       0       0       0      -1      -1       0
-
-# (3) estimate model
-#     set intercept of second dimension (T2) to zero
-beta.fixed <- cbind( 1, 2, 0 )
-mod13c <- TAM::tam.mml( resp=dat[,-1], Q=Q, A=A1, beta.fixed=beta.fixed,
-                   irtmodel="PCM")
-summary(mod13c)
-wle.mod13c <- TAM::tam.wle(mod13c) # WLEs of dimension T1 and T2
-
-#############################################################################
-# EXAMPLE 14: Facet model with latent regression
-#############################################################################
-data( data.ex14 )
-dat <- data.ex14
-
-#***
-# Model 14a: facet model
-resp <- dat[, paste0("crit",1:7,sep="") ]    # item data
-facets <- data.frame( "rater"=dat$rater )     # define facets
-formulaA <- ~item+item*step + rater
-mod14a <- TAM::tam.mml.mfr( resp, facets=facets, formulaA=formulaA, pid=dat$pid )
-summary(mod14a)
-
-#***
-# Model 14b: facet model with latent regression
-#   Note that dataY must correspond to rows in resp and facets which means
-#   that there must be the same rows in Y for a person with multiple rows
-#   in resp
-dataY <- dat[, c("X1","X2") ]        # latent regressors
-formulaY <- ~ X1+X2            # latent regression formula
-mod14b <- TAM::tam.mml.mfr( resp, facets=facets, formulaA=formulaA,
-            dataY=dataY, formulaY=formulaY, pid=dat$pid)
-summary(mod14b)
-
-#***
-# Model 14c: Multi-facet model with item slope estimation
-# use design matrix and modified response data from Model 1
-# item-specific slopes
-
-resp1 <- mod14a$resp      # extract response data with generalized items
-A <- mod14a$A             # extract design matrix for item intercepts
-colnames(resp1)
-
-# define design matrix for slopes
-E <- matrix( 0, nrow=ncol(resp1), ncol=7 )
-colnames(E) <- paste0("crit",1:7)
-rownames(E) <- colnames(resp1)
-E[ cbind( 1:(7*7), rep(1:7,each=7) ) ] <- 1
-
-mod14c <- TAM::tam.mml.2pl( resp=resp1, A=A, irtmodel="GPCM.design", E=E,
-        control=list(maxiter=100) )
-summary(mod14c)
-
-#############################################################################
-# EXAMPLE 15: Coping with nonconvergent models
-#############################################################################
-
-data(data.ex15)
-data <- data.ex15
-# facet model 'group*item' is of interest
-
-#***
-# Model 15a:
-mod15a <- TAM::tam.mml.mfr(resp=data[,-c(1:2)],facets=data[,"group",drop=FALSE],
-    formulaA=~ item + group*item, pid=data$pid )
-# See output:
-  ##
-  ##   Iteration 47     2013-09-10 16:51:39
-  ##   E Step
-  ##   M Step Intercepts   |----
-  ##     Deviance=75510.2868 | Deviance change: -595.0609
-  ##   !!! Deviance increases!                                        !!!!
-  ##   !!! Choose maybe fac.oldxsi > 0 and/or increment.factor > 1    !!!!
-  ##     Maximum intercept parameter change: 0.925045
-  ##     Maximum regression parameter change: 0
-  ##     Variance:  0.9796  | Maximum change: 0.009226
-
-#***
-# Model 15b: Follow the suggestions of changing the default of fac.oldxsi and
-#            increment.factor
-mod15b <- TAM::tam.mml.mfr(resp=data[,-c(1:2)],facets=data[,"group",drop=FALSE],
-            formulaA=~ group*item, pid=data$pid,
-            control=list( increment.factor=1.03, fac.oldxsi=.4 ) )
-
-#***
-# Model 15c: Alternatively, just choose more iterations in M-step by "Msteps=10"
-mod15c <- TAM::tam.mml.mfr(resp=data[,-c(1:2)],facets=data[,"group",drop=FALSE],
-    formulaA=~ item + group*item, pid=data$pid,
-    control=list(maxiter=250, Msteps=10))
-
-#############################################################################
-# EXAMPLE 16: Differential item function for polytomous items and
-#             differing number of response options per item
-#############################################################################
-
-data(data.timssAusTwn.scored)
-dat <- data.timssAusTwn.scored
-# extract item response data
-resp <- dat[, sort(grep("M", colnames(data.timssAusTwn.scored), value=TRUE)) ]
-# some descriptives
-psych::describe(resp)
-# define facets: 'cnt' is group identifier
-facets <- data.frame( "cnt"=dat$IDCNTRY)
-# create design matrices
-des2 <- TAM::designMatrices.mfr2( resp=resp, facets=facets,
-                   formulaA=~item*step + item*cnt)
-# restructured data set: pseudoitem=item x country
-resp2 <- des2$gresp$gresp.noStep
-# A design matrix
-A <- des2$A$A.3d
-    # redundant xsi parameters must be eliminated from design matrix
-xsi.elim <- des2$xsi.elim
-A <- A[,, - xsi.elim[,2] ]
-# extract loading matrix B
-B <- des2$B$B.3d
-# estimate model
-mod1 <- TAM::tam.mml( resp=resp2, A=A, B=B, control=list(maxiter=100) )
-summary(mod1)
-# The sum of all DIF parameters is set to zero. The DIF parameter for the last
-# item is therefore obtained
-xsi1 <- mod1$xsi
-difxsi <- xsi1[ intersect( grep("cnt",rownames(xsi1)),
-              grep("M03",rownames(xsi1))), ]   - colSums(difxsi)
-    # this is the DIF effect of the remaining item
-
-#############################################################################
-# EXAMPLE 17: Several multidimensional and subdimension models
-#############################################################################
-
-library(mirt)
-#*** (1) simulate data in mirt package
-set.seed(9897)
-# simulate data according to the four-dimensional Rasch model
-# variances
-variances <- c( 1.45, 1.74, .86, 1.48  )
-# correlations
-corrs <- matrix( 1, 4, 4 )
-dd1 <- 1 ; dd2 <- 2 ; corrs[dd1,dd2] <- corrs[dd2,dd1] <- .88
-dd1 <- 1 ; dd2 <- 3 ; corrs[dd1,dd2] <- corrs[dd2,dd1] <- .85
-dd1 <- 1 ; dd2 <- 4 ; corrs[dd1,dd2] <- corrs[dd2,dd1] <- .87
-dd1 <- 2 ; dd2 <- 3 ; corrs[dd1,dd2] <- corrs[dd2,dd1] <- .84
-dd1 <- 2 ; dd2 <- 4 ; corrs[dd1,dd2] <- corrs[dd2,dd1] <- .90
-dd1 <- 3 ; dd2 <- 4 ; corrs[dd1,dd2] <- corrs[dd2,dd1] <- .90
-# covariance matrix
-covar <- outer( sqrt( variances), sqrt(variances) )*corrs
-# item thresholds and item discriminations
-d <- matrix( stats::runif(40, -2, 2 ), ncol=1 )
-a <- matrix(NA, nrow=40,ncol=4)
-a[1:10,1] <- a[11:20,2] <- a[21:30,3] <- a[31:40,4] <- 1
-# simulate data
-dat <- mirt::simdata(a=a, d=d, N=1000, itemtype="dich", sigma=covar )
-# define Q-matrix for testlet and subdimension models estimated below
-Q <- matrix( 0, nrow=40, ncol=5 )
-colnames(Q) <- c("g", paste0( "subd", 1:4) )
-Q[,1] <- 1
-Q[1:10,2] <- Q[11:20,3] <- Q[21:30,4] <- Q[31:40,5] <- 1
-
-# define maximum number of iterations and number of quasi monte carlo nodes
-# maxit <- 5  ; snodes <- 300    # this specification is only for speed reasons
-maxit <- 200 ; snodes <- 1500
-
-#*****************
-# Model 1: Rasch testlet model
-#*****************
-
-# define a user function for restricting the variance according to the
-# Rasch testlet model
-variance.fct1 <- function( variance ){
-            ndim <- ncol(variance)
-            variance.new <- matrix( 0, ndim, ndim )
-            diag(variance.new) <- diag(variance)
-            variance <- variance.new
-            return(variance)
-                    }
-variance.Npars <- 5    # number of estimated parameters in variance matrix
-# estimation using tam.mml
-mod1 <- TAM::tam.mml( dat, Q=Q, userfct.variance=variance.fct1,
-             variance.Npars=variance.Npars, control=list(maxiter=maxit, QMC=TRUE,
-                          snodes=snodes))
-summary(mod1)
-
-#*****************
-# Model 2: Testlet model with correlated testlet effects
-#*****************
-
-# specify a testlet model with general factor g and testlet effects
-# u_1,u_2,u_3 and u_4. Assume that Cov(g,u_t)=0 for all t=1,2,3,4.
-# Additionally, assume that \sum_t,t' Cov( u_t, u_t')=0, i.e.
-# the sum of all testlet covariances is equal to zero
-#=> testlet effects are uncorrelated on average.
-
-# set Cov(g,u_t)=0 and sum of all testlet covariances equals to zero
-variance.fct2 <- function( variance ){
-            ndim <- ncol(variance)
-            variance.new <- matrix( 0, ndim, ndim )
-            diag(variance.new) <- diag(variance)
-            variance.new[1,2:ndim] <- variance.new[2:ndim,1] <- 0
-            # calculate average covariance between testlets
-            v1 <- variance[ -1, -1] - variance.new[-1,-1]
-            M1 <- sum(v1) / ( ( ndim-1)^2 - ( ndim - 1))
-            v1 <- v1 - M1
-            variance.new[ -1, -1 ] <- v1
-            diag(variance.new) <- diag(variance)
-            variance <- variance.new
-            return(variance)
-                    }
-variance.Npars <- 1 + 4 + (4*3)/2 - 1
-# estimate model in TAM
-mod2 <- TAM::tam.mml( dat, Q=Q, userfct.variance=variance.fct2,
-                variance.Npars=variance.Npars,
-                control=list(maxiter=maxit, QMC=TRUE, snodes=snodes) )
-summary(mod2)
-
-#*****************
-# Model 3: Testlet model with correlated testlet effects (different identification)
-#*****************
-
-# Testlet model like in Model 2. But now the constraint is
-# \sum _t,t' Cov(u_t, u_t') + \sum_t Var(u_t)=0, i.e.
-# the sum of all testlet covariances and variances is equal to zero.
-variance.fct3 <- function( variance ){
-            ndim <- ncol(variance)
-            variance.new <- matrix( 0, ndim, ndim )
-            diag(variance.new) <- diag(variance)
-            variance.new[1,2:ndim] <- variance.new[2:ndim,1] <- 0
-            # calculate average covariance and variance between testlets
-            v1 <- variance[ -1, -1]
-            M1 <- mean(v1)
-            v1 <- v1 - M1
-            variance.new[ -1, -1 ] <- v1
-            # ensure positive definiteness of covariance matrix
-            eps <- 10^(-2)
-            diag(variance.new) <- diag( variance.new) + eps
-            variance.new <- psych::cor.smooth( variance.new )  # smoothing in psych
-            variance <- variance.new
-            return(variance)
-                    }
-variance.Npars <- 1 + 4 + (4*3)/2 - 1
-# estimate model in TAM
-mod3 <- TAM::tam.mml( dat, Q=Q, userfct.variance=variance.fct3,
-                variance.Npars=variance.Npars,
-                control=list(maxiter=maxit, QMC=TRUE, snodes=snodes) )
-summary(mod3)
-
-#*****************
-# Model 4: Rasch subdimension model
-#*****************
-
-# The Rasch subdimension model is specified according to Brandt (2008).
-# The fourth testlet effect is defined as u4=- (u1+u2+u3)
-# specify an alternative Q-matrix with 4 dimensions
-Q2 <- Q[,-5]
-Q2[31:40,2:4] <- -1
-
-# set Cov(g,u1)=Cov(g,u2)=Cov(g,u3)=0
-variance.fixed <- rbind( c(1,2,0), c(1,3,0), c(1,4,0) )
-# estimate model in TAM
-mod4 <- TAM::tam.mml( dat, Q=Q2,variance.fixed=variance.fixed,
-                control=list(maxiter=maxit, QMC=TRUE, snodes=snodes) )
-summary(mod4)
-
-#*****************
-# Model 5: Higher-order model
-#*****************
-
-# A four-dimensional model with a higher-order factor is specified.
-# F_t=a_t g + eps_g
-Q3 <- Q[,-1]
-# define fitting function using the lavaan package and ULS estimation
-N0 <- nrow(dat)         # sample size of dataset
-library(lavaan)        # requires lavaan package for fitting covariance
-variance.fct5 <- function( variance ){
-    ndim <- ncol(variance)
-    rownames(variance) <- colnames(variance) <- paste0("F",1:ndim)
-    lavmodel <- paste0(
-        "FHO=~", paste0( paste0( "F", 1:ndim ), collapse="+" ) )
-    lavres <- lavaan::cfa( model=lavmodel, sample.cov=variance, estimator="ULS",
-                       std.lv=TRUE, sample.nobs=N0)
-    variance.new <- fitted(lavres)$cov
-    variance <- variance.new
-    # print coefficients
-    cat( paste0( "\n **** Higher order loadings: ",
-            paste0( paste0( round( coef(lavres)[ 1:ndim ], 3 )), collapse=" ")
-                        ), "\n")
-    return(variance)
-                    }
-variance.Npars <- 4+4
-# estimate model in TAM
-mod5 <- TAM::tam.mml( dat, Q=Q3, userfct.variance=variance.fct5,
-                variance.Npars=variance.Npars,
-                control=list(maxiter=maxit, QMC=TRUE, snodes=snodes) )
-summary(mod5)
-
-#*****************
-# Model 6: Generalized Rasch subdimension model (Brandt, 2012)
-#*****************
-
-Q2 <- Q[,-5]
-Q2[31:40,2:4] <- -1
-# fixed covariances
-variance.fixed2 <- rbind( c(1,2,0), c(1,3,0), c(1,4,0)  )
-# design matrix for item loading parameters
-#      items x category x dimension x xsi parameter
-E <- array( 0, dim=c( 40, 2, 4, 4 ) )
-E[ 1:10, 2, c(1,2), 1 ] <- 1
-E[ 11:20, 2, c(1,3), 2 ] <- 1
-E[ 21:30, 2, c(1,4), 3 ] <- 1
-E[ 31:40, 2, 1, 4 ] <- 1
-E[ 31:40, 2, 2:4, 4 ] <- -1
-
-# constraint on slope parameters, see Brandt (2012)
-gammaconstr <- function( gammaslope ){
-        K <- length( gammaslope)
-        g1 <- sum( gammaslope^2  )
-        gammaslope.new <- sqrt(K) / sqrt(g1) * gammaslope
-        return(gammaslope.new)
-                    }
-# estimate model
-mod6 <- TAM::tam.mml.3pl( dat, E=E, Q=Q2, variance.fixed=variance.fixed2,
-           skillspace="normal", userfct.gammaslope=gammaconstr, gammaslope.constr.Npars=1,
-           control=list(maxiter=maxit, QMC=TRUE, snodes=snodes ) )
-summary(mod6)
-
-#############################################################################
-# EXAMPLE 18: Partial credit model with dimension-specific sum constraints
-#             on item difficulties
-#############################################################################
-
-data(data.Students, package="CDM")
-dat <- data.Students[, c( paste0("sc",1:4), paste0("mj",1:4) ) ]
-# specify dimensions in Q-matrix
-Q <- matrix( 0,  nrow=8, ncol=2 )
-Q[1:4,1] <- Q[5:8,2] <- 1
-# partial credit model with some constraint on item parameters
-mod1 <- TAM::tam.mml( dat, Q=Q, irtmodel="PCM2", constraint="items")
-summary(mod1)
-
-#############################################################################
-# EXAMPLE 19: Partial credit scoring: 0.5 points for partial credit items
-#             and 1 point for dichotomous items
-#############################################################################
-
-data(data.timssAusTwn.scored)
-dat <- data.timssAusTwn.scored
-# extrcat item response data
-dat <- dat[, grep("M03", colnames(dat) ) ]
-
-# select items with do have maximum score of 2 (polytomous items)
-ind <- which( apply( dat,  2, max, na.rm=TRUE )==2 )
-I <- ncol(dat)
-# define Q-matrix with scoring variant
-Q <- matrix( 1, nrow=I, ncol=1 )
-Q[ ind, 1 ] <- .5    # score of 0.5 for polyomous items
-
-# estimate model
-mod1 <- TAM::tam.mml( dat, Q=Q, irtmodel="PCM2", control=list(nodes=seq(-10,10,len=21)))
-summary(mod1)
-
-#############################################################################
-# EXAMPLE 20: Specification of loading matrix in multidimensional model
-#############################################################################
-
-data(data.gpcm)
-psych::describe(data.gpcm)
-resp <- data.gpcm
-
-# define three dimensions and different loadings of item categories
-# on these dimensions in B loading matrix
-I <- 3  # 3 items
-D <- 3  # 3 dimensions
-# define loading matrix B
-# 4 categories for each item (0,1,2,3)
-B <- array( 0, dim=c(I,4,D) )
-for (ii in 1:I){
-    B[ ii, 1:4, 1 ] <- 0:3
-    B[ ii, 1,2 ] <- 1
-    B[ ii, 4,3 ] <- 1
-            }
-dimnames(B)[[1]] <- colnames(resp)
-B[1,,]
-  ##   > B[1,,]
-  ##        [,1] [,2] [,3]
-  ##   [1,]    0    1    0
-  ##   [2,]    1    0    0
-  ##   [3,]    2    0    0
-  ##   [4,]    3    0    1
-#-- test run
-mod1 <- TAM::tam.mml( resp, B=B, control=list( snodes=1000, maxiter=5)  )
-summary(mod1)
-
-# Same model with TAM::tam.mml.3pl instead
-
-dim4 <- sum(apply(B, c(1, 3), function(x) any(!(x==0))))
-E1 <- array(0, dim=c(dim(B), dim4))
-
-kkk <- 0
-for (iii in seq_len(dim(E1)[1])) {
-    for (jjj in seq_len(dim(E1)[3])) {
-        if (any(B[iii,, jjj] !=0)) {
-            kkk <- kkk + 1
-            E1[iii,, jjj, kkk] <- B[iii,, jjj]
-        }
-    }
-}
-if (kkk !=dim4) stop("Something went wrong in the loop, because 'kkk !=dim4'.")
-
-mod2 <- TAM::tam.mml.3pl(resp, E=E1, est.some.slopes=FALSE, control=list(maxiter=50))
-summary(mod2)
-
-cor(mod1$person$EAP.Dim3, mod2$person$EAP.Dim3)
-cor(mod1$person$EAP.Dim2, mod2$person$EAP.Dim2)
-cor(mod1$person$EAP.Dim1, mod2$person$EAP.Dim1)
-cor(mod1$xsi$xsi, mod2$xsi$xsi)
-
-#############################################################################
-# EXAMPLE 21: Acceleration of EM algorithm | dichotomous data
-#############################################################################
-
-N <- 1000      # number of persons
-I <- 100       # number of items
-set.seed(987)
-# simulate data according to the Rasch model
-dat <- sirt::sim.raschtype( stats::rnorm(N), b=seq(-2,2,len=I)  )
-# estimate models
-mod1n <- TAM::tam.mml( resp=dat, control=list( acceleration="none") )  # no acceler.
-mod1y <- TAM::tam.mml( resp=dat, control=list( acceleration="Yu") )  # Yu acceler.
-mod1r <- TAM::tam.mml( resp=dat, control=list( acceleration="Ramsay") )  # Ramsay acceler.
-# compare number of iterations
-mod1n$iter ; mod1y$iter ; mod1r$iter
-# log-likelihood values
-logLik(mod1n); logLik(mod1y) ; logLik(mod1r)
-
-#############################################################################
-# EXAMPLE 22: Acceleration of EM algorithm | polytomous data
-#############################################################################
-
-data(data.gpcm)
-dat <- data.gpcm
-
-# no acceleration
-mod1n <- TAM::tam.mml.2pl( resp=dat, irtmodel="GPCM",
-                control=list( conv=1E-4, acceleration="none") )
-# Yu acceleration
-mod1y <- TAM::tam.mml.2pl( resp=dat, irtmodel="GPCM",
-                control=list( conv=1E-4, acceleration="Yu") )
-# Ramsay acceleration
-mod1r <- TAM::tam.mml.2pl( resp=dat, irtmodel="GPCM",
-                control=list( conv=1E-4, acceleration="Ramsay") )
-# number of iterations
-mod1n$iter ; mod1y$iter ; mod1r$iter
-
-#############################################################################
-# EXAMPLE 23: Multidimensional polytomous Rasch model in which
-#             dimensions are defined by categories
-#############################################################################
-
-data(data.Students, package="CDM")
-dat <- data.Students[, grep( "act", colnames(data.Students) ) ]
-
-# define multidimensional model in which categories of item define dimensions
-
-# * Category 0 -> loading of one on Dimension 0
-# * Category 1 -> no loadings
-# * Category 2 -> loading of one on Dimension 2
-
-# extract default design matrices
-res <- TAM::designMatrices( resp=dat )
-A <- res$A
-B0 <- 0*res$B
-# create design matrix B
-B <- array( 0, dim=c( dim(B0)[c(1,2) ], 2  ) )
-dimnames(B)[[1]] <- dimnames(B0)[[1]]
-dimnames(B)[[2]] <- dimnames(B0)[[2]]
-dimnames(B)[[3]] <- c( "Dim0", "Dim2" )
-B[,1,1]  <- 1
-B[,3,2]  <- 1
-
-# estimate multdimensional Rasch model
-mod1 <- TAM::tam.mml( resp=dat, A=A, B=B, control=list( maxiter=100) )
-summary(mod1)
-
-# alternative definition of B
-# * Category 1: negative loading on Dimension 1 and Dimension 2
-B <- array( 0, dim=c( dim(B0)[c(1,2) ], 2  ) )
-dimnames(B)[[1]] <- dimnames(B0)[[1]]
-dimnames(B)[[2]] <- dimnames(B0)[[2]]
-dimnames(B)[[3]] <- c( "Dim0", "Dim2" )
-B[,1, 1]  <- 1
-B[,3, 2]  <- 1
-B[,2, c(1,2)]  <- -1
-
-# estimate model
-mod2 <- TAM::tam.mml( resp=dat, A=A, B=B, control=list( maxiter=100) )
-summary(mod2)
-
-#############################################################################
-# EXAMPLE 24: Sum constraint on item-category parameters in partial credit model
-#############################################################################
-
-data(data.gpcm,package="TAM")
-dat <- data.gpcm
-
-# check number of categories
-c1 <- TAM::tam.ctt3(dat)
-
-#--- fit with PCM
-mod1 <- TAM::tam.mml( dat )
-summary(mod1, file="mod1")
-
-#--- fit with constraint on sum of categories
-#** redefine design matrix
-A1 <- 0*mod1$A
-A1 <- A1[,, - dim(A1)[[3]]]
-str(A1)
-NP <- dim(A1)[[3]]
-# define item category parameters
-A1[1,2,1] <- A1[1,3,2] <- A1[1,4,3] <- -1
-A1[2,2,4] <- A1[2,3,5] <- A1[2,4,6] <- -1
-A1[3,2,7] <- A1[3,3,8] <- -1
-A1[3,4,1:8] <- 1
-# check definition
-A1[1,,]
-A1[2,,]
-A1[3,,]
-
-#** estimate model
-mod2 <- TAM::tam.mml( dat, A=A1, beta.fixed=FALSE)
-summary(mod2, file="mod2")
-
-#--- compare model fit
-IRT.compareModels(mod1, mod2 )  # -> equivalent model fit
-
-#############################################################################
-# EXAMPLE 25: Different GPCM parametrizations in IRT packages
-#############################################################################
-
-library(TAM)
-library(mirt)
-library(ltm)
-
-data(data.gpcm, package="TAM")
-dat <- data.gpcm
-
-#*** TAM
-mod1 <- TAM::tam.mml.2pl(dat, irtmodel="GPCM")
-#*** mirt
-mod2 <- mirt::mirt(dat, 1, itemtype="gpcm", verbose=TRUE)
-#*** ltm
-mod3 <- ltm::gpcm( dat, control=list(verbose=TRUE) )
-mod3b <- ltm::gpcm( dat, control=list(verbose=TRUE), IRT.param=FALSE)
-
-#-- comparison log likelihood
-logLik(mod1)
-logLik(mod2)
-logLik(mod3)
-logLik(mod3b)
-
-#*** intercept parametrization (like in TAM)
-
-# TAM
-mod1$B[,2,1]   # slope
-mod1$AXsi      # intercepts
-# mirt
-coef(mod2)
-# ltm
-coef(mod3b, IRT.param=FALSE)[, c(4,1:3)]
-
-#*** IRT parametrization
-
-# TAM
-mod1$AXsi / mod1$B[,2,1]
-# mirt
-coef(mod2, IRTpars=TRUE)
-# ltm
-coef(mod3)[, c(4,1:3)]
-
-#############################################################################
-# EXAMPLE 26: Differential item functioning in multdimensional models
-#############################################################################
-
-data(data.ex08, package="TAM")
-formulaA <- ~ item+female+item*female
-resp <- data.ex08[["resp"]]
-facets <- as.data.frame(data.ex08[["facets"]])
-
-#***  Model 8a: investigate gender DIF in undimensional model
-mod8a <- TAM::tam.mml.mfr(resp=resp, facets=facets, formulaA=formulaA)
-summary(mod8a)
-
-#*** multidimensional 2PL Model
-I <- 10
-Q <- array(0, dim=c(I, 3))
-Q[cbind(1:I, c(rep(1, 3), rep(2, 3), rep(3, 4)))] <- 1
-rownames(Q) <- colnames(resp)
-mod3dim2pl <- TAM::tam.mml.2pl(resp=resp, Q=Q, irtmodel="2PL",
-                          control=list(snodes=2000))
-
-#*** Combine both approaches
-thisRows <- gsub("-.*", "", colnames(mod8a$resp)) #select item names
-
-#*** uniform DIF (note irtmodel="2PL.groups" & est.slopegroups)
-mod3dim2pl_udiff <- TAM::tam.mml.2pl(resp=mod8a$resp, A=mod8a$A, Q=Q[thisRows, ],
-                               irtmodel="2PL.groups",
-                               est.slopegroups=as.numeric(as.factor(thisRows)),
-                               control=list(snodes=2000))
-
-#*** non-uniform DIF (?); different slope parameters for each item administered to each group
-mod3dim2pl_nudiff <- TAM::tam.mml.2pl(resp=mod8a$resp, A=mod8a$A, Q=Q[thisRows, ],
-                                irtmodel="2PL", control=list(snodes=2000))
-
-#*** check results
-print(mod8a$xsi)
-print(mod3dim2pl_udiff$xsi)
-summary(mod3dim2pl_nudiff)
-
-#*** within item dimensionality (one item loads on two dimensions)
-Q2 <- Q
-Q2[4,1] <- 1
-
-# uniform DIF (note irtmodel="2PL.groups" & est.slopegroups)
-mod3dim2pl_udiff2 <- TAM::tam.mml.2pl(resp=mod8a$resp, A=mod8a$A, Q=Q2[thisRows, ],
-                                irtmodel="2PL.groups",
-                                est.slopegroups=as.numeric(as.factor(thisRows)),
-                                control=list(snodes=2000))
-print(mod8a$xsi)
-print(mod3dim2pl_udiff2$xsi)
-print(mod3dim2pl_udiff2$xsi)
-
-#############################################################################
-# EXAMPLE 27: IRT parameterization for generalized partial credit model (GPCM) in TAM
-#############################################################################
-
-#--- read item parameters
-pars <- as.numeric(miceadds::scan.vec(
-"0.19029 1.25309 0.51737 -1.77046 0.94803
-  0.19407 1.22680 0.34986 -1.57666 1.29726
-  -0.00888 1.07093 0.31662 -1.38755 1.14809
-  -0.33810 1.08205 0.48490 -1.56696 0.79547
-  -0.18866 0.99587 0.37880 -1.37468 0.81114" ))
-pars <- matrix( pars, nrow=5, byrow=TRUE)
-beta <- pars[,1]
-alpha <- pars[,5]
-tau <- pars[,2:4]
-
-#--- data simulation function for GPCM
-sim_gpcm_irt_param <- function(alpha, beta, tau, N, mu=0, sigma=1)
-{
-    theta <- stats::rnorm(N, mean=mu, sd=sigma)
-    I <- length(beta)
-    K <- ncol(tau)
-    dat <- matrix(0, nrow=N, ncol=I)
-    colnames(dat) <- paste0("I",1:I)
-    for (ii in 1:I){
-        probs <- matrix(0, nrow=N, ncol=K+1)
-        for (kk in 1:K){
-            probs[,kk+1] <- probs[,kk] + alpha[ii]*( theta - beta[ii] - tau[ii,kk] )
-        }
-        probs <- exp(probs)
-        probs <- probs/rowSums(probs)
-        rn <- stats::runif(N)
-        cumprobs <- t(apply(probs,1,cumsum))
-        for (kk in 1:K){
-            dat[,ii] <- dat[,ii] + ( rn > cumprobs[,kk] )
-        }
-    }
-    return(dat)
-}
-
-#-- simulate data
-N <- 20000     # number of persons
-set.seed(98)
-dat1 <- sim_gpcm_irt_param(alpha=alpha, beta=beta, tau=tau, N=N, mu=0, sigma=1)
-head(dat1)
-
-#* generate design matrix for IRT parameterization
-A1 <- TAM::.A.PCM2( resp=dat1)
-
-#- estimate GPCM model
-mod1 <- TAM::tam.mml.2pl( resp=dat1, irtmodel="GPCM", A=A1)
-summary(mod1)
-
-# compare true and estimated slope estimates (alpha)
-cbind( alpha, mod1$B[,2,] )
-
-# compare true and estimated item difficulties (beta)
-cbind( beta, mod1$xsi$xsi[1:5] / mod1$B[,2,1] )
-
-# compare true and estimated tau parameters
-cbind( tau[,-3], matrix( mod1$xsi$xsi[-c(1:5)], nrow=5, byrow=TRUE ) / mod1$B[,2,1] )
-}

+mirt::mirt in the mirt package.

+    

+
+    

+    
Examples

+    
#############################################################################
+# EXAMPLE 1: dichotomous data
+# data.sim.rasch: 2000 persons, 40 items
+#############################################################################
+data(data.sim.rasch)
+
+#************************************************************
+# Model 1: Rasch model (MML estimation)
+mod1 <- TAM::tam.mml(resp=data.sim.rasch)
+# extract item parameters
+mod1$item    # item difficulties
+
+if (FALSE) {
+# WLE estimation
+wle1 <- TAM::tam.wle( mod1 )
+# item fit
+fit1 <- TAM::tam.fit(mod1)
+# plausible value imputation
+pv1 <- TAM::tam.pv(mod1, normal.approx=TRUE, ntheta=300)
+# standard errors
+se1 <- TAM::tam.se( mod1 )
+# summary
+summary(mod1)
+
+#-- specification with tamaan
+tammodel <- "
+ LAVAAN MODEL:
+   F=~ I1__I40;
+   F ~~ F
+ ITEM TYPE:
+   ALL(Rasch)
+   "
+mod1t <- TAM::tamaan( tammodel, data.sim.rasch)
+summary(mod1t)
+
+#************************************************************
+# Model 1a: Rasch model with fixed item difficulties from 'mod1'
+xsi0 <- mod1$xsi$xsi
+xsi.fixed <- cbind( 1:(length(xsi0)), xsi0 )
+        # define vector with fixed item difficulties
+mod1a <- TAM::tam.mml( resp=data.sim.rasch, xsi.fixed=xsi.fixed )
+summary(mod1a)
+
+# Usage of the output value mod1$xsi.fixed.estimated has the right format
+# as the input of xsi.fixed
+mod1aa <- TAM::tam.mml( resp=data.sim.rasch, xsi.fixed=mod1$xsi.fixed.estimated )
+summary(mod1b)
+
+#************************************************************
+# Model 1b: Rasch model with initial xsi parameters for items 2 (item difficulty b=-1.8),
+# item 4 (b=-1.6) and item 40 (b=2)
+xsi.inits <- cbind( c(2,4,40), c(-1.8,-1.6,2))
+mod1b <- TAM::tam.mml( resp=data.sim.rasch, xsi.inits=xsi.inits )
+
+#-- tamaan specification
+tammodel <- "
+ LAVAAN MODEL:
+   F=~ I1__I40
+   F ~~ F
+   # Fix item difficulties. Note that item intercepts instead of difficulties
+   # must be specified.
+   I2 | 1.8*t1
+   I4 | 1.6*t1
+ ITEM TYPE:
+   ALL(Rasch)
+   "
+mod1bt <- TAM::tamaan( tammodel, data.sim.rasch)
+summary(mod1bt)
+
+#************************************************************
+# Model 1c: 1PL estimation with sum constraint on item difficulties
+dat <- data.sim.rasch
+# modify A design matrix to include the sum constraint
+des <- TAM::designMatrices(resp=dat)
+A1 <- des$A[,, - ncol(dat) ]
+A1[ ncol(dat),2, ] <- 1
+A1[,2,]
+# estimate model
+mod1c <- TAM::tam.mml( resp=dat, A=A1, beta.fixed=FALSE,
+           control=list(fac.oldxsi=.1) )
+summary(mod1c)
+
+#************************************************************
+# Model 1d: estimate constraint='items' using tam.mml.mfr
+formulaA=~ 0 + item
+mod1d <- TAM::tam.mml.mfr( resp=dat, formulaA=formulaA,
+                     control=list(fac.oldxsi=.1), constraint="items")
+summary(mod1d)
+
+#************************************************************
+# Model 1e: This sum constraint can also be obtained by using the argument
+# constraint="items" in tam.mml
+mod1e <- TAM::tam.mml( resp=data.sim.rasch, constraint="items" )
+summary(mod1e)
+
+#************************************************************
+# Model 1d2: estimate constraint='items' using tam.mml.mfr
+# long format response data
+resp.long <- c(dat)
+
+# pid and item facet specifications are necessary
+#     Note, that we recommend the facet labels to be sortable in the same order that the
+#     results are desired.
+#     compare to: facets <- data.frame( "item"=rep(colnames(dat), each=nrow(dat)) )
+pid <- rep(1:nrow(dat), ncol(dat))
+itemnames <- paste0("I", sprintf(paste('%0', max(nchar(1:ncol(dat))), 'i', sep='' ),
+                    c(1:ncol(dat)) ) )
+facets   <- data.frame( "item_"=rep(itemnames, each=nrow(dat)) )
+formulaA=~ 0 + item_
+
+mod1d2 <- TAM::tam.mml.mfr( resp=resp.long, formulaA=formulaA, control=list(fac.oldxsi=.1),
+                       constraint="items", facets=facets, pid=pid)
+stopifnot( all(mod1d$xsi.facets$xsi==mod1d2$xsi.facets$xsi) )
+}
+
+
+#************************************************************
+# Model 2: 2PL model
+mod2 <- TAM::tam.mml.2pl(resp=data.sim.rasch,irtmodel="2PL")
+
+# extract item parameters
+mod2$xsi    # item difficulties
+mod2$B      # item slopes
+
+#--- tamaan specification
+tammodel <- "
+ LAVAAN MODEL:
+   F=~ I1__I40
+   F ~~ 1*F
+   # item type of 2PL is the default for dichotomous data
+   "
+# estimate model
+mod2t <- TAM::tamaan( tammodel, data.sim.rasch)
+summary(mod2t)
+
+if (FALSE) {
+#************************************************************
+# Model 2a: 2PL with fixed item difficulties and slopes from 'mod2'
+xsi0 <- mod2$xsi$xsi
+xsi.fixed <- cbind( 1:(length(xsi0)), xsi0 )
+        # define vector with fixed item difficulties
+mod2a <- TAM::tam.mml( resp=data.sim.rasch, xsi.fixed=xsi.fixed,
+                 B=mod2$B # fix slopes
+            )
+summary(mod2a)
+mod2a$B     # inspect used slope matrix
+
+#************************************************************
+# Model 3: constrained 2PL estimation
+# estimate item parameters in different slope groups
+# items 1-10, 21-30 group 1
+# items 11-20 group 2 and items 31-40 group 3
+est.slope <- rep(1,40)
+est.slope[ 11:20 ] <- 2
+est.slope[ 31:40 ] <- 3
+mod3 <- TAM::tam.mml.2pl( resp=data.sim.rasch, irtmodel="2PL.groups",
+               est.slopegroups=est.slope )
+mod3$B
+summary(mod3)
+
+#--- tamaan specification (A)
+tammodel <- "
+ LAVAAN MODEL:
+   F=~ lam1*I1__I10 + lam2*I11__I20 + lam1*I21__I30 + lam3*I31__I40;
+   F ~~ 1*F
+   "
+# estimate model
+mod3tA <- TAM::tamaan( tammodel, data.sim.rasch)
+summary(mod3tA)
+
+#--- tamaan specification (alternative B)
+tammodel <- "
+ LAVAAN MODEL:
+   F=~ a1__a40*I1__I40;
+   F ~~ 1*F
+ MODEL CONSTRAINT:
+   a1__a10==lam1
+   a11__a20==lam2
+   a21__a30==lam1
+   a31__a40==lam3
+   "
+mod3tB <- TAM::tamaan( tammodel, data.sim.rasch)
+summary(mod3tB)
+
+#--- tamaan specification (alternative C using DO operator)
+tammodel <- "
+ LAVAAN MODEL:
+ DO(1,10,1)
+   F=~ lam1*I%
+ DOEND
+ DO(11,20,1)
+   F=~ lam2*I%
+ DOEND
+ DO(21,30,1)
+   F=~ lam1*I%
+ DOEND
+ DO(31,40,1)
+   F=~ lam3*I%
+ DOEND
+   F ~~ 1*F
+   "
+# estimate model
+mod3tC <- TAM::tamaan( tammodel, data.sim.rasch)
+summary(mod3tC)
+
+#############################################################################
+# EXAMPLE 2: Unidimensional calibration with latent regressors
+#############################################################################
+
+# (1) simulate data
+set.seed(6778)     # set simulation seed
+N <- 2000          # number of persons
+# latent regressors Y
+Y <- cbind( stats::rnorm( N, sd=1.5), stats::rnorm(N, sd=.3 ) )
+# simulate theta
+theta <- stats::rnorm( N ) + .4 * Y[,1] + .2 * Y[,2]  # latent regression model
+# number of items
+I <- 40
+p1 <- stats::plogis( outer( theta, seq( -2, 2, len=I ), "-" ) )
+# simulate response matrix
+resp <- 1 * ( p1 > matrix( stats::runif( N*I ), nrow=N, ncol=I ) )
+colnames(resp) <- paste("I", 1:I, sep="")
+
+# (2) estimate model
+mod2_1 <- TAM::tam.mml(resp=resp, Y=Y)
+summary(mod2_1)
+
+# (3) setting initial values for beta coefficients
+#   beta_2=.20, beta_3=.35 for dimension 1
+beta.inits <- cbind( c(2,3), 1, c(.2, .35 ) )
+mod2_2 <- TAM::tam.mml(resp=resp, Y=Y, beta.inits=beta.inits)
+
+# (4) fix intercept to zero and third coefficient to .3
+beta.fixed <- cbind( c(1,3), 1, c(0, .3 ) )
+mod2_3 <- TAM::tam.mml(resp=resp, Y=Y, beta.fixed=beta.fixed )
+
+# (5) same model but with R regression formula for Y
+dataY <- data.frame(Y)
+colnames(dataY) <- c("Y1","Y2")
+mod2_4 <- TAM::tam.mml(resp=resp, dataY=dataY, formulaY=~ Y1+Y2 )
+summary(mod2_4)
+
+# (6) model with interaction of regressors
+mod2_5 <- TAM::tam.mml(resp=resp, dataY=dataY, formulaY=~ Y1*Y2 )
+summary(mod2_5)
+
+# (7) no constraint on regressors (removing constraint from intercept)
+mod2_6 <- TAM::tam.mml(resp=resp, Y=Y, beta.fixed=FALSE )
+
+#############################################################################
+# EXAMPLE 3: Multiple group estimation
+#############################################################################
+
+# (1) simulate data
+set.seed(6778)
+N <- 3000
+theta <- c( stats::rnorm(N/2,mean=0,sd=1.5), stats::rnorm(N/2,mean=.5,sd=1)  )
+I <- 20
+p1 <- stats::plogis( outer( theta, seq( -2, 2, len=I ), "-" ) )
+resp <- 1 * ( p1 > matrix( stats::runif( N*I ), nrow=N, ncol=I ) )
+colnames(resp) <- paste("I", 1:I, sep="")
+group <- rep(1:2, each=N/2 )
+
+# (2) estimate model
+mod3_1 <- TAM::tam.mml( resp,  group=group )
+summary(mod3_1)
+
+#############################################################################
+# EXAMPLE 4: Multidimensional estimation
+# with two dimensional theta's - simulate some bivariate data,
+# and regressors
+# 40 items: first 20 items load on dimension 1,
+#           second 20 items load on dimension 2
+#############################################################################
+
+# (1) simulate some data
+set.seed(6778)
+library(mvtnorm)
+N <- 1000
+Y <- cbind( stats::rnorm( N ), stats::rnorm(N) )
+theta <- mvtnorm::rmvnorm( N,mean=c(0,0), sigma=matrix( c(1,.5,.5,1), 2, 2 ))
+theta[,1] <- theta[,1] + .4 * Y[,1] + .2 * Y[,2]  # latent regression model
+theta[,2] <- theta[,2] + .8 * Y[,1] + .5 * Y[,2]  # latent regression model
+I <- 20
+p1 <- stats::plogis( outer( theta[,1], seq( -2, 2, len=I ), "-" ) )
+resp1 <- 1 * ( p1 > matrix( stats::runif( N*I ), nrow=N, ncol=I ) )
+p1 <- stats::plogis( outer( theta[,2], seq( -2, 2, len=I ), "-" ) )
+resp2 <- 1 * ( p1 > matrix( stats::runif( N*I ), nrow=N, ncol=I ) )
+resp <- cbind(resp1,resp2)
+colnames(resp) <- paste("I", 1:(2*I), sep="")
+
+# (2) define loading Matrix
+Q <- array( 0, dim=c( 2*I, 2 ))
+Q[cbind(1:(2*I), c( rep(1,I), rep(2,I) ))] <- 1
+
+# (3) estimate models
+
+#************************************************************
+# Model 4.1: Rasch model: without regressors
+mod4_1 <- TAM::tam.mml( resp=resp, Q=Q )
+
+#--- tamaan specification
+tammodel <- "
+  LAVAAN MODEL:
+    F1=~ 1*I1__I20
+    F2=~ 1*I21__I40
+    # Alternatively to the factor 1 one can use the item type Rasch
+    F1 ~~ F1
+    F2 ~~ F2
+    F1 ~~ F2
+    "
+mod4_1t <- TAM::tamaan( tammodel, resp, control=list(maxiter=100))
+summary(mod4_1t)
+
+#************************************************************
+# Model 4.1b: estimate model with sum constraint of items for each dimension
+mod4_1b <- TAM::tam.mml( resp=resp, Q=Q,constraint="items")
+
+#************************************************************
+# Model 4.2: Rasch model: set covariance between dimensions to zero
+variance_fixed <- cbind( 1, 2, 0 )
+mod4_2 <- TAM::tam.mml( resp=resp, Q=Q, variance.fixed=variance_fixed )
+summary(mod4_2)
+
+#--- tamaan specification
+tammodel <- "
+  LAVAAN MODEL:
+    F1=~ I1__I20
+    F2=~ I21__I40
+    F1 ~~ F1
+    F2 ~~ F2
+    F1 ~~ 0*F2
+  ITEM TYPE:
+    ALL(Rasch)
+    "
+mod4_2t <- TAM::tamaan( tammodel, resp)
+summary(mod4_2t)
+
+#************************************************************
+# Model 4.3: 2PL model
+mod4_3 <- TAM::tam.mml.2pl( resp=resp, Q=Q, irtmodel="2PL" )
+
+#--- tamaan specification
+tammodel <- "
+  LAVAAN MODEL:
+    F1=~ I1__I20
+    F2=~ I21__I40
+    F1 ~~ F1
+    F2 ~~ F2
+    F1 ~~ F2
+    "
+mod4_3t <- TAM::tamaan( tammodel, resp )
+summary(mod4_3t)
+
+#************************************************************
+# Model 4.4: Rasch model with 2000 quasi monte carlo nodes
+# -> nodes are useful for more than 3 or 4 dimensions
+mod4_4 <- TAM::tam.mml( resp=resp, Q=Q, control=list(snodes=2000) )
+
+#************************************************************
+# Model 4.5: Rasch model with 2000 stochastic nodes
+mod4_5 <- TAM::tam.mml( resp=resp, Q=Q,control=list(snodes=2000,QMC=FALSE))
+
+#************************************************************
+# Model 4.6: estimate two dimensional Rasch model with regressors
+mod4_6 <- TAM::tam.mml( resp=resp, Y=Y, Q=Q )
+
+#--- tamaan specification
+tammodel <- "
+  LAVAAN MODEL:
+    F1=~ I1__I20
+    F2=~ I21__I40
+    F1 ~~ F1
+    F2 ~~ F2
+    F1 ~~ F2
+  ITEM TYPE:
+    ALL(Rasch)
+    "
+mod4_6t <- TAM::tamaan( tammodel, resp, Y=Y )
+summary(mod4_6t)
+
+#############################################################################
+# EXAMPLE 5: 2-dimensional estimation with within item dimensionality
+#############################################################################
+library(mvtnorm)
+# (1) simulate data
+set.seed(4762)
+N <- 2000 # 2000 persons
+Y <- stats::rnorm( N )
+theta <- mvtnorm::rmvnorm( N,mean=c(0,0), sigma=matrix( c(1,.5,.5,1), 2, 2 ))
+I <- 10
+# 10 items load on the first dimension
+p1 <- stats::plogis( outer( theta[,1], seq( -2, 2, len=I ), "-" ) )
+resp1 <- 1 * ( p1 > matrix( stats::runif( N*I ), nrow=N, ncol=I ) )
+# 10 items load on the second dimension
+p1 <- stats::plogis( outer( theta[,2], seq( -2, 2, len=I ), "-" ) )
+resp2 <- 1 * ( p1 > matrix( stats::runif( N*I ), nrow=N, ncol=I ) )
+# 20 items load on both dimensions
+p1 <- stats::plogis( outer( 0.5*theta[,1] + 1.5*theta[,2], seq(-2,2,len=2*I ), "-" ))
+resp3 <- 1 * ( p1 > matrix( stats::runif( N*2*I ), nrow=N, ncol=2*I ) )
+#Combine the two sets of items into one response matrix
+resp <- cbind(resp1, resp2, resp3 )
+colnames(resp) <- paste("I", 1:(4*I), sep="")
+
+# (2) define loading matrix
+Q <- cbind(c(rep(1,10),rep(0,10),rep(1,20)), c(rep(0,10),rep(1,10),rep(1,20)))
+
+# (3) model: within item dimensionality and 2PL estimation
+mod5 <- TAM::tam.mml.2pl(resp, Q=Q, irtmodel="2PL" )
+summary(mod5)
+
+# item difficulties
+mod5$item
+# item loadings
+mod5$B
+
+#--- tamaan specification
+tammodel <- "
+  LAVAAN MODEL:
+    F1=~ I1__I10 + I21__I40
+    F2=~ I11__I20 + I21__I40
+    F1 ~~ 1*F1
+    F1 ~~ F2
+    F2 ~~ 1*F2
+    "
+mod5t <- TAM::tamaan( tammodel, resp,  control=list(maxiter=10))
+summary(mod5t)
+
+#############################################################################
+# EXAMPLE 6: ordered data - Generalized partial credit model
+#############################################################################
+data(data.gpcm, package="TAM")
+
+#************************************************************
+# Ex6.1: Nominal response model (irtmodel="2PL")
+mod6_1 <- TAM::tam.mml.2pl( resp=data.gpcm, irtmodel="2PL", control=list(maxiter=200) )
+mod6_1$item # item intercepts
+mod6_1$B    # for every category a separate slope parameter is estimated
+
+# reestimate the model with fixed item parameters
+mod6_1a <- TAM::tam.mml.2pl( resp=data.gpcm, irtmodel="2PL",
+       xsi.fixed=mod6_1$xsi.fixed.estimated,  B.fixed=mod6_1$B.fixed.estimated,
+       est.variance=TRUE )
+
+# estimate the model with initial item parameters from mod6_1
+mod6_1b <- TAM::tam.mml.2pl( resp=data.gpcm, irtmodel="2PL",
+       xsi.inits=mod6_1$xsi.fixed.estimated,  B=mod6_1$B )
+
+#************************************************************
+# Ex6.2: Generalized partial credit model
+mod6_2 <- TAM::tam.mml.2pl( resp=data.gpcm, irtmodel="GPCM", control=list(maxiter=200))
+mod6_2$B[,2,]    # joint slope parameter for all categories
+
+#************************************************************
+# Ex6.3: some fixed entries of slope matrix B
+# B: nitems x maxK x ndim
+#   ( number of items x maximum number of categories x number of dimensions)
+# set two constraints
+B.fixed <- matrix( 0, 2, 4 )
+# set second item, score of 2 (category 3), at first dimension to 2.3
+B.fixed[1,] <- c(2,3,1,2.3)
+# set third item, score of 1 (category 2), at first dimension to 1.4
+B.fixed[2,] <- c(3,2,1,1.4)
+
+# estimate item parameter with variance fixed (by default)
+mod6_3 <- TAM::tam.mml.2pl( resp=data.gpcm, irtmodel="2PL", B.fixed=B.fixed,
+                 control=list( maxiter=200) )
+mod6_3$B
+
+#************************************************************
+# Ex 6.4: estimate the same model, but estimate variance
+mod6_4 <- TAM::tam.mml.2pl( resp=data.gpcm, irtmodel="2PL", B.fixed=B.fixed,
+               est.variance=TRUE, control=list( maxiter=350) )
+mod6_4$B
+
+#************************************************************
+# Ex 6.5: partial credit model
+mod6_5 <- TAM::tam.mml( resp=data.gpcm,control=list( maxiter=200) )
+mod6_5$B
+
+#************************************************************
+# Ex 6.6: partial credit model: Conquest parametrization 'item+item*step'
+mod6_6 <- TAM::tam.mml( resp=data.gpcm, irtmodel="PCM2" )
+summary(mod6_6)
+
+# estimate mod6_6 applying the sum constraint of item difficulties
+# modify design matrix of xsi paramters
+A1 <- TAM::.A.PCM2(resp=data.gpcm )
+A1[3,2:4,"Comfort"] <- 1:3
+A1[3,2:4,"Work"] <- 1:3
+A1 <- A1[,, -3] # remove Benefit xsi item parameter
+# estimate model
+mod6_6b <- TAM::tam.mml( resp=data.gpcm, A=A1, beta.fixed=FALSE )
+summary(mod6_6b)
+
+# estimate model with argument constraint="items"
+mod6_6c <- TAM::tam.mml( resp=data.gpcm, irtmodel="PCM2", constraint="items")
+
+# estimate mod6_6 using tam.mml.mfr
+mod6_6d <- TAM::tam.mml.mfr( resp=data.gpcm, formulaA=~ 0 + item + item:step,
+    control=list(fac.oldxsi=.1), constraint="items" )
+summary(mod6_6d)
+
+#************************************************************
+# Ex 6.7: Rating scale model: Conquest parametrization 'item+step'
+mod6_7 <- TAM::tam.mml( resp=data.gpcm, irtmodel="RSM" )
+summary(mod6_7)
+
+#************************************************************
+# Ex 6.8: sum constraint on item difficulties
+#         partial credit model: ConQuest parametrization 'item+item*step'
+#         polytomous scored TIMMS data
+#         compare to Example 16
+#
+
+data(data.timssAusTwn.scored)
+dat <- data.timssAusTwn.scored[,1:11]
+
+## > tail(sort(names(dat)),1) # constrained item
+## [1] "M032761"
+
+# modify design matrix of xsi paramters
+A1 <- TAM::.A.PCM2( resp=dat )
+# constrained item loads on every other main item parameter
+# with opposing margin it had been loaded on its own main item parameter
+A1["M032761",,setdiff(colnames(dat), "M032761")] <- -A1["M032761",,"M032761"]
+# remove main item parameter for constrained item
+A1 <- A1[,, setdiff(dimnames(A1)[[3]],"M032761")]
+
+# estimate model
+mod6_8a <- TAM::tam.mml( resp=dat, A=A1, beta.fixed=FALSE )
+summary(mod6_8a)
+# extract fixed item parameter for item M032761
+## - sum(mod6_8a$xsi[setdiff(colnames(dat), "M032761"),"xsi"])
+
+# estimate mod6_8a using tam.mml.mfr
+## fixed a bug in 'tam.mml.mfr' for differing number of categories
+## per item -> now a xsi vector with parameter fixings to values
+## of 99 is used
+mod6_8b <- TAM::tam.mml.mfr( resp=dat, formulaA=~ 0 + item + item:step,
+                        control=list(fac.oldxsi=.1), constraint="items" )
+summary(mod6_8b)
+
+#************************************************************
+# Ex 6.9: sum constraint on item difficulties for irtmodel="PCM"
+
+data(data.timssAusTwn.scored)
+dat <- data.timssAusTwn.scored[,2:11]
+dat[ dat==9 ] <- NA
+
+# obtain the design matrix for the PCM parametrization and
+# the number of categories for each item
+maxKi <- apply(dat, 2, max, na.rm=TRUE)
+des <- TAM::designMatrices(resp=dat)
+A1 <- des$A
+
+# define the constrained item category and remove the respective parameter
+(par <- unlist( strsplit(dimnames(A1)[[3]][dim(A1)[3]], split="_") ))
+A1 <- A1[,,-dim(A1)[3]]
+
+# the item category loads on every other item category parameter with
+# opposing margin, balancing the number of categories for each item
+item.id <- which(colnames(dat)==par[1])
+cat.id <- maxKi[par[1]]+1
+loading <- 1/rep(maxKi, maxKi)
+loading <- loading [-which(names(loading)==par[1])[1]]
+A1[item.id, cat.id, ] <- loading
+A1[item.id,,]
+
+# estimate model
+mod6_9 <- TAM::tam.mml( resp=dat, A=A1, beta.fixed=FALSE )
+summary(mod6_9)
+
+## extract fixed item category parameter
+# calculate mean for each item
+ind.item.cat.pars <- sapply(colnames(dat), grep, rownames(mod6_8$xsi))
+item.means <- lapply(ind.item.cat.pars, function(ii) mean(mod6_8$xsi$xsi[ii]))
+
+# these sum up to the negative of the fixed parameter
+fix.par <- -sum( unlist(item.means), na.rm=TRUE)
+
+#************************************************************
+# Ex 6.10: Generalized partial credit model with equality constraints
+#          on item discriminations
+
+data(data.gpcm)
+dat <- data.gpcm
+
+# Ex 6.10a: set all slopes of three items equal to each other
+E <- matrix( 1, nrow=3, ncol=1 )
+mod6_10a <- TAM::tam.mml.2pl( dat, irtmodel="GPCM.design", E=E  )
+summary(mod6_10a)
+mod6_10a$B[,,]
+
+# Ex 6.10b: equal slope for first and third item
+E <- matrix( 0, nrow=3, ncol=2 )
+E[c(1,3),1] <- 1
+E[ 2, 2 ] <- 1
+mod6_10b <- TAM::tam.mml.2pl( dat, irtmodel="GPCM.design", E=E  )
+summary(mod6_10b)
+mod6_10b$B[,,]
+
+#############################################################################
+# EXAMPLE 7: design matrix for slopes for the generalized partial credit model
+#############################################################################
+
+# (1) simulate data from a model with a (item slope) design matrix E
+set.seed(789)
+I <- 42
+b <- seq( -2, 2, len=I)
+# create design matrix for loadings
+E <- matrix( 0, I, 5 )
+E[ seq(1,I,3), 1 ] <- 1
+E[ seq(2,I,3), 2 ] <- 1
+E[ seq(3,I,3), 3 ] <- 1
+ind <- seq( 1, I, 2 ) ; E[ ind, 4 ] <- rep( c( .3, -.2 ), I )[ 1:length(ind) ]
+ind <- seq( 2, I, 4 ) ; E[ ind, 5 ] <- rep( .15, I )[ 1:length(ind) ]
+E
+
+# true basis slope parameters
+lambda <- c( 1, 1.2, 0.8, 1, 1.1 )
+# calculate item slopes
+a <- E %*% lambda
+
+# simulate
+N <- 4000
+theta <- stats::rnorm( N )
+aM <- outer( rep(1,N), a[,1] )
+bM <- outer( rep(1,N), b )
+pM <- stats::plogis( aM * ( matrix( theta, nrow=N, ncol=I  ) - bM ) )
+dat <- 1 * ( pM > stats::runif( N*I ) )
+colnames(dat) <- paste("I", 1:I, sep="")
+
+# estimate model
+mod7 <- TAM::tam.mml.2pl( resp=dat, irtmodel="GPCM.design", E=E )
+mod7$B
+
+# recalculate estimated basis parameters
+stats::lm( mod7$B[,2,1] ~ 0+ as.matrix(E ) )
+  ##   Call:
+  ##   lm(formula=mod7$B[, 2, 1] ~ 0 + as.matrix(E))
+  ##   Coefficients:
+  ##   as.matrix(E)1  as.matrix(E)2  as.matrix(E)3  as.matrix(E)4  as.matrix(E)5
+  ##          0.9904         1.1896         0.7817         0.9601         1.2132
+
+#############################################################################
+# EXAMPLE 8: Differential item functioning                                  #
+#  A first example of a Multifaceted Rasch Model                            #
+#  Facet is only female; 10 items are studied                               #
+#############################################################################
+data(data.ex08)
+
+formulaA <- ~ item+female+item*female
+# this formula is in R equivalent to 'item*female'
+resp <- data.ex08[["resp"]]
+facets <- as.data.frame( data.ex08[["facets"]] )
+
+#***
+# Model 8a: investigate gender DIF on all items
+mod8a <- TAM::tam.mml.mfr( resp=resp, facets=facets, formulaA=formulaA )
+summary(mod8a)
+
+#***
+# Model 8a 2: specification with long format response data
+resp.long <- c( data.ex08[["resp"]] )
+pid <- rep( 1:nrow(data.ex08[["resp"]]), ncol(data.ex08[["resp"]]) )
+
+itemnames <- rep(colnames(data.ex08[["resp"]]), each=nrow(data.ex08[["resp"]]))
+facets.long <- cbind( data.frame( "item"=itemnames ),
+                 data.ex08[["facets"]][pid,,drop=F] )
+
+mod8a_2 <- TAM::tam.mml.mfr( resp=resp.long, facets=facets.long,
+                      formulaA=formulaA, pid=pid)
+stopifnot( all(mod8a$xsi.facets$xsi==mod8a_2$xsi.facets$xsi) )
+
+#***
+# Model 8b: Differential bundle functioning (DBF)
+#   - investigate differential item functioning in item groups
+
+# modify pre-specified design matrix to define 'appropriate' DBF effects
+formulaA <- ~ item*female
+des <- TAM::designMatrices.mfr( resp=resp, facets=facets, formulaA=formulaA)
+A1 <- des$A$A.3d
+# item group A: items 1-5
+# item group B: items 6-8
+# item group C: items 9-10
+A1 <- A1[,,1:13]
+dimnames(A1)[[3]][ c(12,13) ] <- c("A:female1", "B:female1")
+# item group A
+A1[,2,12] <- 0
+A1[c(1,5,7,9,11),2,12] <- -1
+A1[c(1,5,7,9,11)+1,2,12] <- 1
+# item group B
+A1[,2,13] <- 0
+A1[c(13,15,17),2,13] <- -1
+A1[c(13,15,17)+1,2,13] <- 1
+# item group C (define effect(A)+effect(B)+effect(C)=0)
+A1[c(19,3),2,c(12,13)] <- 1
+A1[c(19,3)+1,2,c(12,13)] <- -1
+#   A1[,2,]   # look at modified design matrix
+# estimate model
+mod8b <- TAM::tam.mml( resp=des$gresp$gresp.noStep, A=A1 )
+summary(mod8b)
+
+#############################################################################
+# EXAMPLE 9: Multifaceted Rasch Model
+#############################################################################
+
+data(data.sim.mfr)
+data(data.sim.facets)
+
+# two way interaction item and rater
+formulaA <- ~item+item:step + item*rater
+mod9a <- TAM::tam.mml.mfr( resp=data.sim.mfr, facets=data.sim.facets, formulaA=formulaA)
+mod9a$xsi.facets
+summary(mod9a)
+
+# three way interaction item, female and rater
+formulaA <- ~item+item:step + female*rater + female*item*step
+mod9b <- TAM::tam.mml.mfr( resp=data.sim.mfr, facets=data.sim.facets, formulaA=formulaA)
+summary(mod9b)
+
+#############################################################################
+# EXAMPLE 10: Model with raters.
+#   Persons are arranged in multiple rows which is indicated
+#   by multiple person identifiers.
+#############################################################################
+data(data.ex10)
+dat <- data.ex10
+head(dat)
+  ##     pid rater I0001 I0002 I0003 I0004 I0005
+  ## 1     1     1     0     1     1     0     0
+  ## 451   1     2     1     1     1     1     0
+  ## 901   1     3     1     1     1     0     1
+  ## 452   2     2     1     1     1     0     1
+  ## 902   2     3     1     1     0     1     1
+
+facets <- dat[, "rater", drop=FALSE ] # define facet (rater)
+pid <- dat$pid      # define person identifier (a person occurs multiple times)
+resp <- dat[, -c(1:2) ]        # item response data
+formulaA <- ~ item * rater      # formula
+
+mod10 <- TAM::tam.mml.mfr( resp=resp, facets=facets, formulaA=formulaA, pid=dat$pid )
+summary(mod10)
+
+# estimate person parameter with WLE
+wmod10 <- TAM::tam.wle( mod10 )
+
+#--- Example 10a
+# compare model containing only item
+formulaA <- ~ item + rater      # pseudo formula for item
+xsi.setnull <- "rater"          # set all rater effects to zero
+mod10a <- TAM::tam.mml.mfr( resp=resp, facets=facets, formulaA=formulaA,
+            xsi.setnull=xsi.setnull, pid=dat$pid, beta.fixed=cbind(1,1,0))
+summary(mod10a)
+
+# A shorter way for specifying this example is
+formulaA <- ~ item + 0*rater        # set all rater effects to zero
+mod10a1 <- TAM::tam.mml.mfr( resp=resp, facets=facets, formulaA=formulaA, pid=dat$pid )
+summary(mod10a1)
+
+# tam.mml.mfr also appropriately extends the facets data frame with pseudo facets
+# if necessary
+formulaA <- ~ item     # omitting the rater term
+mod10a2 <- TAM::tam.mml.mfr( resp=resp, facets=facets, formulaA=formulaA, pid=dat$pid )
+  ##   Item Parameters Xsi
+  ##              xsi se.xsi
+  ##   I0001   -1.931  0.111
+  ##   I0002   -1.023  0.095
+  ##   I0003   -0.089  0.089
+  ##   I0004    1.015  0.094
+  ##   I0005    1.918  0.110
+  ##   psfPF11  0.000  0.000
+  ##   psfPF12  0.000  0.000
+
+#***
+# Model 10_2: specification with long format response data
+resp.long <- c(unlist( dat[, -c(1:2) ] ))
+
+pid <- rep( dat$pid, ncol(dat[, -c(1:2) ]) )
+itemnames <- rep(colnames(dat[, -c(1:2) ]), each=nrow(dat[, -c(1:2) ]))
+
+# quick note: the 'trick' to use pid as the row index of the facet  (cf., used in Ex 8a_2)
+# is not working here, since pid already occures multiple times in the original response data
+facets <- cbind( data.frame("item"=itemnames),
+                 dat[ rep(1:nrow(dat), ncol(dat[,-c(1:2)])), "rater",drop=F]
+)
+
+mod10_2 <- TAM::tam.mml.mfr( resp=resp.long, facets=facets, formulaA=formulaA, pid=pid)
+
+stopifnot( all(mod10$xsi.facets$xsi==mod10_2$xsi.facets$xsi) )
+
+#############################################################################
+# EXAMPLE 11: Dichotomous data with missing and omitted responses
+#############################################################################
+data(data.ex11) ; dat <- data.ex11
+
+#***
+# Model 11a: Calibration (item parameter estimating) in which omitted
+#            responses (code 9) are set to missing
+dat1 <- dat[,-1]
+dat1[ dat1==9 ] <- NA
+# estimate Rasch model
+mod11a <- TAM::tam.mml( resp=dat1 )
+summary(mod11a)
+# compute person parameters
+wmod11a <- TAM::tam.wle( mod11a )
+
+#***
+# Model 11b: Scaling persons (WLE estimation) setting omitted
+#            responses as incorrect and using fixed
+#            item parameters form Model 11a
+
+# set matrix with fixed item difficulties as the input
+xsi1 <- mod11a$xsi    # xsi output from Model 11a
+xsi.fixed <- cbind( seq(1,nrow(xsi1) ), xsi1$xsi )
+# recode 9 to 0
+dat2 <- dat[,-1]
+dat2[ dat2==9 ] <- 0
+# run Rasch model with fixed item difficulties
+mod11b <- TAM::tam.mml( resp=dat2, xsi.fixed=xsi.fixed )
+summary(mod11b)
+# WLE estimation
+wmod11b <- TAM::tam.wle( mod11b )
+
+#############################################################################
+# EXAMPLE 12: Avoiding nonconvergence using the argument increment.factor
+#############################################################################
+data(data.ex12)
+dat <- data.ex12
+
+# non-convergence without increment.factor
+mod1 <- TAM::tam.mml.2pl( resp=data.ex12, control=list( maxiter=1000) )
+
+# avoiding non-convergence with increment.factor=1.02
+mod2 <- TAM::tam.mml.2pl( resp=data.ex12,
+            control=list( maxiter=1000, increment.factor=1.02) )
+summary(mod1)
+summary(mod2)
+
+#############################################################################
+# EXAMPLE 13: Longitudinal data 'data.long' from sirt package
+#############################################################################
+library(sirt)
+data(data.long, package="sirt")
+dat <- data.long
+  ##   > colnames(dat)
+  ##    [1] "idstud" "I1T1"   "I2T1"   "I3T1"   "I4T1"   "I5T1"   "I6T1"
+  ##    [8] "I3T2"   "I4T2"   "I5T2"   "I6T2"   "I7T2"   "I8T2"
+
+## item 1 to 6 administered at T1 and items 3 to 8 at T2
+## items 3 to 6 are anchor items
+
+#***
+# Model 13a: 2-dimensional Rasch model assuming invariant item difficulties
+
+# define matrix loadings
+Q <- matrix(0,12,2)
+colnames(Q) <- c("T1","T2")
+Q[1:6,1] <- 1       # items at T1
+Q[7:12,2] <- 1      # items at T2
+
+# assume equal item difficulty of I3T1 and I3T2, I4T1 and I4T2, ...
+# create draft design matrix and modify it
+A <- TAM::designMatrices(resp=data.long[,-1])$A
+dimnames(A)[[1]] <- colnames(data.long)[-1]
+  ##   > str(A)
+  ##    num [1:12, 1:2, 1:12] 0 0 0 0 0 0 0 0 0 0 ...
+  ##    - attr(*, "dimnames")=List of 3
+  ##     ..$ : chr [1:12] "Item01" "Item02" "Item03" "Item04" ...
+  ##     ..$ : chr [1:2] "Category0" "Category1"
+  ##     ..$ : chr [1:12] "I1T1" "I2T1" "I3T1" "I4T1" ...
+A1 <- A[,, c(1:6, 11:12 ) ]
+dimnames(A1)[[3]] <- substring( dimnames(A1)[[3]],1,2)
+A1[7,2,3] <- -1     # difficulty(I3T1)=difficulty(I3T2)
+A1[8,2,4] <- -1     # I4T1=I4T2
+A1[9,2,5] <- A1[10,2,6] <- -1
+  ##   > A1[,2,]
+  ##        I1 I2 I3 I4 I5 I6 I7 I8
+  ##   I1T1 -1  0  0  0  0  0  0  0
+  ##   I2T1  0 -1  0  0  0  0  0  0
+  ##   I3T1  0  0 -1  0  0  0  0  0
+  ##   I4T1  0  0  0 -1  0  0  0  0
+  ##   I5T1  0  0  0  0 -1  0  0  0
+  ##   I6T1  0  0  0  0  0 -1  0  0
+  ##   I3T2  0  0 -1  0  0  0  0  0
+  ##   I4T2  0  0  0 -1  0  0  0  0
+  ##   I5T2  0  0  0  0 -1  0  0  0
+  ##   I6T2  0  0  0  0  0 -1  0  0
+  ##   I7T2  0  0  0  0  0  0 -1  0
+  ##   I8T2  0  0  0  0  0  0  0 -1
+
+# estimate model
+# set intercept of second dimension (T2) to zero
+beta.fixed <- cbind( 1, 2, 0 )
+mod13a <- TAM::tam.mml( resp=data.long[,-1], Q=Q, A=A1, beta.fixed=beta.fixed)
+summary(mod13a)
+
+#--- tamaan specification
+tammodel <- "
+  LAVAAN MODEL:
+    T1=~ 1*I1T1__I6T1
+    T2=~ 1*I3T2__I8T2
+    T1 ~~ T1
+    T2 ~~ T2
+    T1 ~~ T2
+    # constraint on item difficulties
+    I3T1 + I3T2 | b3*t1
+    I4T1 + I4T2 | b4*t1
+    I5T1 + I5T2 | b5*t1
+    I6T1 + I6T2 | b6*t1
+    "
+# The constraint on item difficulties can be more efficiently written as
+  ##       DO(3,6,1)
+  ##         I%T1 + I%T2 | b%*t1
+  ##       DOEND
+# estimate model
+mod13at <- TAM::tamaan( tammodel, resp=data.long,  beta.fixed=beta.fixed )
+summary(mod13at)
+
+#***
+# Model 13b: invariant item difficulties with zero mean item difficulty
+#           of anchor items
+
+A <- TAM::designMatrices(resp=data.long[,-1])$A
+dimnames(A)[[1]] <- colnames(data.long)[-1]
+A1 <- A[,, c(1:5, 11:12 ) ]
+dimnames(A1)[[3]] <- substring( dimnames(A1)[[3]],1,2)
+A1[7,2,3] <- -1     # difficulty(I3T1)=difficulty(I3T2)
+A1[8,2,4] <- -1     # I4T1=I4T2
+A1[9,2,5] <- -1
+A1[6,2,3] <- A1[6,2,4] <- A1[6,2,5] <- 1     # I6T1=-(I3T1+I4T1+I5T1)
+A1[10,2,3] <- A1[10,2,4] <- A1[10,2,5] <- 1  # I6T2=-(I3T2+I4T2+I5T2)
+A1[,2,]
+  ##      I1 I2 I3 I4 I5 I7 I8
+  ## I1T1 -1  0  0  0  0  0  0
+  ## I2T1  0 -1  0  0  0  0  0
+  ## I3T1  0  0 -1  0  0  0  0
+  ## I4T1  0  0  0 -1  0  0  0
+  ## I5T1  0  0  0  0 -1  0  0
+  ## I6T1  0  0  1  1  1  0  0
+  ## I3T2  0  0 -1  0  0  0  0
+  ## I4T2  0  0  0 -1  0  0  0
+  ## I5T2  0  0  0  0 -1  0  0
+  ## I6T2  0  0  1  1  1  0  0
+  ## I7T2  0  0  0  0  0 -1  0
+  ## I8T2  0  0  0  0  0  0 -1
+
+mod13b <- TAM::tam.mml( resp=data.long[,-1], Q=Q, A=A1, beta.fixed=FALSE)
+summary(mod13b)
+
+#***
+# Model 13c: longitudinal polytomous data
+#
+
+# modifiy Items I1T1, I4T1, I4T2 in order to be trichotomous (codes: 0,1,2)
+set.seed(42)
+dat <- data.long
+dat[(1:50),2] <- sample(c(0,1,2), 50, replace=TRUE)
+dat[(1:50),5] <- sample(c(0,1,2), 50, replace=TRUE)
+dat[(1:50),9] <- sample(c(0,1,2), 50, replace=TRUE)
+  ##   > colnames(dat)
+  ##    [1] "idstud" "I1T1"   "I2T1"   "I3T1"   "I4T1"   "I5T1"   "I6T1"
+  ##    [8] "I3T2"   "I4T2"   "I5T2"   "I6T2"   "I7T2"   "I8T2"
+
+## item 1 to 6 administered at T1, items 3 to 8 at T2
+## items 3 to 6 are anchor items
+
+# (1) define matrix loadings
+Q <- matrix(0,12,2)
+colnames(Q) <- c("T1","T2")
+Q[1:6,1] <- 1       # items at T1
+Q[7:12,2] <- 1      # items at T2
+
+# (2) assume equal item difficulty of anchor items
+#     create draft design matrix and modify it
+A <- TAM::designMatrices(resp=dat[,-1])$A
+dimnames(A)[[1]] <- colnames(dat)[-1]
+  ## > str(A)
+  ## num [1:12, 1:3, 1:15] 0 0 0 0 0 0 0 0 0 0 ...
+  ## - attr(*, "dimnames")=List of 3
+  ## ..$ : chr [1:12] "I1T1" "I2T1" "I3T1" "I4T1" ...
+  ## ..$ : chr [1:3] "Category0" "Category1" "Category2"
+  ## ..$ : chr [1:15] "I1T1_Cat1" "I1T1_Cat2" "I2T1_Cat1" "I3T1_Cat1" ...
+
+# define matrix A
+# Items 1 to 3 administered at T1, Items 3 to 6 are anchor items
+# Item 7 to 8 administered at T2
+# Item I1T1, I4T1, I4T2 are trichotomous (codes: 0,1,2)
+A1 <- A[,, c(1:8, 14:15) ]
+dimnames(A1)[[3]] <- gsub("T1|T2", "",  dimnames(A1)[[3]])
+
+# Modifications are shortened compared to Model 13 a, but are still valid
+A1[7,,] <- A1[3,,]  # item 7, i.e. I3T2, loads on same parameters as
+                    # item 3, I3T1
+A1[8,,] <- A1[4,,]  # same for item 8 and item 4
+A1[9,,] <- A1[5,,]  # same for item 9 and item 5
+A1[10,,] <- A1[6,,] # same for item 10 and item 6
+  ## > A1[8,,]
+  ##           I1_Cat1 I1_Cat2 I2_Cat1 I3_Cat1 I4_Cat1 I4_Cat2 I5_Cat1 ...
+  ## Category0       0       0       0       0       0       0       0
+  ## Category1       0       0       0       0      -1       0       0
+  ## Category2       0       0       0       0      -1      -1       0
+
+# (3) estimate model
+#     set intercept of second dimension (T2) to zero
+beta.fixed <- cbind( 1, 2, 0 )
+mod13c <- TAM::tam.mml( resp=dat[,-1], Q=Q, A=A1, beta.fixed=beta.fixed,
+                   irtmodel="PCM")
+summary(mod13c)
+wle.mod13c <- TAM::tam.wle(mod13c) # WLEs of dimension T1 and T2
+
+#############################################################################
+# EXAMPLE 14: Facet model with latent regression
+#############################################################################
+data( data.ex14 )
+dat <- data.ex14
+
+#***
+# Model 14a: facet model
+resp <- dat[, paste0("crit",1:7,sep="") ]    # item data
+facets <- data.frame( "rater"=dat$rater )     # define facets
+formulaA <- ~item+item*step + rater
+mod14a <- TAM::tam.mml.mfr( resp, facets=facets, formulaA=formulaA, pid=dat$pid )
+summary(mod14a)
+
+#***
+# Model 14b: facet model with latent regression
+#   Note that dataY must correspond to rows in resp and facets which means
+#   that there must be the same rows in Y for a person with multiple rows
+#   in resp
+dataY <- dat[, c("X1","X2") ]        # latent regressors
+formulaY <- ~ X1+X2            # latent regression formula
+mod14b <- TAM::tam.mml.mfr( resp, facets=facets, formulaA=formulaA,
+            dataY=dataY, formulaY=formulaY, pid=dat$pid)
+summary(mod14b)
+
+#***
+# Model 14c: Multi-facet model with item slope estimation
+# use design matrix and modified response data from Model 1
+# item-specific slopes
+
+resp1 <- mod14a$resp      # extract response data with generalized items
+A <- mod14a$A             # extract design matrix for item intercepts
+colnames(resp1)
+
+# define design matrix for slopes
+E <- matrix( 0, nrow=ncol(resp1), ncol=7 )
+colnames(E) <- paste0("crit",1:7)
+rownames(E) <- colnames(resp1)
+E[ cbind( 1:(7*7), rep(1:7,each=7) ) ] <- 1
+
+mod14c <- TAM::tam.mml.2pl( resp=resp1, A=A, irtmodel="GPCM.design", E=E,
+        control=list(maxiter=100) )
+summary(mod14c)
+
+#############################################################################
+# EXAMPLE 15: Coping with nonconvergent models
+#############################################################################
+
+data(data.ex15)
+data <- data.ex15
+# facet model 'group*item' is of interest
+
+#***
+# Model 15a:
+mod15a <- TAM::tam.mml.mfr(resp=data[,-c(1:2)],facets=data[,"group",drop=FALSE],
+    formulaA=~ item + group*item, pid=data$pid )
+# See output:
+  ##
+  ##   Iteration 47     2013-09-10 16:51:39
+  ##   E Step
+  ##   M Step Intercepts   |----
+  ##     Deviance=75510.2868 | Deviance change: -595.0609
+  ##   !!! Deviance increases!                                        !!!!
+  ##   !!! Choose maybe fac.oldxsi > 0 and/or increment.factor > 1    !!!!
+  ##     Maximum intercept parameter change: 0.925045
+  ##     Maximum regression parameter change: 0
+  ##     Variance:  0.9796  | Maximum change: 0.009226
+
+#***
+# Model 15b: Follow the suggestions of changing the default of fac.oldxsi and
+#            increment.factor
+mod15b <- TAM::tam.mml.mfr(resp=data[,-c(1:2)],facets=data[,"group",drop=FALSE],
+            formulaA=~ group*item, pid=data$pid,
+            control=list( increment.factor=1.03, fac.oldxsi=.4 ) )
+
+#***
+# Model 15c: Alternatively, just choose more iterations in M-step by "Msteps=10"
+mod15c <- TAM::tam.mml.mfr(resp=data[,-c(1:2)],facets=data[,"group",drop=FALSE],
+    formulaA=~ item + group*item, pid=data$pid,
+    control=list(maxiter=250, Msteps=10))
+
+#############################################################################
+# EXAMPLE 16: Differential item function for polytomous items and
+#             differing number of response options per item
+#############################################################################
+
+data(data.timssAusTwn.scored)
+dat <- data.timssAusTwn.scored
+# extract item response data
+resp <- dat[, sort(grep("M", colnames(data.timssAusTwn.scored), value=TRUE)) ]
+# some descriptives
+psych::describe(resp)
+# define facets: 'cnt' is group identifier
+facets <- data.frame( "cnt"=dat$IDCNTRY)
+# create design matrices
+des2 <- TAM::designMatrices.mfr2( resp=resp, facets=facets,
+                   formulaA=~item*step + item*cnt)
+# restructured data set: pseudoitem=item x country
+resp2 <- des2$gresp$gresp.noStep
+# A design matrix
+A <- des2$A$A.3d
+    # redundant xsi parameters must be eliminated from design matrix
+xsi.elim <- des2$xsi.elim
+A <- A[,, - xsi.elim[,2] ]
+# extract loading matrix B
+B <- des2$B$B.3d
+# estimate model
+mod1 <- TAM::tam.mml( resp=resp2, A=A, B=B, control=list(maxiter=100) )
+summary(mod1)
+# The sum of all DIF parameters is set to zero. The DIF parameter for the last
+# item is therefore obtained
+xsi1 <- mod1$xsi
+difxsi <- xsi1[ intersect( grep("cnt",rownames(xsi1)),
+              grep("M03",rownames(xsi1))), ]   - colSums(difxsi)
+    # this is the DIF effect of the remaining item
+
+#############################################################################
+# EXAMPLE 17: Several multidimensional and subdimension models
+#############################################################################
+
+library(mirt)
+#*** (1) simulate data in mirt package
+set.seed(9897)
+# simulate data according to the four-dimensional Rasch model
+# variances
+variances <- c( 1.45, 1.74, .86, 1.48  )
+# correlations
+corrs <- matrix( 1, 4, 4 )
+dd1 <- 1 ; dd2 <- 2 ; corrs[dd1,dd2] <- corrs[dd2,dd1] <- .88
+dd1 <- 1 ; dd2 <- 3 ; corrs[dd1,dd2] <- corrs[dd2,dd1] <- .85
+dd1 <- 1 ; dd2 <- 4 ; corrs[dd1,dd2] <- corrs[dd2,dd1] <- .87
+dd1 <- 2 ; dd2 <- 3 ; corrs[dd1,dd2] <- corrs[dd2,dd1] <- .84
+dd1 <- 2 ; dd2 <- 4 ; corrs[dd1,dd2] <- corrs[dd2,dd1] <- .90
+dd1 <- 3 ; dd2 <- 4 ; corrs[dd1,dd2] <- corrs[dd2,dd1] <- .90
+# covariance matrix
+covar <- outer( sqrt( variances), sqrt(variances) )*corrs
+# item thresholds and item discriminations
+d <- matrix( stats::runif(40, -2, 2 ), ncol=1 )
+a <- matrix(NA, nrow=40,ncol=4)
+a[1:10,1] <- a[11:20,2] <- a[21:30,3] <- a[31:40,4] <- 1
+# simulate data
+dat <- mirt::simdata(a=a, d=d, N=1000, itemtype="dich", sigma=covar )
+# define Q-matrix for testlet and subdimension models estimated below
+Q <- matrix( 0, nrow=40, ncol=5 )
+colnames(Q) <- c("g", paste0( "subd", 1:4) )
+Q[,1] <- 1
+Q[1:10,2] <- Q[11:20,3] <- Q[21:30,4] <- Q[31:40,5] <- 1
+
+# define maximum number of iterations and number of quasi monte carlo nodes
+# maxit <- 5  ; snodes <- 300    # this specification is only for speed reasons
+maxit <- 200 ; snodes <- 1500
+
+#*****************
+# Model 1: Rasch testlet model
+#*****************
+
+# define a user function for restricting the variance according to the
+# Rasch testlet model
+variance.fct1 <- function( variance ){
+            ndim <- ncol(variance)
+            variance.new <- matrix( 0, ndim, ndim )
+            diag(variance.new) <- diag(variance)
+            variance <- variance.new
+            return(variance)
+                    }
+variance.Npars <- 5    # number of estimated parameters in variance matrix
+# estimation using tam.mml
+mod1 <- TAM::tam.mml( dat, Q=Q, userfct.variance=variance.fct1,
+             variance.Npars=variance.Npars, control=list(maxiter=maxit, QMC=TRUE,
+                          snodes=snodes))
+summary(mod1)
+
+#*****************
+# Model 2: Testlet model with correlated testlet effects
+#*****************
+
+# specify a testlet model with general factor g and testlet effects
+# u_1,u_2,u_3 and u_4. Assume that Cov(g,u_t)=0 for all t=1,2,3,4.
+# Additionally, assume that \sum_t,t' Cov( u_t, u_t')=0, i.e.
+# the sum of all testlet covariances is equal to zero
+#=> testlet effects are uncorrelated on average.
+
+# set Cov(g,u_t)=0 and sum of all testlet covariances equals to zero
+variance.fct2 <- function( variance ){
+            ndim <- ncol(variance)
+            variance.new <- matrix( 0, ndim, ndim )
+            diag(variance.new) <- diag(variance)
+            variance.new[1,2:ndim] <- variance.new[2:ndim,1] <- 0
+            # calculate average covariance between testlets
+            v1 <- variance[ -1, -1] - variance.new[-1,-1]
+            M1 <- sum(v1) / ( ( ndim-1)^2 - ( ndim - 1))
+            v1 <- v1 - M1
+            variance.new[ -1, -1 ] <- v1
+            diag(variance.new) <- diag(variance)
+            variance <- variance.new
+            return(variance)
+                    }
+variance.Npars <- 1 + 4 + (4*3)/2 - 1
+# estimate model in TAM
+mod2 <- TAM::tam.mml( dat, Q=Q, userfct.variance=variance.fct2,
+                variance.Npars=variance.Npars,
+                control=list(maxiter=maxit, QMC=TRUE, snodes=snodes) )
+summary(mod2)
+
+#*****************
+# Model 3: Testlet model with correlated testlet effects (different identification)
+#*****************
+
+# Testlet model like in Model 2. But now the constraint is
+# \sum _t,t' Cov(u_t, u_t') + \sum_t Var(u_t)=0, i.e.
+# the sum of all testlet covariances and variances is equal to zero.
+variance.fct3 <- function( variance ){
+            ndim <- ncol(variance)
+            variance.new <- matrix( 0, ndim, ndim )
+            diag(variance.new) <- diag(variance)
+            variance.new[1,2:ndim] <- variance.new[2:ndim,1] <- 0
+            # calculate average covariance and variance between testlets
+            v1 <- variance[ -1, -1]
+            M1 <- mean(v1)
+            v1 <- v1 - M1
+            variance.new[ -1, -1 ] <- v1
+            # ensure positive definiteness of covariance matrix
+            eps <- 10^(-2)
+            diag(variance.new) <- diag( variance.new) + eps
+            variance.new <- psych::cor.smooth( variance.new )  # smoothing in psych
+            variance <- variance.new
+            return(variance)
+                    }
+variance.Npars <- 1 + 4 + (4*3)/2 - 1
+# estimate model in TAM
+mod3 <- TAM::tam.mml( dat, Q=Q, userfct.variance=variance.fct3,
+                variance.Npars=variance.Npars,
+                control=list(maxiter=maxit, QMC=TRUE, snodes=snodes) )
+summary(mod3)
+
+#*****************
+# Model 4: Rasch subdimension model
+#*****************
+
+# The Rasch subdimension model is specified according to Brandt (2008).
+# The fourth testlet effect is defined as u4=- (u1+u2+u3)
+# specify an alternative Q-matrix with 4 dimensions
+Q2 <- Q[,-5]
+Q2[31:40,2:4] <- -1
+
+# set Cov(g,u1)=Cov(g,u2)=Cov(g,u3)=0
+variance.fixed <- rbind( c(1,2,0), c(1,3,0), c(1,4,0) )
+# estimate model in TAM
+mod4 <- TAM::tam.mml( dat, Q=Q2,variance.fixed=variance.fixed,
+                control=list(maxiter=maxit, QMC=TRUE, snodes=snodes) )
+summary(mod4)
+
+#*****************
+# Model 5: Higher-order model
+#*****************
+
+# A four-dimensional model with a higher-order factor is specified.
+# F_t=a_t g + eps_g
+Q3 <- Q[,-1]
+# define fitting function using the lavaan package and ULS estimation
+N0 <- nrow(dat)         # sample size of dataset
+library(lavaan)        # requires lavaan package for fitting covariance
+variance.fct5 <- function( variance ){
+    ndim <- ncol(variance)
+    rownames(variance) <- colnames(variance) <- paste0("F",1:ndim)
+    lavmodel <- paste0(
+        "FHO=~", paste0( paste0( "F", 1:ndim ), collapse="+" ) )
+    lavres <- lavaan::cfa( model=lavmodel, sample.cov=variance, estimator="ULS",
+                       std.lv=TRUE, sample.nobs=N0)
+    variance.new <- fitted(lavres)$cov
+    variance <- variance.new
+    # print coefficients
+    cat( paste0( "\n **** Higher order loadings: ",
+            paste0( paste0( round( coef(lavres)[ 1:ndim ], 3 )), collapse=" ")
+                        ), "\n")
+    return(variance)
+                    }
+variance.Npars <- 4+4
+# estimate model in TAM
+mod5 <- TAM::tam.mml( dat, Q=Q3, userfct.variance=variance.fct5,
+                variance.Npars=variance.Npars,
+                control=list(maxiter=maxit, QMC=TRUE, snodes=snodes) )
+summary(mod5)
+
+#*****************
+# Model 6: Generalized Rasch subdimension model (Brandt, 2012)
+#*****************
+
+Q2 <- Q[,-5]
+Q2[31:40,2:4] <- -1
+# fixed covariances
+variance.fixed2 <- rbind( c(1,2,0), c(1,3,0), c(1,4,0)  )
+# design matrix for item loading parameters
+#      items x category x dimension x xsi parameter
+E <- array( 0, dim=c( 40, 2, 4, 4 ) )
+E[ 1:10, 2, c(1,2), 1 ] <- 1
+E[ 11:20, 2, c(1,3), 2 ] <- 1
+E[ 21:30, 2, c(1,4), 3 ] <- 1
+E[ 31:40, 2, 1, 4 ] <- 1
+E[ 31:40, 2, 2:4, 4 ] <- -1
+
+# constraint on slope parameters, see Brandt (2012)
+gammaconstr <- function( gammaslope ){
+        K <- length( gammaslope)
+        g1 <- sum( gammaslope^2  )
+        gammaslope.new <- sqrt(K) / sqrt(g1) * gammaslope
+        return(gammaslope.new)
+                    }
+# estimate model
+mod6 <- TAM::tam.mml.3pl( dat, E=E, Q=Q2, variance.fixed=variance.fixed2,
+           skillspace="normal", userfct.gammaslope=gammaconstr, gammaslope.constr.Npars=1,
+           control=list(maxiter=maxit, QMC=TRUE, snodes=snodes ) )
+summary(mod6)
+
+#############################################################################
+# EXAMPLE 18: Partial credit model with dimension-specific sum constraints
+#             on item difficulties
+#############################################################################
+
+data(data.Students, package="CDM")
+dat <- data.Students[, c( paste0("sc",1:4), paste0("mj",1:4) ) ]
+# specify dimensions in Q-matrix
+Q <- matrix( 0,  nrow=8, ncol=2 )
+Q[1:4,1] <- Q[5:8,2] <- 1
+# partial credit model with some constraint on item parameters
+mod1 <- TAM::tam.mml( dat, Q=Q, irtmodel="PCM2", constraint="items")
+summary(mod1)
+
+#############################################################################
+# EXAMPLE 19: Partial credit scoring: 0.5 points for partial credit items
+#             and 1 point for dichotomous items
+#############################################################################
+
+data(data.timssAusTwn.scored)
+dat <- data.timssAusTwn.scored
+# extrcat item response data
+dat <- dat[, grep("M03", colnames(dat) ) ]
+
+# select items with do have maximum score of 2 (polytomous items)
+ind <- which( apply( dat,  2, max, na.rm=TRUE )==2 )
+I <- ncol(dat)
+# define Q-matrix with scoring variant
+Q <- matrix( 1, nrow=I, ncol=1 )
+Q[ ind, 1 ] <- .5    # score of 0.5 for polyomous items
+
+# estimate model
+mod1 <- TAM::tam.mml( dat, Q=Q, irtmodel="PCM2", control=list(nodes=seq(-10,10,len=21)))
+summary(mod1)
+
+#############################################################################
+# EXAMPLE 20: Specification of loading matrix in multidimensional model
+#############################################################################
+
+data(data.gpcm)
+psych::describe(data.gpcm)
+resp <- data.gpcm
+
+# define three dimensions and different loadings of item categories
+# on these dimensions in B loading matrix
+I <- 3  # 3 items
+D <- 3  # 3 dimensions
+# define loading matrix B
+# 4 categories for each item (0,1,2,3)
+B <- array( 0, dim=c(I,4,D) )
+for (ii in 1:I){
+    B[ ii, 1:4, 1 ] <- 0:3
+    B[ ii, 1,2 ] <- 1
+    B[ ii, 4,3 ] <- 1
+            }
+dimnames(B)[[1]] <- colnames(resp)
+B[1,,]
+  ##   > B[1,,]
+  ##        [,1] [,2] [,3]
+  ##   [1,]    0    1    0
+  ##   [2,]    1    0    0
+  ##   [3,]    2    0    0
+  ##   [4,]    3    0    1
+#-- test run
+mod1 <- TAM::tam.mml( resp, B=B, control=list( snodes=1000, maxiter=5)  )
+summary(mod1)
+
+# Same model with TAM::tam.mml.3pl instead
+
+dim4 <- sum(apply(B, c(1, 3), function(x) any(!(x==0))))
+E1 <- array(0, dim=c(dim(B), dim4))
+
+kkk <- 0
+for (iii in seq_len(dim(E1)[1])) {
+    for (jjj in seq_len(dim(E1)[3])) {
+        if (any(B[iii,, jjj] !=0)) {
+            kkk <- kkk + 1
+            E1[iii,, jjj, kkk] <- B[iii,, jjj]
+        }
+    }
+}
+if (kkk !=dim4) stop("Something went wrong in the loop, because 'kkk !=dim4'.")
+
+mod2 <- TAM::tam.mml.3pl(resp, E=E1, est.some.slopes=FALSE, control=list(maxiter=50))
+summary(mod2)
+
+cor(mod1$person$EAP.Dim3, mod2$person$EAP.Dim3)
+cor(mod1$person$EAP.Dim2, mod2$person$EAP.Dim2)
+cor(mod1$person$EAP.Dim1, mod2$person$EAP.Dim1)
+cor(mod1$xsi$xsi, mod2$xsi$xsi)
+
+#############################################################################
+# EXAMPLE 21: Acceleration of EM algorithm | dichotomous data
+#############################################################################
+
+N <- 1000      # number of persons
+I <- 100       # number of items
+set.seed(987)
+# simulate data according to the Rasch model
+dat <- sirt::sim.raschtype( stats::rnorm(N), b=seq(-2,2,len=I)  )
+# estimate models
+mod1n <- TAM::tam.mml( resp=dat, control=list( acceleration="none") )  # no acceler.
+mod1y <- TAM::tam.mml( resp=dat, control=list( acceleration="Yu") )  # Yu acceler.
+mod1r <- TAM::tam.mml( resp=dat, control=list( acceleration="Ramsay") )  # Ramsay acceler.
+# compare number of iterations
+mod1n$iter ; mod1y$iter ; mod1r$iter
+# log-likelihood values
+logLik(mod1n); logLik(mod1y) ; logLik(mod1r)
+
+#############################################################################
+# EXAMPLE 22: Acceleration of EM algorithm | polytomous data
+#############################################################################
+
+data(data.gpcm)
+dat <- data.gpcm
+
+# no acceleration
+mod1n <- TAM::tam.mml.2pl( resp=dat, irtmodel="GPCM",
+                control=list( conv=1E-4, acceleration="none") )
+# Yu acceleration
+mod1y <- TAM::tam.mml.2pl( resp=dat, irtmodel="GPCM",
+                control=list( conv=1E-4, acceleration="Yu") )
+# Ramsay acceleration
+mod1r <- TAM::tam.mml.2pl( resp=dat, irtmodel="GPCM",
+                control=list( conv=1E-4, acceleration="Ramsay") )
+# number of iterations
+mod1n$iter ; mod1y$iter ; mod1r$iter
+
+#############################################################################
+# EXAMPLE 23: Multidimensional polytomous Rasch model in which
+#             dimensions are defined by categories
+#############################################################################
+
+data(data.Students, package="CDM")
+dat <- data.Students[, grep( "act", colnames(data.Students) ) ]
+
+# define multidimensional model in which categories of item define dimensions
+
+# * Category 0 -> loading of one on Dimension 0
+# * Category 1 -> no loadings
+# * Category 2 -> loading of one on Dimension 2
+
+# extract default design matrices
+res <- TAM::designMatrices( resp=dat )
+A <- res$A
+B0 <- 0*res$B
+# create design matrix B
+B <- array( 0, dim=c( dim(B0)[c(1,2) ], 2  ) )
+dimnames(B)[[1]] <- dimnames(B0)[[1]]
+dimnames(B)[[2]] <- dimnames(B0)[[2]]
+dimnames(B)[[3]] <- c( "Dim0", "Dim2" )
+B[,1,1]  <- 1
+B[,3,2]  <- 1
+
+# estimate multdimensional Rasch model
+mod1 <- TAM::tam.mml( resp=dat, A=A, B=B, control=list( maxiter=100) )
+summary(mod1)
+
+# alternative definition of B
+# * Category 1: negative loading on Dimension 1 and Dimension 2
+B <- array( 0, dim=c( dim(B0)[c(1,2) ], 2  ) )
+dimnames(B)[[1]] <- dimnames(B0)[[1]]
+dimnames(B)[[2]] <- dimnames(B0)[[2]]
+dimnames(B)[[3]] <- c( "Dim0", "Dim2" )
+B[,1, 1]  <- 1
+B[,3, 2]  <- 1
+B[,2, c(1,2)]  <- -1
+
+# estimate model
+mod2 <- TAM::tam.mml( resp=dat, A=A, B=B, control=list( maxiter=100) )
+summary(mod2)
+
+#############################################################################
+# EXAMPLE 24: Sum constraint on item-category parameters in partial credit model
+#############################################################################
+
+data(data.gpcm,package="TAM")
+dat <- data.gpcm
+
+# check number of categories
+c1 <- TAM::tam.ctt3(dat)
+
+#--- fit with PCM
+mod1 <- TAM::tam.mml( dat )
+summary(mod1, file="mod1")
+
+#--- fit with constraint on sum of categories
+#** redefine design matrix
+A1 <- 0*mod1$A
+A1 <- A1[,, - dim(A1)[[3]]]
+str(A1)
+NP <- dim(A1)[[3]]
+# define item category parameters
+A1[1,2,1] <- A1[1,3,2] <- A1[1,4,3] <- -1
+A1[2,2,4] <- A1[2,3,5] <- A1[2,4,6] <- -1
+A1[3,2,7] <- A1[3,3,8] <- -1
+A1[3,4,1:8] <- 1
+# check definition
+A1[1,,]
+A1[2,,]
+A1[3,,]
+
+#** estimate model
+mod2 <- TAM::tam.mml( dat, A=A1, beta.fixed=FALSE)
+summary(mod2, file="mod2")
+
+#--- compare model fit
+IRT.compareModels(mod1, mod2 )  # -> equivalent model fit
+
+#############################################################################
+# EXAMPLE 25: Different GPCM parametrizations in IRT packages
+#############################################################################
+
+library(TAM)
+library(mirt)
+library(ltm)
+
+data(data.gpcm, package="TAM")
+dat <- data.gpcm
+
+#*** TAM
+mod1 <- TAM::tam.mml.2pl(dat, irtmodel="GPCM")
+#*** mirt
+mod2 <- mirt::mirt(dat, 1, itemtype="gpcm", verbose=TRUE)
+#*** ltm
+mod3 <- ltm::gpcm( dat, control=list(verbose=TRUE) )
+mod3b <- ltm::gpcm( dat, control=list(verbose=TRUE), IRT.param=FALSE)
+
+#-- comparison log likelihood
+logLik(mod1)
+logLik(mod2)
+logLik(mod3)
+logLik(mod3b)
+
+#*** intercept parametrization (like in TAM)
+
+# TAM
+mod1$B[,2,1]   # slope
+mod1$AXsi      # intercepts
+# mirt
+coef(mod2)
+# ltm
+coef(mod3b, IRT.param=FALSE)[, c(4,1:3)]
+
+#*** IRT parametrization
+
+# TAM
+mod1$AXsi / mod1$B[,2,1]
+# mirt
+coef(mod2, IRTpars=TRUE)
+# ltm
+coef(mod3)[, c(4,1:3)]
+
+#############################################################################
+# EXAMPLE 26: Differential item functioning in multdimensional models
+#############################################################################
+
+data(data.ex08, package="TAM")
+formulaA <- ~ item+female+item*female
+resp <- data.ex08[["resp"]]
+facets <- as.data.frame(data.ex08[["facets"]])
+
+#***  Model 8a: investigate gender DIF in undimensional model
+mod8a <- TAM::tam.mml.mfr(resp=resp, facets=facets, formulaA=formulaA)
+summary(mod8a)
+
+#*** multidimensional 2PL Model
+I <- 10
+Q <- array(0, dim=c(I, 3))
+Q[cbind(1:I, c(rep(1, 3), rep(2, 3), rep(3, 4)))] <- 1
+rownames(Q) <- colnames(resp)
+mod3dim2pl <- TAM::tam.mml.2pl(resp=resp, Q=Q, irtmodel="2PL",
+                          control=list(snodes=2000))
+
+#*** Combine both approaches
+thisRows <- gsub("-.*", "", colnames(mod8a$resp)) #select item names
+
+#*** uniform DIF (note irtmodel="2PL.groups" & est.slopegroups)
+mod3dim2pl_udiff <- TAM::tam.mml.2pl(resp=mod8a$resp, A=mod8a$A, Q=Q[thisRows, ],
+                               irtmodel="2PL.groups",
+                               est.slopegroups=as.numeric(as.factor(thisRows)),
+                               control=list(snodes=2000))
+
+#*** non-uniform DIF (?); different slope parameters for each item administered to each group
+mod3dim2pl_nudiff <- TAM::tam.mml.2pl(resp=mod8a$resp, A=mod8a$A, Q=Q[thisRows, ],
+                                irtmodel="2PL", control=list(snodes=2000))
+
+#*** check results
+print(mod8a$xsi)
+print(mod3dim2pl_udiff$xsi)
+summary(mod3dim2pl_nudiff)
+
+#*** within item dimensionality (one item loads on two dimensions)
+Q2 <- Q
+Q2[4,1] <- 1
+
+# uniform DIF (note irtmodel="2PL.groups" & est.slopegroups)
+mod3dim2pl_udiff2 <- TAM::tam.mml.2pl(resp=mod8a$resp, A=mod8a$A, Q=Q2[thisRows, ],
+                                irtmodel="2PL.groups",
+                                est.slopegroups=as.numeric(as.factor(thisRows)),
+                                control=list(snodes=2000))
+print(mod8a$xsi)
+print(mod3dim2pl_udiff2$xsi)
+print(mod3dim2pl_udiff2$xsi)
+
+#############################################################################
+# EXAMPLE 27: IRT parameterization for generalized partial credit model (GPCM) in TAM
+#############################################################################
+
+#--- read item parameters
+pars <- as.numeric(miceadds::scan.vec(
+"0.19029 1.25309 0.51737 -1.77046 0.94803
+  0.19407 1.22680 0.34986 -1.57666 1.29726
+  -0.00888 1.07093 0.31662 -1.38755 1.14809
+  -0.33810 1.08205 0.48490 -1.56696 0.79547
+  -0.18866 0.99587 0.37880 -1.37468 0.81114" ))
+pars <- matrix( pars, nrow=5, byrow=TRUE)
+beta <- pars[,1]
+alpha <- pars[,5]
+tau <- pars[,2:4]
+
+#--- data simulation function for GPCM
+sim_gpcm_irt_param <- function(alpha, beta, tau, N, mu=0, sigma=1)
+{
+    theta <- stats::rnorm(N, mean=mu, sd=sigma)
+    I <- length(beta)
+    K <- ncol(tau)
+    dat <- matrix(0, nrow=N, ncol=I)
+    colnames(dat) <- paste0("I",1:I)
+    for (ii in 1:I){
+        probs <- matrix(0, nrow=N, ncol=K+1)
+        for (kk in 1:K){
+            probs[,kk+1] <- probs[,kk] + alpha[ii]*( theta - beta[ii] - tau[ii,kk] )
+        }
+        probs <- exp(probs)
+        probs <- probs/rowSums(probs)
+        rn <- stats::runif(N)
+        cumprobs <- t(apply(probs,1,cumsum))
+        for (kk in 1:K){
+            dat[,ii] <- dat[,ii] + ( rn > cumprobs[,kk] )
+        }
+    }
+    return(dat)
+}
+
+#-- simulate data
+N <- 20000     # number of persons
+set.seed(98)
+dat1 <- sim_gpcm_irt_param(alpha=alpha, beta=beta, tau=tau, N=N, mu=0, sigma=1)
+head(dat1)
+
+#* generate design matrix for IRT parameterization
+A1 <- TAM::.A.PCM2( resp=dat1)
+
+#- estimate GPCM model
+mod1 <- TAM::tam.mml.2pl( resp=dat1, irtmodel="GPCM", A=A1)
+summary(mod1)
+
+# compare true and estimated slope estimates (alpha)
+cbind( alpha, mod1$B[,2,] )
+
+# compare true and estimated item difficulties (beta)
+cbind( beta, mod1$xsi$xsi[1:5] / mod1$B[,2,1] )
+
+# compare true and estimated tau parameters
+cbind( tau[,-3], matrix( mod1$xsi$xsi[-c(1:5)], nrow=5, byrow=TRUE ) / mod1$B[,2,1] )
+}

+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/reference/tam.modelfit.html b/docs/reference/tam.modelfit.html
index 1320be4..39bed14 100644
--- a/docs/reference/tam.modelfit.html
+++ b/docs/reference/tam.modelfit.html
@@ -1,46 +1,5 @@
-
 
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-Model Fit Statistics in <span class="pkg">TAM</span> — tam.modelfit • TAM
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-Model Fit Statistics in TAM — tam.modelfit • TAM
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Model Fit Statistics in TAM

@@ -133,84 +65,76 @@ 
Model Fit Statistics in TAM

 \(SRMR\)) are also available.

 
The function IRT.modelfit is a wrapper to tam.modelfit,
 but allows convenient model comparisons by using the
-CDM::IRT.compareModels function.

+CDM::IRT.compareModels function.

 
The tam.modelfit function can also be used for fitted
 models outside the TAM package by applying
 tam.modelfit.IRT or tam.modelfit.args.

 
The function tam.Q3 computes the \(Q_3\) statistic based on
-weighted likelihood estimates (see tam.wle).

+weighted likelihood estimates (see tam.wle).

+    

+
+    

+    
tam.modelfit(tamobj, progress=TRUE)
+
+# S3 method for tam.modelfit
+summary(object,...)
+
+# S3 method for tam.mml
+IRT.modelfit(object, ...)
+# S3 method for tam.mml.3pl
+IRT.modelfit(object, ...)
+# S3 method for tamaan
+IRT.modelfit(object, ...)
+
+# S3 method for IRT.modelfit.tam.mml
+summary(object, ...)
+# S3 method for IRT.modelfit.tam.mml.3pl
+summary(object, ...)
+# S3 method for IRT.modelfit.tamaan
+summary(object, ...)
+
+tam.modelfit.IRT( object, progress=TRUE )
+
+tam.modelfit.args( resp, probs, theta, post, progress=TRUE )
+
+tam.Q3(tamobj, ... )
+
+# S3 method for tam.Q3
+summary(object,...)

     

 
-    
tam.modelfit(tamobj, progress=TRUE)
-
-# S3 method for tam.modelfit
-summary(object,...)
-
-# S3 method for tam.mml
-IRT.modelfit(object, ...)
-# S3 method for tam.mml.3pl
-IRT.modelfit(object, ...)
-# S3 method for tamaan
-IRT.modelfit(object, ...)
-
-# S3 method for IRT.modelfit.tam.mml
-summary(object, ...)
-# S3 method for IRT.modelfit.tam.mml.3pl
-summary(object, ...)
-# S3 method for IRT.modelfit.tamaan
-summary(object, ...)
-
-tam.modelfit.IRT( object, progress=TRUE )
-
-tam.modelfit.args( resp, probs, theta, post, progress=TRUE )
-
-tam.Q3(tamobj, ... )
-
-# S3 method for tam.Q3
-summary(object,...)

-
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Arguments

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-    
tamobj
Object of class tam
progress
An optional logical indicating whether progress should
-be displayed
object
Object of class tam.modelfit (for summary)
+    

+    
Arguments

+    
tamobj

+
Object of class tam

+
+  
progress

+
An optional logical indicating whether progress should
+be displayed

+
+
object

+
Object of class tam.modelfit (for summary)
   or objects for which IRT.data, IRT.irfprob
-and IRT.posterior have been defined (for tam.modelfit.IRT).
resp
Dataset with item responses
probs
Array with item response functions evaluated at theta
theta
Matrix with used \(\bold{\theta}\) grid
post
Individual posterior distribution
...
Further arguments to be passed

-
-    
Details

+and IRT.posterior have been defined (for tam.modelfit.IRT).

+
+
resp

+
Dataset with item responses

 
+
probs

+
Array with item response functions evaluated at theta

+
+
theta

+
Matrix with used \(\bold{\theta}\) grid

+
+
post

+
Individual posterior distribution

+
+
...

+
Further arguments to be passed

+
+

+    

+    
Details

     
For each item \(i\) and each person \(n\), residuals
 \(e_{ni}=X_{ni}-E(X_{ni})\) are computed. The expected
 value \(E(X_{ni})\) is obtained by integrating the individual
@@ -220,7 +144,7 @@ 
Details
 tam.modelfit are
 calculated by integrating values of the individual posterior distribution.
 Residuals in tam.Q3 are calculated by using weighted likelihood
-estimates (WLEs) from tam.wle.

+estimates (WLEs) from tam.wle.

 
It is known that under local independence, the expected value of \(Q_3\)
 is slightly smaller than zero. Therefore,
 an adjusted Q3 statistic (aQ3; \(aQ3_{ij}\))
@@ -246,31 +170,54 @@ 
Details
 $$ MADRESIDCOV=\frac{1}{ J(J-1)/2 } \sum_{i < j}
     | c_{ij} - \hat{c}_{ij} |  $$
 This statistic is just multiplied by 100 in the output of this function.

-    
Value

+    

+    

+    
Value

+    
 
-    
A list with following entries

-
stat.MADaQ3
Global fit statistic MADaQ3 and
+
A list with following entries

+
stat.MADaQ3

+
Global fit statistic MADaQ3 and
   global model test with p value obtained
   by Holm adjustment

-  
chi2.stat
Data frame with chi square tests of conditional independence
+
+  
chi2.stat

+
Data frame with chi square tests of conditional independence
      for every item pair (Chen & Thissen, 1997)

-  
fitstat
Model fit statistics \(100 \cdot MADRESIDCOV\),
+
+  
fitstat

+
Model fit statistics \(100 \cdot MADRESIDCOV\),
       \(SRMR\) and \(SRMSR\)

-  
modelfit.test
Test statistic of global fit based on multiple
+
+  
modelfit.test

+
Test statistic of global fit based on multiple
   testing correction of \(\chi^2\) statistics

-  
stat.itempair
Q3 and adjusted Q3 statistic for all item pairs

-  
residuals
Residuals

-  
Q3.matr
Matrix of \(Q_3\) statistics

-  
aQ3.matr
Matrix of adjusted \(Q_3\) statistics

-
Q3_summary
Summary of \(Q_3\) statistics

-
N_itempair
Sample size for each item pair

 
-    
References

+  
stat.itempair

+
Q3 and adjusted Q3 statistic for all item pairs

+
+  
residuals

+
Residuals

+
+  
Q3.matr

+
Matrix of \(Q_3\) statistics

+
+  
aQ3.matr

+
Matrix of adjusted \(Q_3\) statistics

+
+
Q3_summary

+
Summary of \(Q_3\) statistics

 
+
N_itempair

+
Sample size for each item pair

+
+

+    

+    
References

     
Chen, J., de la Torre, J., & Zhang, Z. (2013).
 Relative and absolute fit evaluation in cognitive diagnosis modeling.
 Journal of Educational Measurement, 50, 123-140.
-doi: 10.1111/j.1745-3984.2012.00185.x

+doi:10.1111/j.1745-3984.2012.00185.x

 
Chen, W., & Thissen, D. (1997). Local dependence indexes for item pairs
 using item response theory. Journal of Educational and Behavioral Statistics,
 22, 265-289.

@@ -278,137 +225,136 @@ 
R
 generalized dimensionality discrepancy measure and a standardized model-based
 covariance for dimensionality assessment for multidimensional models.
 Journal of Educational Measurement, 52(2), 144--158.
-doi: 10.1111/jedm.12070

+doi:10.1111/jedm.12070

 
Maydeu-Olivares, A. (2013). Goodness-of-fit assessment of item response
 theory models (with discussion).
 Measurement: Interdisciplinary Research and Perspectives,
 11, 71-137.
-doi: 10.1080/15366367.2013.831680

+doi:10.1080/15366367.2013.831680

 
McDonald, R. P., & Mok, M. M.-C. (1995). Goodness of fit in item response models.
 Multivariate Behavioral Research, 30, 23-40.
-doi: 10.1207/s15327906mbr3001_2

+doi:10.1207/s15327906mbr3001_2

 
Yen, W. M. (1984). Effects of local item dependence on the fit and equating
 performance of the three-parameter logistic model.
 Applied Psychological Measurement, 8, 125-145.
-doi: 10.1177/014662168400800201

-
-    
Examples

-    
#############################################################################
-# EXAMPLE 1: data.cqc01
-#############################################################################
-
-data(data.cqc01)
-dat <- data.cqc01
-
-#*****************************************************
-#*** Model 1: Rasch model
-mod1 <- TAM::tam.mml( dat )
-# assess model fit
-res1 <- TAM::tam.modelfit( tamobj=mod1 )
-summary(res1)
-# display item pairs with five largest adjusted Q3 statistics
-res1$stat.itempair[1:5,c("item1","item2","aQ3","p","p.holm")]
-
-if (FALSE) {
-# IRT.modelfit
-fmod1 <- IRT.modelfit(mod1)
-summary(fmod1)
-
-#*****************************************************
-#*** Model 2: 2PL model
-mod2 <- TAM::tam.mml.2pl( dat )
-# IRT.modelfit
-fmod2 <- IRT.modelfit(mod2)
-summary(fmod2)
-
-# model comparison
-IRT.compareModels(fmod1, fmod2 )
-
-#############################################################################
-# SIMULATED EXAMPLE 2: Rasch model
-#############################################################################
-
-set.seed(8766)
-N <- 1000    # number of persons
-I <- 20      # number of items
-# simulate responses
-library(sirt)
-dat <- sirt::sim.raschtype( stats::rnorm(N), b=seq(-1.5,1.5,len=I) )
-#*** estimation
-mod1 <- TAM::tam.mml( dat )
-summary(dat)
-#*** model fit
-res1 <- TAM::tam.modelfit( tamobj=mod1)
-summary(res1)
-
-#############################################################################
-# EXAMPLE 3: Model fit data.gpcm | Partial credit model
-#############################################################################
-
-data(data.gpcm)
-dat <- data.gpcm
-
-# estimate partial credit model
-mod1 <- TAM::tam.mml( dat)
-summary(mod1)
-
-# assess model fit
-tmod1 <- TAM::tam.modelfit( mod1 )
-summary(tmod1)
-
-#############################################################################
-# EXAMPLE 4: data.read | Comparison Q3 statistic
-#############################################################################
-
-library(sirt)
-data(data.read, package="sirt")
-dat <- data.read
-
-#**** Model 1: 1PL model
-mod1 <- TAM::tam.mml( dat )
-summary(mod1)
-
-#**** Model 2: 2PL model
-mod2 <- TAM::tam.mml.2pl( dat )
-summary(mod2)
-
-#**** assess model fits
-# Q3 based on posterior
-fmod1 <- TAM::tam.modelfit(mod1)
-fmod2 <- TAM::tam.modelfit(mod2)
-# Q3 based on WLEs
-q3_mod1 <- TAM::tam.Q3(mod1)
-q3_mod2 <- TAM::tam.Q3(mod2)
-summary(fmod1)
-summary(fmod2)
-summary(q3_mod1)
-summary(q3_mod2)
-}

+doi:10.1177/014662168400800201

+    

+
+    

+    
Examples

+    
#############################################################################
+# EXAMPLE 1: data.cqc01
+#############################################################################
+
+data(data.cqc01)
+dat <- data.cqc01
+
+#*****************************************************
+#*** Model 1: Rasch model
+mod1 <- TAM::tam.mml( dat )
+# assess model fit
+res1 <- TAM::tam.modelfit( tamobj=mod1 )
+summary(res1)
+# display item pairs with five largest adjusted Q3 statistics
+res1$stat.itempair[1:5,c("item1","item2","aQ3","p","p.holm")]
+
+if (FALSE) {
+# IRT.modelfit
+fmod1 <- IRT.modelfit(mod1)
+summary(fmod1)
+
+#*****************************************************
+#*** Model 2: 2PL model
+mod2 <- TAM::tam.mml.2pl( dat )
+# IRT.modelfit
+fmod2 <- IRT.modelfit(mod2)
+summary(fmod2)
+
+# model comparison
+IRT.compareModels(fmod1, fmod2 )
+
+#############################################################################
+# SIMULATED EXAMPLE 2: Rasch model
+#############################################################################
+
+set.seed(8766)
+N <- 1000    # number of persons
+I <- 20      # number of items
+# simulate responses
+library(sirt)
+dat <- sirt::sim.raschtype( stats::rnorm(N), b=seq(-1.5,1.5,len=I) )
+#*** estimation
+mod1 <- TAM::tam.mml( dat )
+summary(dat)
+#*** model fit
+res1 <- TAM::tam.modelfit( tamobj=mod1)
+summary(res1)
+
+#############################################################################
+# EXAMPLE 3: Model fit data.gpcm | Partial credit model
+#############################################################################
+
+data(data.gpcm)
+dat <- data.gpcm
+
+# estimate partial credit model
+mod1 <- TAM::tam.mml( dat)
+summary(mod1)
+
+# assess model fit
+tmod1 <- TAM::tam.modelfit( mod1 )
+summary(tmod1)
+
+#############################################################################
+# EXAMPLE 4: data.read | Comparison Q3 statistic
+#############################################################################
+
+library(sirt)
+data(data.read, package="sirt")
+dat <- data.read
+
+#**** Model 1: 1PL model
+mod1 <- TAM::tam.mml( dat )
+summary(mod1)
+
+#**** Model 2: 2PL model
+mod2 <- TAM::tam.mml.2pl( dat )
+summary(mod2)
+
+#**** assess model fits
+# Q3 based on posterior
+fmod1 <- TAM::tam.modelfit(mod1)
+fmod2 <- TAM::tam.modelfit(mod2)
+# Q3 based on WLEs
+q3_mod1 <- TAM::tam.Q3(mod1)
+q3_mod2 <- TAM::tam.Q3(mod2)
+summary(fmod1)
+summary(fmod2)
+summary(q3_mod1)
+summary(q3_mod2)
+}

+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/reference/tam.np.html b/docs/reference/tam.np.html
index ddd9cc3..ff5379e 100644
--- a/docs/reference/tam.np.html
+++ b/docs/reference/tam.np.html
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-Unidimensional Non- and Semiparametric Item Response Model — tam.np • TAM
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+      

   

     

     
Unidimensional Non- and Semiparametric Item Response Model

@@ -131,86 +63,71 @@ 
Unidimensional Non- and Semiparametric Item Response Model

 See Details for model specification.

     

 
-    
tam.np( dat, probs_init=NULL, pweights=NULL, lambda=NULL, control=list(),
-    model="2PL", n_basis=0, basis_type="hermite", penalty_type="lasso",
-    pars_init=NULL, orthonormalize=TRUE)
-
-# S3 method for tam.np
-summary(object, file=NULL, ...)
-
-# S3 method for tam.np
-IRT.cv(object, kfold=10, ...)

-
-    
Arguments

-    
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
dat
Matrix of integer item responses (starting from zero)
probs_init
Array containing initial probabilities
pweights
Optional vector of person weights
lambda
Numeric or vector of regularization parameter
control
List of control arguments, see tam.mml.
model
Specified target model. Can be "2PL" or "1PL".
n_basis
Number of basis functions
basis_type
Type of basis function: "bspline" for B-splines
-or "hermite" for Gauss-Hermite polynomials
penalty_type
Lasso type penalty ("lasso") or ridge
-penalty ("ridge")
pars_init
Optional matrix of initial item parameters
orthonormalize
Logical indicating whether basis functions should
-be orthonormalized
object
Object of class tam.np
file
Optional file name for summary output
kfold
Number of folds in \(k\)-fold cross-validation
...
Further arguments to be passed

-
-    
Details

+    

+    
tam.np( dat, probs_init=NULL, pweights=NULL, lambda=NULL, control=list(),
+    model="2PL", n_basis=0, basis_type="hermite", penalty_type="lasso",
+    pars_init=NULL, orthonormalize=TRUE)
+
+# S3 method for tam.np
+summary(object, file=NULL, ...)
+
+# S3 method for tam.np
+IRT.cv(object, kfold=10, ...)

+    

+
+    

+    
Arguments

+    
dat

+
Matrix of integer item responses (starting from zero)

+
+
probs_init

+
Array containing initial probabilities

 
+
pweights

+
Optional vector of person weights

+
+
lambda

+
Numeric or vector of regularization parameter

+
+
control

+
List of control arguments, see tam.mml.

+
+
model

+
Specified target model. Can be "2PL" or "1PL".

+
+
n_basis

+
Number of basis functions

+
+
basis_type

+
Type of basis function: "bspline" for B-splines
+or "hermite" for Gauss-Hermite polynomials

+
+
penalty_type

+
Lasso type penalty ("lasso") or ridge
+penalty ("ridge")

+
+
pars_init

+
Optional matrix of initial item parameters

+
+
orthonormalize

+
Logical indicating whether basis functions should
+be orthonormalized

+
+
object

+
Object of class tam.np

+
+
file

+
Optional file name for summary output

+
+
kfold

+
Number of folds in \(k\)-fold cross-validation

+
+
...

+
Further arguments to be passed

+
+

+    

+    
Details

     
The basis expansion approach is applied for the logit transformation of item
 response functions for dichotomous data. In more detail, it this assumed that
 $$P(X_i=1|\theta)=\psi( H_0(\theta) + H_1(\theta)$$
@@ -226,182 +143,205 @@ 
Details
 penalty \(J_{i,L1}=N \lambda \sqrt{p} \sqrt{ \sum_{h=1}^p \beta_{ih}^2 }\) while for
 the ridge penalty it is \(J_{i,L2}=N \lambda \sum_{h=1}^p \beta_{ih}^2 \)
 (\(N\) denoting the sample size).

-    
Value

-
-    
List containing several entries

-
rprobs
Item response probabilities

-
theta
Used nodes for approximation of \(\theta\) distribution

-
n.ik
Expected counts

-
like
Individual likelihood

-
hwt
Individual posterior

-
item
Summary item parameter table

-
pars
Estimated parameters

-
regularized
Logical indicating which items are regularized

-
ic
List containing

-
...
Further values

-
-    
References

+    

+    

+    
Value

+    
+
+
List containing several entries

+
rprobs

+
Item response probabilities

 
+
theta

+
Used nodes for approximation of \(\theta\) distribution

+
+
n.ik

+
Expected counts

+
+
like

+
Individual likelihood

+
+
hwt

+
Individual posterior

+
+
item

+
Summary item parameter table

+
+
pars

+
Estimated parameters

+
+
regularized

+
Logical indicating which items are regularized

+
+
ic

+
List containing

+
+
...

+
Further values

+
+

+    

+    
References

     
Breheny, P., & Huang, J. (2015). Group descent algorithms for nonconvex penalized linear
 and logistic regression models with grouped predictors.
 Statistics and Computing, 25(2), 173-187.
-doi: 10.1007/s11222-013-9424-2

+doi:10.1007/s11222-013-9424-2

 
Rossi, N., Wang, X., & Ramsay, J. O. (2002). Nonparametric item response function
 estimates with the EM algorithm.
 Journal of Educational and Behavioral Statistics, 27(3), 291-317.
-doi: 10.3102/10769986027003291

+doi:10.3102/10769986027003291

 
Yang, Y., & Zou, H. (2015). A fast unified algorithm for solving group-lasso penalized
 learning problems. Statistics and Computing, 25(6), 1129-1141.
-doi: 10.1007/s11222-014-9498-5

-    
See also

-
-    
Nonparametric item response models can also be estimated with the
-mirt::itemGAM function in the mirt package and the
+doi:10.1007/s11222-014-9498-5

+    

+    

+    
See also

+    
Nonparametric item response models can also be estimated with the
+mirt::itemGAM function in the mirt package and the
 KernSmoothIRT::ksIRT in the KernSmoothIRT package.

-
See tam.mml and tam.mml.2pl for parametric item response
+
See tam.mml and tam.mml.2pl for parametric item response
 models.

+    

 
-    
Examples

-    
if (FALSE) {
-#############################################################################
-# EXAMPLE 1: Nonparametric estimation polytomous data
-#############################################################################
-
-data(data.cqc02, package="TAM")
-dat <- data.cqc02
-
-#** nonparametric estimation
-mod <- TAM::tam.np(dat)
-
-#** extractor functions for objects of class 'tam.np'
-lmod <- IRT.likelihood(mod)
-pmod <- IRT.posterior(mod)
-rmod <- IRT.irfprob(mod)
-emod <- IRT.expectedCounts(mod)
-
-#############################################################################
-# EXAMPLE 2: Semiparametric estimation and detection of item misfit
-#############################################################################
-
-#- simulate data with two misfitting items
-set.seed(998)
-I <- 10
-N <- 1000
-a <- stats::rnorm(I, mean=1, sd=.3)
-b <- stats::rnorm(I, mean=0, sd=1)
-dat <- matrix(NA, nrow=N, ncol=I)
-colnames(dat) <- paste0("I",1:I)
-theta <- stats::rnorm(N)
-for (ii in 1:I){
-    dat[,ii] <- 1*(stats::runif(N) < stats::plogis( a[ii]*(theta-b[ii] ) ))
-}
-
-#* first misfitting item with lower and upper asymptote
-ii <- 1
-l <- .3
-u <- 1
-b[ii] <- 1.5
-dat[,ii] <- 1*(stats::runif(N) < l + (u-l)*stats::plogis( a[ii]*(theta-b[ii] ) ))
-
-#* second misfitting item with non-monotonic item response function
-ii <- 3
-dat[,ii] <- (stats::runif(N) < stats::plogis( theta-b[ii]+.6*theta^2))
-
-#- 2PL model
-mod0 <- TAM::tam.mml.2pl(dat)
-
-#- lasso penalty with lambda of .05
-mod1 <- TAM::tam.np(dat, n_basis=4, lambda=.05)
-
-#- lambda value of .03 using starting value of previous model
-mod2 <- TAM::tam.np(dat, n_basis=4, lambda=.03, pars_init=mod1$pars)
-cmod2 <- TAM::IRT.cv(mod2)  # cross-validated deviance
-
-#- lambda=.015
-mod3 <- TAM::tam.np(dat, n_basis=4, lambda=.015, pars_init=mod2$pars)
-cmod3 <- TAM::IRT.cv(mod3)
-
-#- lambda=.007
-mod4 <- TAM::tam.np(dat, n_basis=4, lambda=.007, pars_init=mod3$pars)
-
-#- lambda=.001
-mod5 <- TAM::tam.np(dat, n_basis=4, lambda=.001, pars_init=mod4$pars)
-
-#- final estimation using solution of mod3
-eps <- .0001
-lambda_final <- eps+(1-eps)*mod3$regularized   # lambda parameter for final estimate
-mod3b <- TAM::tam.np(dat, n_basis=4, lambda=lambda_final, pars_init=mod3$pars)
-summary(mod1)
-summary(mod2)
-summary(mod3)
-summary(mod3b)
-summary(mod4)
-
-# compare models with respect to information criteria
-IRT.compareModels(mod0, mod1, mod2, mod3, mod3b, mod4, mod5)
-
-#-- compute item fit statistics RISE
-# regularized solution
-TAM::IRT.RISE(mod_p=mod1, mod_np=mod3)
-# regularized solution, final estimation
-TAM::IRT.RISE(mod_p=mod1, mod_np=mod3b, use_probs=TRUE)
-TAM::IRT.RISE(mod_p=mod1, mod_np=mod3b, use_probs=FALSE)
-# use TAM::IRT.RISE() function for computing the RMSD statistic
-TAM::IRT.RISE(mod_p=mod1, mod_np=mod1, use_probs=FALSE)
-
-#############################################################################
-# EXAMPLE 3: Mixed 1PL/2PL model
-#############################################################################
-
-#* simulate data with 2 2PL items and 8 1PL items
-set.seed(9877)
-N <- 2000
-I <- 10
-b <- seq(-1,1,len=I)
-a <- rep(1,I)
-a[c(3,8)] <- c(.5, 2)
-theta <- stats::rnorm(N, sd=1)
-dat <- sirt::sim.raschtype(theta, b=b, fixed.a=a)
-
-#- 1PL model
-mod1 <- TAM::tam.mml(dat)
-#- 2PL model
-mod2 <- TAM::tam.mml.2pl(dat)
-#- 2PL model with penalty on slopes
-mod3 <- TAM::tam.np(dat, lambda=.04, model="1PL", n_basis=0)
-summary(mod3)
-#- final mixed 1PL/2PL model
-lambda <- 1*mod3$regularized
-mod4 <- TAM::tam.np(dat, lambda=lambda, model="1PL", n_basis=0)
-summary(mod4)
-
-IRT.compareModels(mod1, mod2, mod3, mod4)
-}

+    

+    
Examples

+    
if (FALSE) {
+#############################################################################
+# EXAMPLE 1: Nonparametric estimation polytomous data
+#############################################################################
+
+data(data.cqc02, package="TAM")
+dat <- data.cqc02
+
+#** nonparametric estimation
+mod <- TAM::tam.np(dat)
+
+#** extractor functions for objects of class 'tam.np'
+lmod <- IRT.likelihood(mod)
+pmod <- IRT.posterior(mod)
+rmod <- IRT.irfprob(mod)
+emod <- IRT.expectedCounts(mod)
+
+#############################################################################
+# EXAMPLE 2: Semiparametric estimation and detection of item misfit
+#############################################################################
+
+#- simulate data with two misfitting items
+set.seed(998)
+I <- 10
+N <- 1000
+a <- stats::rnorm(I, mean=1, sd=.3)
+b <- stats::rnorm(I, mean=0, sd=1)
+dat <- matrix(NA, nrow=N, ncol=I)
+colnames(dat) <- paste0("I",1:I)
+theta <- stats::rnorm(N)
+for (ii in 1:I){
+    dat[,ii] <- 1*(stats::runif(N) < stats::plogis( a[ii]*(theta-b[ii] ) ))
+}
+
+#* first misfitting item with lower and upper asymptote
+ii <- 1
+l <- .3
+u <- 1
+b[ii] <- 1.5
+dat[,ii] <- 1*(stats::runif(N) < l + (u-l)*stats::plogis( a[ii]*(theta-b[ii] ) ))
+
+#* second misfitting item with non-monotonic item response function
+ii <- 3
+dat[,ii] <- (stats::runif(N) < stats::plogis( theta-b[ii]+.6*theta^2))
+
+#- 2PL model
+mod0 <- TAM::tam.mml.2pl(dat)
+
+#- lasso penalty with lambda of .05
+mod1 <- TAM::tam.np(dat, n_basis=4, lambda=.05)
+
+#- lambda value of .03 using starting value of previous model
+mod2 <- TAM::tam.np(dat, n_basis=4, lambda=.03, pars_init=mod1$pars)
+cmod2 <- TAM::IRT.cv(mod2)  # cross-validated deviance
+
+#- lambda=.015
+mod3 <- TAM::tam.np(dat, n_basis=4, lambda=.015, pars_init=mod2$pars)
+cmod3 <- TAM::IRT.cv(mod3)
+
+#- lambda=.007
+mod4 <- TAM::tam.np(dat, n_basis=4, lambda=.007, pars_init=mod3$pars)
+
+#- lambda=.001
+mod5 <- TAM::tam.np(dat, n_basis=4, lambda=.001, pars_init=mod4$pars)
+
+#- final estimation using solution of mod3
+eps <- .0001
+lambda_final <- eps+(1-eps)*mod3$regularized   # lambda parameter for final estimate
+mod3b <- TAM::tam.np(dat, n_basis=4, lambda=lambda_final, pars_init=mod3$pars)
+summary(mod1)
+summary(mod2)
+summary(mod3)
+summary(mod3b)
+summary(mod4)
+
+# compare models with respect to information criteria
+IRT.compareModels(mod0, mod1, mod2, mod3, mod3b, mod4, mod5)
+
+#-- compute item fit statistics RISE
+# regularized solution
+TAM::IRT.RISE(mod_p=mod1, mod_np=mod3)
+# regularized solution, final estimation
+TAM::IRT.RISE(mod_p=mod1, mod_np=mod3b, use_probs=TRUE)
+TAM::IRT.RISE(mod_p=mod1, mod_np=mod3b, use_probs=FALSE)
+# use TAM::IRT.RISE() function for computing the RMSD statistic
+TAM::IRT.RISE(mod_p=mod1, mod_np=mod1, use_probs=FALSE)
+
+#############################################################################
+# EXAMPLE 3: Mixed 1PL/2PL model
+#############################################################################
+
+#* simulate data with 2 2PL items and 8 1PL items
+set.seed(9877)
+N <- 2000
+I <- 10
+b <- seq(-1,1,len=I)
+a <- rep(1,I)
+a[c(3,8)] <- c(.5, 2)
+theta <- stats::rnorm(N, sd=1)
+dat <- sirt::sim.raschtype(theta, b=b, fixed.a=a)
+
+#- 1PL model
+mod1 <- TAM::tam.mml(dat)
+#- 2PL model
+mod2 <- TAM::tam.mml.2pl(dat)
+#- 2PL model with penalty on slopes
+mod3 <- TAM::tam.np(dat, lambda=.04, model="1PL", n_basis=0)
+summary(mod3)
+#- final mixed 1PL/2PL model
+lambda <- 1*mod3$regularized
+mod4 <- TAM::tam.np(dat, lambda=lambda, model="1PL", n_basis=0)
+summary(mod4)
+
+IRT.compareModels(mod1, mod2, mod3, mod4)
+}

+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/reference/tam.personfit.html b/docs/reference/tam.personfit.html
index 1163e3b..6ada6af 100644
--- a/docs/reference/tam.personfit.html
+++ b/docs/reference/tam.personfit.html
@@ -1,67 +1,12 @@
-
 
-
-  
-  
-
-
-
-Person Outfit and Infit Statistics — tam.personfit • TAM
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
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-
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-
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-
-
-Person Outfit and Infit Statistics — tam.personfit • TAM
-
-
-
-  
+
+    
 
-  
     

-      

-      
 
       
 
-      

-
-

+      

   

     

     
Person Outfit and Infit Statistics

@@ -117,65 +49,66 @@ 
Person Outfit and Infit Statistics

     
Computes person outfit and infit statistics.

     

 
-    
tam.personfit(tamobj)

-
-    
Arguments

-    
-    
-    
-      
-      
-    
-    
tamobj
Fitted object in TAM

+    

+    
tam.personfit(tamobj)

+    

 
-    
Value

+    

+    
Arguments

+    
tamobj

+
Fitted object in TAM

 
-    
Data frame containing person outfit and infit statistics

-    
See also

+

+    

+    
Value

+    
 
-    
See tam.fit and msq.itemfit for item fit
+
Data frame containing person outfit and infit statistics

+    

+    

+    
See also

+    
See tam.fit and msq.itemfit for item fit
 statistics.

+    

 
-    
Examples

-    
#############################################################################
-# EXAMPLE 1: Person fit dichotomous data
-#############################################################################
-
-data(data.sim.rasch, package="TAM")
-resp <- data.sim.rasch
-
-#*** estimate Rasch model
-mod1 <- TAM::tam.mml(resp=resp)
-summary(mod1)
-
-#*** compute person fit statistics
-fmod1 <- TAM::tam.personfit(mod1)
-head(fmod1)

+    

+    
Examples

+    
#############################################################################
+# EXAMPLE 1: Person fit dichotomous data
+#############################################################################
+
+data(data.sim.rasch, package="TAM")
+resp <- data.sim.rasch
+
+#*** estimate Rasch model
+mod1 <- TAM::tam.mml(resp=resp)
+summary(mod1)
+
+#*** compute person fit statistics
+fmod1 <- TAM::tam.personfit(mod1)
+head(fmod1)

+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/reference/tam.pv.html b/docs/reference/tam.pv.html
index d63815d..7058c10 100644
--- a/docs/reference/tam.pv.html
+++ b/docs/reference/tam.pv.html
@@ -1,46 +1,5 @@
-
 
-
-  
-  
-
-
-
-Plausible Value Imputation — tam.pv • TAM
-
-
-
-
-
-
-
-
-
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-
-Plausible Value Imputation — tam.pv • TAM
-
-
-
-
-
-
-
-
-
-
-
-
-  
+
+    
 
-  
     

-      

-      
 
       
 
-      

-
-

+      

   

     

     
Plausible Value Imputation

@@ -128,7 +60,7 @@ 
Plausible Value Imputation

     

     
Plausible value imputation for objects of the classes tam and tam.mml
 (Adams & Wu, 2007). For converting generated plausible values into
-a list of multiply imputed datasets see tampv2datalist
+a list of multiply imputed datasets see tampv2datalist
 and the Examples 2 and 3 of this function.

 
The function tam.pv.mcmc employs fully Bayesian estimation for drawing
 plausible values and is recommended in cases when the latent regression model
@@ -141,601 +73,602 @@ 
Plausible Value Imputation

 can be used for the Bootstrap step by obtaining posterior draws of regression parameters.

     

 
-    
tam.pv(tamobj, nplausible=10, ntheta=2000, normal.approx=FALSE,
-    samp.regr=FALSE, theta.model=FALSE, np.adj=8, na.grid=5, verbose=TRUE)
-
-tam.pv.mcmc( tamobj, Y=NULL, group=NULL, beta_groups=TRUE, nplausible=10, level=.95,
-    n.iter=1000, n.burnin=500, adj_MH=.5, adj_change_MH=.05, refresh_MH=50,
-    accrate_bound_MH=c(.45, .55), sample_integers=FALSE, theta_init=NULL,
-    print_iter=20, verbose=TRUE, calc_ic=TRUE)
+    

+    
tam.pv(tamobj, nplausible=10, ntheta=2000, normal.approx=FALSE,
+    samp.regr=FALSE, theta.model=FALSE, np.adj=8, na.grid=5, verbose=TRUE)
+
+tam.pv.mcmc( tamobj, Y=NULL, group=NULL, beta_groups=TRUE, nplausible=10, level=.95,
+    n.iter=1000, n.burnin=500, adj_MH=.5, adj_change_MH=.05, refresh_MH=50,
+    accrate_bound_MH=c(.45, .55), sample_integers=FALSE, theta_init=NULL,
+    print_iter=20, verbose=TRUE, calc_ic=TRUE)
+
+# S3 method for tam.pv.mcmc
+summary(object, file=NULL, ...)
+
+# S3 method for tam.pv.mcmc
+plot(x, ...)

+    

 
-# S3 method for tam.pv.mcmc
-summary(object, file=NULL, ...)
+    

+    
Arguments

+    
tamobj

+
Object of class tam or tam.mml. For tam.pv.mcmc, it must not
+     be an object of this class but rather a list with (at least the)
+     entries AXsi, B, resp.

 
-# S3 method for tam.pv.mcmc
-plot(x, ...)

+ 
nplausible

+
Number of plausible values to be drawn

 
-    
Arguments

-    
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
tamobj
Object of class tam or tam.mml. For tam.pv.mcmc, it must not
-     be an object of this class but rather a list with (at least the)
-     entries AXsi, B, resp.
nplausible
Number of plausible values to be drawn
ntheta
Number of ability nodes for plausible value imputation. Note
+
ntheta

+
Number of ability nodes for plausible value imputation. Note
     that in this function ability nodes are simulated for the
-    whole sample, not for every person (contrary to the software ConQuest).
normal.approx
An optional logical indicating whether the individual posterior distributions
+    whole sample, not for every person (contrary to the software ConQuest).

+
+  
normal.approx

+
An optional logical indicating whether the individual posterior distributions
      should be approximated by a normal distribution?
      The default is FALSE. In the case normal.approx=TRUE
      (normal distribution approximation), the number of ability nodes
      ntheta can be substantially smaller than 2000, say 200 or 500.
      The normal approximation is implemented for unidimensional and
-     multidimensional models.
samp.regr
An optional logical indicating whether regression coefficients
+     multidimensional models.

+
+  
samp.regr

+
An optional logical indicating whether regression coefficients
      should be fixed in the plausible value imputation or
      also sampled from their posterior distribution?
      The default is FALSE. Sampled regression coefficients are
-     obtained by nonparametric bootstrap.
theta.model
Logical indicating whether the theta grid from the
+     obtained by nonparametric bootstrap.

+
+
theta.model

+
Logical indicating whether the theta grid from the
     tamobj object should be used for plausible value
     imputation. In case of normal.approx=TRUE, this should
-    be sufficient in many applications.
np.adj
This parameter defines the "spread" of the random theta values
+    be sufficient in many applications.

+
+  
np.adj

+
This parameter defines the "spread" of the random theta values
      for drawing plausible values when normal.approx=FALSE.
      If \(s_{EAP}\) denotes the standard deviation of the posterior
      distribution of theta (in the one-dimensional case), then theta
      is simulated from a normal distribution with standard deviation
-     np.adj times \(s_{EAP}\).
na.grid
Range of the grid in normal approximation. Default is from
--5 to 5.
...
Further arguments to be passed
Y
Optional matrix of regressors
group
Optional vector of group identifiers
beta_groups
Logical indicating whether group specific beta coefficients
-   shall be estimated.
level
Confidence level
n.iter
Number of iterations
n.burnin
Number of burnin-iterations
adj_MH
Adjustment factor for Metropolis-Hastings (MH) steps which controls
+     np.adj times \(s_{EAP}\).

+
+
na.grid

+
Range of the grid in normal approximation. Default is from
+-5 to 5.

+
+
...

+
Further arguments to be passed

+
+
Y

+
Optional matrix of regressors

+
+
group

+
Optional vector of group identifiers

+
+
beta_groups

+
Logical indicating whether group specific beta coefficients
+   shall be estimated.

+
+
level

+
Confidence level

+
+
n.iter

+
Number of iterations

+
+
n.burnin

+
Number of burnin-iterations

+
+
adj_MH

+
Adjustment factor for Metropolis-Hastings (MH) steps which controls
     the variance of the proposal distribution for \(\theta\). Can be also
-    a vector of length equal to the number of persons.
adj_change_MH
Allowed change for MH adjustment factor after refreshing
refresh_MH
Number of iterations after which the variance of the proposal
- distribution should be updated
accrate_bound_MH
Bounds for target acceptance rates of sampled \(\theta\)
-   values.
sample_integers
Logical indicating whether weights for complete cases
-should be sampled in bootstrap
theta_init
Optional matrix with initial \(\bold{\theta}\) values
print_iter
Print iteration progress every print_iterth iteration
verbose
Logical indicating whether iteration progress should be displayed.
calc_ic
Logical indicating whether information criteria should be computed.
object
Object of class tam.pv.mcmc
x
Object of class tam.pv.mcmc
file
A file name in which the summary output will be written

-
-    
Value

-
-    
The value of tam.pv is a list with following entries:

-
pv
A data frame containing a person identifier (pid)
+    a vector of length equal to the number of persons.

+
+
adj_change_MH

+
Allowed change for MH adjustment factor after refreshing

+
+
refresh_MH

+
Number of iterations after which the variance of the proposal
+ distribution should be updated

+
+
accrate_bound_MH

+
Bounds for target acceptance rates of sampled \(\theta\)
+   values.

+
+
sample_integers

+
Logical indicating whether weights for complete cases
+should be sampled in bootstrap

+
+
theta_init

+
Optional matrix with initial \(\bold{\theta}\) values

+
+
print_iter

+
Print iteration progress every print_iterth iteration

+
+
verbose

+
Logical indicating whether iteration progress should be displayed.

+
+
calc_ic

+
Logical indicating whether information criteria should be computed.

+
+
object

+
Object of class tam.pv.mcmc

+
+
x

+
Object of class tam.pv.mcmc

+
+
file

+
A file name in which the summary output will be written

+
+

+    

+    
Value

+    
+
+
The value of tam.pv is a list with following entries:

+
pv

+
A data frame containing a person identifier (pid)
     and plausible values denoted by PVxx.Dimyy which
     is the xxth plausible value of
     dimension yy.

-  
hwt
Individual posterior distribution evaluated at
+
+  
hwt

+
Individual posterior distribution evaluated at
     the ability grid theta

-  
hwt1
Cumulated individual posterior distribution

-  
theta
Simulated ability nodes

-
-The value of tam.pv.mcmc is a list containing entries
-
pv
Data frame containing plausible values

-
parameter_samples
Sampled regression parameters

-
ic
Information criteria

-
beta
Estimate of regression parameters \(\bold{\beta}\)

-
variance
Estimate of residual variance matrix \(\bold{\Sigma}\)

-
correlation
Estimate of residual correlation matrix corresponding to
+
+  
hwt1

+
Cumulated individual posterior distribution

+
+  
theta

+
Simulated ability nodes

+
+
+
The value of tam.pv.mcmc is a list containing entries

+
pv

+
Data frame containing plausible values

+
+
parameter_samples

+
Sampled regression parameters

+
+
ic

+
Information criteria

+
+
beta

+
Estimate of regression parameters \(\bold{\beta}\)

+
+
variance

+
Estimate of residual variance matrix \(\bold{\Sigma}\)

+
+
correlation

+
Estimate of residual correlation matrix corresponding to
 variance

-
theta_acceptance_MH
Acceptance rates and acceptance MH factors for each
+
+
theta_acceptance_MH

+
Acceptance rates and acceptance MH factors for each
 individual

-
theta_last
Last sampled \(\bold{\theta}\) value

-
...
Further values

 
-    
References

+
theta_last

+
Last sampled \(\bold{\theta}\) value

+
+
...

+
Further values

 
+

+    

+    
References

     
Adams, R. J., & Wu, M. L. (2007). The mixed-coefficients multinomial logit model.
 A generalized form of the Rasch model. In M. von Davier & C. H. Carstensen (Eds.):
 Multivariate and mixture distribution Rasch models: Extensions and applications
 (pp. 55-76). New York: Springer.
-doi: 10.1007/978-0-387-49839-3_4

+doi:10.1007/978-0-387-49839-3_4

 
Rubin, D. B. (1981). The Bayesian bootstrap. The Annals of Statistics, 9(1),
 130-134.

-    
See also

-
-    
See tam.latreg for further examples of
+    

+    

+    
See also

+    
See tam.latreg for further examples of
 fitting latent regression models and drawing plausible values
 from models which provides an individual likelihood as an input.

+    

 
-    
Examples

-    
#############################################################################
-# EXAMPLE 1: Dichotomous unidimensional data sim.rasch
-#############################################################################
-
-data(data.sim.rasch)
-resp <- data.sim.rasch[ 1:500, 1:15 ]  # select subsample of students and items
-
-# estimate Rasch model
-mod <- TAM::tam.mml(resp)
-
-# draw 5 plausible values without a normality
-# assumption of the posterior and 2000 ability nodes
-pv1a <- TAM::tam.pv( mod, nplausible=5, ntheta=2000 )
-
-# draw 5 plausible values with a normality
-# assumption of the posterior and 500 ability nodes
-pv1b <- TAM::tam.pv( mod, nplausible=5, ntheta=500, normal.approx=TRUE )
-
-# distribution of first plausible value from imputation pv1
-hist(pv1a$pv$PV1.Dim1 )
-# boxplot of all plausible values from imputation pv2
-boxplot(pv1b$pv[, 2:6 ] )
-
-if (FALSE) {
-# draw plausible values with tam.pv.mcmc function
-Y <- matrix(1, nrow=500, ncol=1)
-pv2 <- TAM::tam.pv.mcmc( tamobj=mod, Y=Y, nplausible=5 )
-str(pv2)
-
-# summary output
-summary(pv2)
-# assessing convergence with traceplots
-plot(pv2, ask=TRUE)
-
-# use starting values for theta and MH factors which fulfill acceptance rates
-# from previously fitted model
-pv3 <- TAM::tam.pv.mcmc( tamobj=mod, Y=Y, nplausible=5, theta_init=pv2$theta_last,
-            adj_MH=pv2$theta_acceptance_MH$adj_MH )
-
-#############################################################################
-# EXAMPLE 2: Unidimensional plausible value imputation with
-#            background variables; dataset data.pisaRead from sirt package
-#############################################################################
-
-data(data.pisaRead, package="sirt")
-dat <- data.pisaRead$data
-  ##   > colnames(dat)
-  ##    [1] "idstud"   "idschool" "female"   "hisei"    "migra"    "R432Q01"
-  ##    [7] "R432Q05"  "R432Q06"  "R456Q01"  "R456Q02"  "R456Q06"  "R460Q01"
-  ##   [13] "R460Q05"  "R460Q06"  "R466Q02"  "R466Q03"  "R466Q06"
-
-## Note that reading items have variable names starting with R4
-
-# estimate 2PL model without covariates
-items <- grep("R4", colnames(dat) )    # select test items from data
-mod2a <- TAM::tam.mml.2pl( resp=dat[,items] )
-summary(mod2a)
-
-# fix item parameters for plausible value imputation
-   # fix item intercepts by defining xsi.fixed
-xsi0 <- mod2a$xsi$xsi
-xsi.fixed <- cbind( seq(1,length(xsi0)), xsi0 )
-   # fix item slopes using mod2$B
-# matrix of latent regressors female, hisei and migra
-Y <- dat[, c("female", "hisei", "migra") ]
-mod2b <- TAM::tam.mml( resp=dat[,items], B=mod2a$B, xsi.fixed=xsi.fixed, Y=Y,
-            pid=dat$idstud)
-
-# plausible value imputation with normality assumption
-# and ignoring uncertainty about regression coefficients
-#    -> the default is samp.regr=FALSE
-pv2c <- TAM::tam.pv( mod2b, nplausible=10, ntheta=500, normal.approx=TRUE )
-# sampling of regression coefficients
-pv2d <- TAM::tam.pv( mod2b, nplausible=10, ntheta=500, samp.regr=TRUE)
-# sampling of regression coefficients, normal approximation using the
-# theta grid from the model
-pv2e <- TAM::tam.pv( mod2b, samp.regr=TRUE, theta.model=TRUE, normal.approx=TRUE)
-
-#--- create list of multiply imputed datasets with plausible values
-# define dataset with covariates to be matched
-Y <- dat[, c("idstud", "idschool", "female", "hisei", "migra") ]
-
-# define plausible value names
-pvnames <- c("PVREAD")
-# create list of imputed datasets
-datlist1 <- TAM::tampv2datalist( pv2e, pvnames=pvnames, Y=Y, Y.pid="idstud")
-str(datlist1)
-
-# create a matrix of covariates with different set of students than in pv2e
-Y1 <- Y[ seq( 1, 600, 2 ), ]
-# create list of multiply imputed datasets
-datlist2 <- TAM::tampv2datalist( pv2e, pvnames=c("PVREAD"), Y=Y1, Y.pid="idstud")
-
-#--- fit some models in lavaan and semTools
-library(lavaan)
-library(semTools)
-
-#*** Model 1: Linear regression
-lavmodel <- "
-   PVREAD ~ migra + hisei
-   PVREAD ~~ PVREAD
-        "
-mod1 <- semTools::lavaan.mi( lavmodel, data=datlist1, m=0)
-summary(mod1, standardized=TRUE, rsquare=TRUE)
-
-# apply lavaan for third imputed dataset
-mod1a <- lavaan::lavaan( lavmodel, data=datlist1[[3]] )
-summary(mod1a, standardized=TRUE, rsquare=TRUE)
-
-# compare with mod1 by looping over all datasets
-mod1b <- lapply( datlist1, FUN=function(dat0){
-    mod1a <- lavaan( lavmodel, data=dat0 )
-    coef( mod1a)
-        } )
-mod1b
-mod1b <- matrix( unlist( mod1b ), ncol=length( coef(mod1)), byrow=TRUE )
-mod1b
-round( colMeans(mod1b), 3 )
-coef(mod1)   # -> results coincide
-
-#*** Model 2: Path model
-lavmodel <- "
-   PVREAD ~ migra + hisei
-   hisei ~ migra
-   PVREAD ~~ PVREAD
-   hisei ~~ hisei
-        "
-mod2 <- semTools::lavaan.mi( lavmodel, data=datlist1 )
-summary(mod2, standardized=TRUE, rsquare=TRUE)
-# fit statistics
-inspect( mod2, what="fit")
-
-#--- using mitools package
-library(mitools)
-# convert datalist into an object of class imputationList
-datlist1a <- mitools::imputationList( datlist1 )
-# fit linear regression
-mod1c <- with( datlist1a, stats::lm( PVREAD ~ migra + hisei ) )
-summary( mitools::MIcombine(mod1c) )
-
-#--- using mice package
-library(mice)
-library(miceadds)
-# convert datalist into a mids object
-mids1 <- miceadds::datalist2mids( datlist1 )
-# fit linear regression
-mod1c <- with( mids1, stats::lm( PVREAD ~ migra + hisei ) )
-summary( mice::pool(mod1c) )
-
-#############################################################################
-# EXAMPLE 3: Multidimensional plausible value imputation
-#############################################################################
-
-# (1) simulate some data
-set.seed(6778)
-library(mvtnorm)
-N <- 1000
-Y <- cbind( stats::rnorm(N), stats::rnorm(N) )
-theta <- mvtnorm::rmvnorm( N, mean=c(0,0), sigma=matrix( c(1,.5,.5,1), 2, 2 ))
-theta[,1] <- theta[,1] + .4 * Y[,1] + .2 * Y[,2]  # latent regression model
-theta[,2] <- theta[,2] + .8 * Y[,1] + .5 * Y[,2]  # latent regression model
-I <- 20
-p1 <- stats::plogis( outer( theta[,1], seq( -2, 2, len=I ), "-" ) )
-resp1 <- 1 * ( p1 > matrix( stats::runif( N*I ), nrow=N, ncol=I ) )
-p1 <- stats::plogis( outer( theta[,2], seq( -2, 2, len=I ), "-" ) )
-resp2 <- 1 * ( p1 > matrix( stats::runif( N*I ), nrow=N, ncol=I ) )
-resp <- cbind(resp1,resp2)
-colnames(resp) <- paste("I", 1:(2*I), sep="")
-
-# (2) define loading Matrix
-Q <- array( 0, dim=c( 2*I, 2 ))
-Q[cbind(1:(2*I), c( rep(1,I), rep(2,I) ))] <- 1
-
-# (3) fit latent regression model
-mod <- TAM::tam.mml( resp=resp, Y=Y, Q=Q )
-
-# (4) draw plausible values
-pv1 <- TAM::tam.pv( mod, theta.model=TRUE )
-
-# (5) convert plausible values to list of imputed datasets
-Y1 <- data.frame(Y)
-colnames(Y1) <- paste0("Y",1:2)
-pvnames <- c("PVFA","PVFB")
-# create list of imputed datasets
-datlist1 <- TAM::tampv2datalist( pv1, pvnames=pvnames, Y=Y1 )
-str(datlist1)
-
-# (6) apply statistical models
-library(semTools)
-# define linear regression
-lavmodel <- "
-   PVFA ~ Y1 + Y2
-   PVFA ~~ PVFA
-        "
-mod1 <- semTools::lavaan.mi( lavmodel, data=datlist1 )
-summary(mod1, standardized=TRUE, rsquare=TRUE)
-
-# (7) draw plausible values with tam.pv.mcmc function
-Y1 <- cbind( 1, Y )
-pv2 <- TAM::tam.pv.mcmc( tamobj=mod, Y=Y1, n.iter=1000, n.burnin=200 )
-
-# (8) group-specific plausible values
-set.seed(908)
-# create artificial grouping variable
-group <- sample( 1:3, N, replace=TRUE )
-pv3 <- TAM::tam.pv.mcmc( tamobj, Y=Y1, n.iter=1000, n.burnin=200, group=group )
-
-# (9) plausible values with no fitted object in TAM
-
-# fit IRT model without covariates
-mod4a <- TAM::tam.mml( resp=resp, Q=Q )
-# define input for tam.pv.mcmc
-tamobj1 <- list( AXsi=mod4a$AXsi, B=mod4a$B, resp=mod4a$resp )
-pmod4 <- TAM::tam.pv.mcmc( tamobj1, Y=Y1 )
-
-#############################################################################
-# EXAMPLE 4: Plausible value imputation with measurement errors in covariates
-#############################################################################
-
-library(sirt)
-set.seed(7756)
-N <- 2000    # number of persons
-I <- 10     # number of items
-
-# simulate covariates
-X <- mvrnorm( N, mu=c(0,0), Sigma=matrix( c(1,.5,.5,1),2,2 ) )
-colnames(X) <- paste0("X",1:2)
-# second covariate with measurement error with variance var.err
-var.err <- .3
-X.err <- X
-X.err[,2] <-X[,2] + rnorm(N, sd=sqrt(var.err) )
-# simulate theta
-theta <- .5*X[,1] + .4*X[,2] + rnorm( N, sd=.5 )
-# simulate item responses
-itemdiff <- seq( -2, 2, length=I)  # item difficulties
-dat <- sirt::sim.raschtype( theta, b=itemdiff )
-
-#***********************
-#*** Model 0: Regression model with true variables
-mod0 <- stats::lm( theta ~ X )
-summary(mod0)
-
-#***********************
-#*** Model 1: latent regression model with true covariates X
-xsi.fixed <- cbind( 1:I, itemdiff )
-mod1 <- TAM::tam.mml( dat, xsi.fixed=xsi.fixed, Y=X)
-summary(mod1)
-
-# draw plausible values
-res1a <- TAM::tam.pv( mod1, normal.approx=TRUE, ntheta=200, samp.regr=TRUE)
-# create list of multiply imputed datasets
-library(miceadds)
-datlist1a <- TAM::tampv2datalist( res1a, Y=X )
-imp1a <- miceadds::datalist2mids( datlist1a )
-
-# fit linear model
-# linear regression with measurement errors in X
-lavmodel <- "
-   PV.Dim1 ~ X1 + X2true
-   X2true=~ 1*X2
-   X2 ~~ 0.3*X2  #=var.err
-   PV.Dim1 ~~ PV.Dim1
-   X2true ~~ X2true
-        "
-mod1a <- semTools::lavaan.mi( lavmodel, datlist1a)
-summary(mod1a, standardized=TRUE, rsquare=TRUE)
-
-#***********************
-#*** Model 2: latent regression model with error-prone covariates X.err
-mod2 <- TAM::tam.mml( dat, xsi.fixed=xsi.fixed, Y=X.err)
-summary(mod2)
-
-#***********************
-#*** Model 3: Adjustment of covariates
-
-cov.X.err <- cov( X.err )
-# matrix of variance of measurement errors
-measerr <- diag( c(0,var.err) )
-# true covariance matrix
-cov.X <- cov.X.err - measerr
-# mean of X.err
-mu <- colMeans(X.err)
-muM <- matrix( mu, nrow=nrow(X.err), ncol=ncol(X.err), byrow=TRUE)
-# reliability matrix
-W <- solve( cov.X.err ) %*% cov.X
-ident <- diag(2)
-# adjusted scores of X
-X.adj <- ( X.err - muM ) %*% W   + muM %*% ( ident - W )
-
-# fit latent regression model
-mod3 <- TAM::tam.mml( dat, xsi.fixed=xsi.fixed, Y=X.adj)
-summary(mod3)
-
-# draw plausible values
-res3a <- TAM::tam.pv( mod3, normal.approx=TRUE, ntheta=200, samp.regr=TRUE)
-
-# create list of multiply imputed datasets
-library(semTools)
-
-#*** PV dataset 1
-# datalist with error-prone covariates
-datlist3a <- TAM::tampv2datalist( res3a, Y=X.err )
-# datalist with adjusted covariates
-datlist3b <- TAM::tampv2datalist( res3a, Y=X.adj )
-
-# linear regression with measurement errors in X
-lavmodel <- "
-   PV.Dim1 ~ X1 + X2true
-   X2true=~ 1*X2
-   X2 ~~ 0.3*X2  #=var.err
-   PV.Dim1 ~~ PV.Dim1
-   X2true ~~ X2true
-        "
-mod3a <- semTools::lavaan.mi( lavmodel, datlist3a)
-summary(mod3a, standardized=TRUE, rsquare=TRUE)
-
-lavmodel <- "
-   PV.Dim1 ~ X1 + X2
-   PV.Dim1 ~~ PV.Dim1
-        "
-mod3b <- semTools::lavaan.mi( lavmodel, datlist3b)
-summary(mod3b, standardized=TRUE, rsquare=TRUE)
-#=> mod3b leads to the correct estimate.
-
-#*********************************************
-# plausible value imputation for abilities and error-prone
-# covariates using the mice package
-
-library(mice)
-library(miceadds)
-
-# creating the likelihood for plausible value for abilities
-mod11 <- TAM::tam.mml( dat, xsi.fixed=xsi.fixed )
-likePV <- IRT.likelihood(mod11)
-# creating the likelihood for error-prone covariate X2
-lavmodel <- "
-  X2true=~ 1*X2
-  X2 ~~ 0.3*X2
-    "
-mod12 <- lavaan::cfa( lavmodel, data=as.data.frame(X.err) )
-summary(mod12)
-likeX2 <- TAM::IRTLikelihood.cfa( data=X.err, cfaobj=mod12)
-str(likeX2)
-
-#-- create data input for mice package
-data <- data.frame( "PVA"=NA, "X1"=X[,1], "X2"=NA  )
-vars <- colnames(data)
-V <- length(vars)
-predictorMatrix <- 1 - diag(V)
-rownames(predictorMatrix) <- colnames(predictorMatrix) <- vars
-imputationMethod <- rep("norm", V )
-names(imputationMethod) <- vars
-imputationMethod[c("PVA","X2")] <- "plausible.values"
-
-#-- create argument lists for plausible value imputation
-# likelihood and theta grid of plausible value derived from IRT model
-like <- list( "PVA"=likePV, "X2"=likeX2 )
-theta <- list( "PVA"=attr(likePV,"theta"), "X2"=attr(likeX2, "theta") )
-#-- initial imputations
-data.init <- data
-data.init$PVA <- mod11$person$EAP
-data.init$X2 <- X.err[,"X2"]
-
-#-- imputation using the mice and miceadds package
-imp1 <- mice::mice( as.matrix(data), predictorMatrix=predictorMatrix, m=4, maxit=6,
-             method=imputationMethod,  allow.na=TRUE,
-             theta=theta, like=like, data.init=data.init )
-summary(imp1)
-
-# compute linear regression
-mod4a <- with( imp1, stats::lm( PVA ~ X1 + X2 ) )
-summary( mice::pool(mod4a) )
-}

+    

+    
Examples

+    
#############################################################################
+# EXAMPLE 1: Dichotomous unidimensional data sim.rasch
+#############################################################################
+
+data(data.sim.rasch)
+resp <- data.sim.rasch[ 1:500, 1:15 ]  # select subsample of students and items
+
+# estimate Rasch model
+mod <- TAM::tam.mml(resp)
+
+# draw 5 plausible values without a normality
+# assumption of the posterior and 2000 ability nodes
+pv1a <- TAM::tam.pv( mod, nplausible=5, ntheta=2000 )
+
+# draw 5 plausible values with a normality
+# assumption of the posterior and 500 ability nodes
+pv1b <- TAM::tam.pv( mod, nplausible=5, ntheta=500, normal.approx=TRUE )
+
+# distribution of first plausible value from imputation pv1
+hist(pv1a$pv$PV1.Dim1 )
+# boxplot of all plausible values from imputation pv2
+boxplot(pv1b$pv[, 2:6 ] )
+
+if (FALSE) {
+# draw plausible values with tam.pv.mcmc function
+Y <- matrix(1, nrow=500, ncol=1)
+pv2 <- TAM::tam.pv.mcmc( tamobj=mod, Y=Y, nplausible=5 )
+str(pv2)
+
+# summary output
+summary(pv2)
+# assessing convergence with traceplots
+plot(pv2, ask=TRUE)
+
+# use starting values for theta and MH factors which fulfill acceptance rates
+# from previously fitted model
+pv3 <- TAM::tam.pv.mcmc( tamobj=mod, Y=Y, nplausible=5, theta_init=pv2$theta_last,
+            adj_MH=pv2$theta_acceptance_MH$adj_MH )
+
+#############################################################################
+# EXAMPLE 2: Unidimensional plausible value imputation with
+#            background variables; dataset data.pisaRead from sirt package
+#############################################################################
+
+data(data.pisaRead, package="sirt")
+dat <- data.pisaRead$data
+  ##   > colnames(dat)
+  ##    [1] "idstud"   "idschool" "female"   "hisei"    "migra"    "R432Q01"
+  ##    [7] "R432Q05"  "R432Q06"  "R456Q01"  "R456Q02"  "R456Q06"  "R460Q01"
+  ##   [13] "R460Q05"  "R460Q06"  "R466Q02"  "R466Q03"  "R466Q06"
+
+## Note that reading items have variable names starting with R4
+
+# estimate 2PL model without covariates
+items <- grep("R4", colnames(dat) )    # select test items from data
+mod2a <- TAM::tam.mml.2pl( resp=dat[,items] )
+summary(mod2a)
+
+# fix item parameters for plausible value imputation
+   # fix item intercepts by defining xsi.fixed
+xsi0 <- mod2a$xsi$xsi
+xsi.fixed <- cbind( seq(1,length(xsi0)), xsi0 )
+   # fix item slopes using mod2$B
+# matrix of latent regressors female, hisei and migra
+Y <- dat[, c("female", "hisei", "migra") ]
+mod2b <- TAM::tam.mml( resp=dat[,items], B=mod2a$B, xsi.fixed=xsi.fixed, Y=Y,
+            pid=dat$idstud)
+
+# plausible value imputation with normality assumption
+# and ignoring uncertainty about regression coefficients
+#    -> the default is samp.regr=FALSE
+pv2c <- TAM::tam.pv( mod2b, nplausible=10, ntheta=500, normal.approx=TRUE )
+# sampling of regression coefficients
+pv2d <- TAM::tam.pv( mod2b, nplausible=10, ntheta=500, samp.regr=TRUE)
+# sampling of regression coefficients, normal approximation using the
+# theta grid from the model
+pv2e <- TAM::tam.pv( mod2b, samp.regr=TRUE, theta.model=TRUE, normal.approx=TRUE)
+
+#--- create list of multiply imputed datasets with plausible values
+# define dataset with covariates to be matched
+Y <- dat[, c("idstud", "idschool", "female", "hisei", "migra") ]
+
+# define plausible value names
+pvnames <- c("PVREAD")
+# create list of imputed datasets
+datlist1 <- TAM::tampv2datalist( pv2e, pvnames=pvnames, Y=Y, Y.pid="idstud")
+str(datlist1)
+
+# create a matrix of covariates with different set of students than in pv2e
+Y1 <- Y[ seq( 1, 600, 2 ), ]
+# create list of multiply imputed datasets
+datlist2 <- TAM::tampv2datalist( pv2e, pvnames=c("PVREAD"), Y=Y1, Y.pid="idstud")
+
+#--- fit some models in lavaan and semTools
+library(lavaan)
+library(semTools)
+
+#*** Model 1: Linear regression
+lavmodel <- "
+   PVREAD ~ migra + hisei
+   PVREAD ~~ PVREAD
+        "
+mod1 <- semTools::lavaan.mi( lavmodel, data=datlist1, m=0)
+summary(mod1, standardized=TRUE, rsquare=TRUE)
+
+# apply lavaan for third imputed dataset
+mod1a <- lavaan::lavaan( lavmodel, data=datlist1[[3]] )
+summary(mod1a, standardized=TRUE, rsquare=TRUE)
+
+# compare with mod1 by looping over all datasets
+mod1b <- lapply( datlist1, FUN=function(dat0){
+    mod1a <- lavaan( lavmodel, data=dat0 )
+    coef( mod1a)
+        } )
+mod1b
+mod1b <- matrix( unlist( mod1b ), ncol=length( coef(mod1)), byrow=TRUE )
+mod1b
+round( colMeans(mod1b), 3 )
+coef(mod1)   # -> results coincide
+
+#*** Model 2: Path model
+lavmodel <- "
+   PVREAD ~ migra + hisei
+   hisei ~ migra
+   PVREAD ~~ PVREAD
+   hisei ~~ hisei
+        "
+mod2 <- semTools::lavaan.mi( lavmodel, data=datlist1 )
+summary(mod2, standardized=TRUE, rsquare=TRUE)
+# fit statistics
+inspect( mod2, what="fit")
+
+#--- using mitools package
+library(mitools)
+# convert datalist into an object of class imputationList
+datlist1a <- mitools::imputationList( datlist1 )
+# fit linear regression
+mod1c <- with( datlist1a, stats::lm( PVREAD ~ migra + hisei ) )
+summary( mitools::MIcombine(mod1c) )
+
+#--- using mice package
+library(mice)
+library(miceadds)
+# convert datalist into a mids object
+mids1 <- miceadds::datalist2mids( datlist1 )
+# fit linear regression
+mod1c <- with( mids1, stats::lm( PVREAD ~ migra + hisei ) )
+summary( mice::pool(mod1c) )
+
+#############################################################################
+# EXAMPLE 3: Multidimensional plausible value imputation
+#############################################################################
+
+# (1) simulate some data
+set.seed(6778)
+library(mvtnorm)
+N <- 1000
+Y <- cbind( stats::rnorm(N), stats::rnorm(N) )
+theta <- mvtnorm::rmvnorm( N, mean=c(0,0), sigma=matrix( c(1,.5,.5,1), 2, 2 ))
+theta[,1] <- theta[,1] + .4 * Y[,1] + .2 * Y[,2]  # latent regression model
+theta[,2] <- theta[,2] + .8 * Y[,1] + .5 * Y[,2]  # latent regression model
+I <- 20
+p1 <- stats::plogis( outer( theta[,1], seq( -2, 2, len=I ), "-" ) )
+resp1 <- 1 * ( p1 > matrix( stats::runif( N*I ), nrow=N, ncol=I ) )
+p1 <- stats::plogis( outer( theta[,2], seq( -2, 2, len=I ), "-" ) )
+resp2 <- 1 * ( p1 > matrix( stats::runif( N*I ), nrow=N, ncol=I ) )
+resp <- cbind(resp1,resp2)
+colnames(resp) <- paste("I", 1:(2*I), sep="")
+
+# (2) define loading Matrix
+Q <- array( 0, dim=c( 2*I, 2 ))
+Q[cbind(1:(2*I), c( rep(1,I), rep(2,I) ))] <- 1
+
+# (3) fit latent regression model
+mod <- TAM::tam.mml( resp=resp, Y=Y, Q=Q )
+
+# (4) draw plausible values
+pv1 <- TAM::tam.pv( mod, theta.model=TRUE )
+
+# (5) convert plausible values to list of imputed datasets
+Y1 <- data.frame(Y)
+colnames(Y1) <- paste0("Y",1:2)
+pvnames <- c("PVFA","PVFB")
+# create list of imputed datasets
+datlist1 <- TAM::tampv2datalist( pv1, pvnames=pvnames, Y=Y1 )
+str(datlist1)
+
+# (6) apply statistical models
+library(semTools)
+# define linear regression
+lavmodel <- "
+   PVFA ~ Y1 + Y2
+   PVFA ~~ PVFA
+        "
+mod1 <- semTools::lavaan.mi( lavmodel, data=datlist1 )
+summary(mod1, standardized=TRUE, rsquare=TRUE)
+
+# (7) draw plausible values with tam.pv.mcmc function
+Y1 <- cbind( 1, Y )
+pv2 <- TAM::tam.pv.mcmc( tamobj=mod, Y=Y1, n.iter=1000, n.burnin=200 )
+
+# (8) group-specific plausible values
+set.seed(908)
+# create artificial grouping variable
+group <- sample( 1:3, N, replace=TRUE )
+pv3 <- TAM::tam.pv.mcmc( tamobj, Y=Y1, n.iter=1000, n.burnin=200, group=group )
+
+# (9) plausible values with no fitted object in TAM
+
+# fit IRT model without covariates
+mod4a <- TAM::tam.mml( resp=resp, Q=Q )
+# define input for tam.pv.mcmc
+tamobj1 <- list( AXsi=mod4a$AXsi, B=mod4a$B, resp=mod4a$resp )
+pmod4 <- TAM::tam.pv.mcmc( tamobj1, Y=Y1 )
+
+#############################################################################
+# EXAMPLE 4: Plausible value imputation with measurement errors in covariates
+#############################################################################
+
+library(sirt)
+set.seed(7756)
+N <- 2000    # number of persons
+I <- 10     # number of items
+
+# simulate covariates
+X <- mvrnorm( N, mu=c(0,0), Sigma=matrix( c(1,.5,.5,1),2,2 ) )
+colnames(X) <- paste0("X",1:2)
+# second covariate with measurement error with variance var.err
+var.err <- .3
+X.err <- X
+X.err[,2] <-X[,2] + rnorm(N, sd=sqrt(var.err) )
+# simulate theta
+theta <- .5*X[,1] + .4*X[,2] + rnorm( N, sd=.5 )
+# simulate item responses
+itemdiff <- seq( -2, 2, length=I)  # item difficulties
+dat <- sirt::sim.raschtype( theta, b=itemdiff )
+
+#***********************
+#*** Model 0: Regression model with true variables
+mod0 <- stats::lm( theta ~ X )
+summary(mod0)
+
+#***********************
+#*** Model 1: latent regression model with true covariates X
+xsi.fixed <- cbind( 1:I, itemdiff )
+mod1 <- TAM::tam.mml( dat, xsi.fixed=xsi.fixed, Y=X)
+summary(mod1)
+
+# draw plausible values
+res1a <- TAM::tam.pv( mod1, normal.approx=TRUE, ntheta=200, samp.regr=TRUE)
+# create list of multiply imputed datasets
+library(miceadds)
+datlist1a <- TAM::tampv2datalist( res1a, Y=X )
+imp1a <- miceadds::datalist2mids( datlist1a )
+
+# fit linear model
+# linear regression with measurement errors in X
+lavmodel <- "
+   PV.Dim1 ~ X1 + X2true
+   X2true=~ 1*X2
+   X2 ~~ 0.3*X2  #=var.err
+   PV.Dim1 ~~ PV.Dim1
+   X2true ~~ X2true
+        "
+mod1a <- semTools::lavaan.mi( lavmodel, datlist1a)
+summary(mod1a, standardized=TRUE, rsquare=TRUE)
+
+#***********************
+#*** Model 2: latent regression model with error-prone covariates X.err
+mod2 <- TAM::tam.mml( dat, xsi.fixed=xsi.fixed, Y=X.err)
+summary(mod2)
+
+#***********************
+#*** Model 3: Adjustment of covariates
+
+cov.X.err <- cov( X.err )
+# matrix of variance of measurement errors
+measerr <- diag( c(0,var.err) )
+# true covariance matrix
+cov.X <- cov.X.err - measerr
+# mean of X.err
+mu <- colMeans(X.err)
+muM <- matrix( mu, nrow=nrow(X.err), ncol=ncol(X.err), byrow=TRUE)
+# reliability matrix
+W <- solve( cov.X.err ) %*% cov.X
+ident <- diag(2)
+# adjusted scores of X
+X.adj <- ( X.err - muM ) %*% W   + muM %*% ( ident - W )
+
+# fit latent regression model
+mod3 <- TAM::tam.mml( dat, xsi.fixed=xsi.fixed, Y=X.adj)
+summary(mod3)
+
+# draw plausible values
+res3a <- TAM::tam.pv( mod3, normal.approx=TRUE, ntheta=200, samp.regr=TRUE)
+
+# create list of multiply imputed datasets
+library(semTools)
+
+#*** PV dataset 1
+# datalist with error-prone covariates
+datlist3a <- TAM::tampv2datalist( res3a, Y=X.err )
+# datalist with adjusted covariates
+datlist3b <- TAM::tampv2datalist( res3a, Y=X.adj )
+
+# linear regression with measurement errors in X
+lavmodel <- "
+   PV.Dim1 ~ X1 + X2true
+   X2true=~ 1*X2
+   X2 ~~ 0.3*X2  #=var.err
+   PV.Dim1 ~~ PV.Dim1
+   X2true ~~ X2true
+        "
+mod3a <- semTools::lavaan.mi( lavmodel, datlist3a)
+summary(mod3a, standardized=TRUE, rsquare=TRUE)
+
+lavmodel <- "
+   PV.Dim1 ~ X1 + X2
+   PV.Dim1 ~~ PV.Dim1
+        "
+mod3b <- semTools::lavaan.mi( lavmodel, datlist3b)
+summary(mod3b, standardized=TRUE, rsquare=TRUE)
+#=> mod3b leads to the correct estimate.
+
+#*********************************************
+# plausible value imputation for abilities and error-prone
+# covariates using the mice package
+
+library(mice)
+library(miceadds)
+
+# creating the likelihood for plausible value for abilities
+mod11 <- TAM::tam.mml( dat, xsi.fixed=xsi.fixed )
+likePV <- IRT.likelihood(mod11)
+# creating the likelihood for error-prone covariate X2
+lavmodel <- "
+  X2true=~ 1*X2
+  X2 ~~ 0.3*X2
+    "
+mod12 <- lavaan::cfa( lavmodel, data=as.data.frame(X.err) )
+summary(mod12)
+likeX2 <- TAM::IRTLikelihood.cfa( data=X.err, cfaobj=mod12)
+str(likeX2)
+
+#-- create data input for mice package
+data <- data.frame( "PVA"=NA, "X1"=X[,1], "X2"=NA  )
+vars <- colnames(data)
+V <- length(vars)
+predictorMatrix <- 1 - diag(V)
+rownames(predictorMatrix) <- colnames(predictorMatrix) <- vars
+imputationMethod <- rep("norm", V )
+names(imputationMethod) <- vars
+imputationMethod[c("PVA","X2")] <- "plausible.values"
+
+#-- create argument lists for plausible value imputation
+# likelihood and theta grid of plausible value derived from IRT model
+like <- list( "PVA"=likePV, "X2"=likeX2 )
+theta <- list( "PVA"=attr(likePV,"theta"), "X2"=attr(likeX2, "theta") )
+#-- initial imputations
+data.init <- data
+data.init$PVA <- mod11$person$EAP
+data.init$X2 <- X.err[,"X2"]
+
+#-- imputation using the mice and miceadds package
+imp1 <- mice::mice( as.matrix(data), predictorMatrix=predictorMatrix, m=4, maxit=6,
+             method=imputationMethod,  allow.na=TRUE,
+             theta=theta, like=like, data.init=data.init )
+summary(imp1)
+
+# compute linear regression
+mod4a <- with( imp1, stats::lm( PVA ~ X1 + X2 ) )
+summary( mice::pool(mod4a) )
+}

+    

   

   
+    

 

 
 
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-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
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-   

+      

 
   
 
 
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+  
 
+  
 
diff --git a/docs/reference/tam.se.html b/docs/reference/tam.se.html
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Standard Error Estimation

@@ -119,135 +51,139 @@ 
Standard Error Estimation

 and tam.mml.

     

 
-    
tam.se(tamobj, item_pars=TRUE, ...)
-
-tam_mml_se_quick(tamobj, numdiff.parm=0.001, item_pars=TRUE )
-
-tam_latreg_se_quick(tamobj, numdiff.parm=0.001 )

-
-    
Arguments

-    
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tamobj
An object generated by tam.mml
item_pars
Logical indicating whether standard errors should also
-be computed for item parameters
numdiff.parm
Step width parameter for numerical
-  differentiation
...
Further arguments to be passed

-
-    
Details

+    

+    
tam.se(tamobj, item_pars=TRUE, ...)
+
+tam_mml_se_quick(tamobj, numdiff.parm=0.001, item_pars=TRUE )
+
+tam_latreg_se_quick(tamobj, numdiff.parm=0.001 )

+    

+
+    

+    
Arguments

+    
tamobj

+
An object generated by tam.mml

+
+
item_pars

+
Logical indicating whether standard errors should also
+be computed for item parameters

+
+
numdiff.parm

+
Step width parameter for numerical
+  differentiation

 
+
...

+
Further arguments to be passed

+
+

+    

+    
Details

     
Covariances between parameters estimates are ignored in this standard
 error calculation. The standard error is obtained by numerical
 differentiation.

-    
Value

+    

+    

+    
Value

+    
 
-    
A list with following entries:

-
xsi
Data frame with \(\xi\) parameters (est)
+
A list with following entries:

+
xsi

+
Data frame with \(\xi\) parameters (est)
     and their corresponding standard errors (se)

-
beta
Data frame with \(\beta\) regression parameters and
+
+
beta

+
Data frame with \(\beta\) regression parameters and
     their standard error estimates

-
B
Data frame with loading  parameters and their
-    corresponding standard errors

 
-    
Note

+
B

+
Data frame with loading  parameters and their
+    corresponding standard errors

 
+

+    

+    
Note

     
Standard error estimation for variances and covariances is not yet
 implemented.
 Standard error estimation for loading parameters in case of
 irtmodel='GPCM.design' is highly experimental.

+    

 
-    
Examples

-    
#############################################################################
-# EXAMPLE 1: 1PL model, data.sim.rasch
-#############################################################################
-
-data(data.sim.rasch)
-# estimate Rasch model
-mod1 <- TAM::tam.mml(resp=data.sim.rasch[1:500,1:10])
-# standard error estimation
-se1 <- TAM::tam.se( mod1 )
-# proportion of standard errors estimated by 'tam.se' and 'tam.mml'
-prop1 <- se1$xsi$se / mod1$xsi$se
-##   > summary( prop1 )
-##      Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
-##     1.030   1.034   1.035   1.036   1.039   1.042
-##=> standard errors estimated by tam.se are a bit larger
-
-if (FALSE) {
-#############################################################################
-# EXAMPLE 2: Standard errors differential item functioning
-#############################################################################
-data(data.ex08)
-
-formulaA <- ~ item*female
-resp <- data.ex08[["resp"]]
-facets <- as.data.frame( data.ex08[["facets"]] )
-# investigate DIF
-mod <- TAM::tam.mml.mfr( resp=resp, facets=facets, formulaA=formulaA )
-summary(mod)
-# estimate standard errors
-semod <- TAM::tam.se(mod)
-prop1 <- semod$xsi$se / mod$xsi$se
-summary(prop1)
-# plot differences in standard errors
-plot( mod$xsi$se, semod$xsi$se, pch=16, xlim=c(0,.15), ylim=c(0,.15),
-    xlab="Standard error 'tam.mml'", ylab="Standard error 'tam.se'" )
-lines( c(-6,6), c(-6,6), col="gray")
-
-round( cbind( mod$xsi, semod$xsi[,-1] ), 3 )
-  ##                    xsi se.xsi   N    est    se
-  ##   I0001         -1.956  0.092 500 -1.956 0.095
-  ##   I0002         -1.669  0.085 500 -1.669 0.088
-  ##   [...]
-  ##   I0010          2.515  0.108 500  2.515 0.110
-  ##   female1       -0.091  0.025 500 -0.091 0.041
-  ##   I0001:female1 -0.051  0.070 500 -0.051 0.071
-  ##   I0002:female1  0.085  0.067 500  0.085 0.068
-  ##   [...]
-  ##   I0009:female1 -0.019  0.068 500 -0.019 0.068
-  ##
-#=> The largest discrepancy in standard errors is observed for the
-#    main female effect (.041 in 'tam.se' instead of .025 in 'tam.mml')
-}

+    

+    
Examples

+    
#############################################################################
+# EXAMPLE 1: 1PL model, data.sim.rasch
+#############################################################################
+
+data(data.sim.rasch)
+# estimate Rasch model
+mod1 <- TAM::tam.mml(resp=data.sim.rasch[1:500,1:10])
+# standard error estimation
+se1 <- TAM::tam.se( mod1 )
+# proportion of standard errors estimated by 'tam.se' and 'tam.mml'
+prop1 <- se1$xsi$se / mod1$xsi$se
+##   > summary( prop1 )
+##      Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
+##     1.030   1.034   1.035   1.036   1.039   1.042
+##=> standard errors estimated by tam.se are a bit larger
+
+if (FALSE) {
+#############################################################################
+# EXAMPLE 2: Standard errors differential item functioning
+#############################################################################
+data(data.ex08)
+
+formulaA <- ~ item*female
+resp <- data.ex08[["resp"]]
+facets <- as.data.frame( data.ex08[["facets"]] )
+# investigate DIF
+mod <- TAM::tam.mml.mfr( resp=resp, facets=facets, formulaA=formulaA )
+summary(mod)
+# estimate standard errors
+semod <- TAM::tam.se(mod)
+prop1 <- semod$xsi$se / mod$xsi$se
+summary(prop1)
+# plot differences in standard errors
+plot( mod$xsi$se, semod$xsi$se, pch=16, xlim=c(0,.15), ylim=c(0,.15),
+    xlab="Standard error 'tam.mml'", ylab="Standard error 'tam.se'" )
+lines( c(-6,6), c(-6,6), col="gray")
+
+round( cbind( mod$xsi, semod$xsi[,-1] ), 3 )
+  ##                    xsi se.xsi   N    est    se
+  ##   I0001         -1.956  0.092 500 -1.956 0.095
+  ##   I0002         -1.669  0.085 500 -1.669 0.088
+  ##   [...]
+  ##   I0010          2.515  0.108 500  2.515 0.110
+  ##   female1       -0.091  0.025 500 -0.091 0.041
+  ##   I0001:female1 -0.051  0.070 500 -0.051 0.071
+  ##   I0002:female1  0.085  0.067 500  0.085 0.068
+  ##   [...]
+  ##   I0009:female1 -0.019  0.068 500 -0.019 0.068
+  ##
+#=> The largest discrepancy in standard errors is observed for the
+#    main female effect (.041 in 'tam.se' instead of .025 in 'tam.mml')
+}

+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/reference/tam.threshold.html b/docs/reference/tam.threshold.html
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Calculation of Thurstonian Thresholds

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Calculation of Thurstonian Thresholds

 parameters of (generalized) partial credit models (see Details).

     

 
-    
tam.threshold(tamobj, prob.lvl=0.5)

+    

+    
tam.threshold(tamobj, prob.lvl=0.5)

+    

 
-    
Arguments

-    
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
tamobj
Object of class tam
prob.lvl
A numeric specifying the probability level of the threshold.
-The default is prob.lvl=0.5.

+    

+    
Arguments

+    
tamobj

+
Object of class tam

 
-    
Details

+
prob.lvl

+
A numeric specifying the probability level of the threshold.
+The default is prob.lvl=0.5.

 
+

+    

+    
Details

     
This function only works appropriately for unidimensional models
 or between item multidimensional models.

-    
Value

+    

+    

+    
Value

+    
 
-    
A data frame with Thurstonian thresholds. Rows correspond to items and
+
A data frame with Thurstonian thresholds. Rows correspond to items and
 columns to item steps.

-    
See also

-
-    
See the WrightMap package and Example 3 for creating Wright maps
+    

+    

+    
See also

+    
See the WrightMap package and Example 3 for creating Wright maps
 with fitted models in TAM, see
-wrightMap.

-
-    
Examples

-    
#############################################################################
-# EXAMPLE 1: ordered data - Partial credit model
-#############################################################################
-data( data.gpcm )
-
-# Model 1: partial credit model
-mod1 <- TAM::tam.mml( resp=data.gpcm,control=list( maxiter=200) )
-summary(mod1)
-  ##   Item Parameters -A*Xsi
-  ##        item   N     M AXsi_.Cat1 AXsi_.Cat2 AXsi_.Cat3 B.Cat1.Dim1 B.Cat2.Dim1 B.Cat3.Dim1
-  ##   1 Comfort 392 0.880     -1.302      1.154      3.881           1           2           3
-  ##   2    Work 392 1.278     -1.706     -0.847      0.833           1           2           3
-  ##   3 Benefit 392 1.163     -1.233     -0.404      1.806           1           2           3
-
-# Calculation of Thurstonian thresholds
-TAM::tam.threshold(mod1)
-  ##                Cat1      Cat2     Cat3
-  ##   Comfort -1.325226 2.0717468 3.139801
-  ##   Work    -1.777679 0.6459045 1.971222
-  ##   Benefit -1.343536 0.7491760 2.403168
-
-if (FALSE) {
-#############################################################################
-# EXAMPLE 2: Multidimensional model data.math
-#############################################################################
-
-library(sirt)
-data(data.math, package="sirt")
-dat <- data.math$data
-# select items
-items1 <- grep("M[A-D]", colnames(dat), value=TRUE)
-items2 <- grep("M[H-I]", colnames(dat), value=TRUE)
-# select dataset
-dat <- dat[ c(items1,items2)]
-# create Q-matrix
-Q <- matrix( 0, nrow=ncol(dat), ncol=2 )
-Q[ seq(1,length(items1) ), 1 ] <- 1
-Q[ length(items1) + seq(1,length(items2) ), 2 ] <- 1
-
-# fit two-dimensional model
-mod1 <- TAM::tam.mml( dat, Q=Q )
-# compute thresholds (specify a probability level of .625)
-tmod1 <- TAM::tam.threshold( mod1, prob.lvl=.625 )
-
-#############################################################################
-# EXAMPLE 3: Creating Wright maps with the WrightMap package
-#############################################################################
-
-library(WrightMap)
-# For conducting Wright maps in combination with TAM, see
-# http://wrightmap.org/post/100850738072/using-wrightmap-with-the-tam-package
-data(sim.rasch)
-dat <- sim.rasch
-
-# estimate Rasch model in TAM
-mod1 <- TAM::tam.mml(dat)
-summary(mod1)
-
-#--- A: creating a Wright map with WLEs
-
-# compute WLE
-wlemod1 <- TAM::tam.wle(mod1)$theta
-# extract thresholds
-tmod1 <- TAM::tam.threshold(mod1)
-# create Wright map
-WrightMap::wrightMap( thetas=wlemod1, thresholds=tmod1, label.items.srt=-90)
-
-#--- B: creating a Wright Map with population distribution
-
-# extract ability distribution and replicate observations
-uni.proficiency <- rep( mod1$theta[,1], round( mod1$pi.k * mod1$ic$n) )
-# draw WrightMap
-WrightMap::wrightMap( thetas=uni.proficiency, thresholds=tmod1, label.items.rows=3)
-}

+wrightMap.

+    

+
+    

+    
Examples

+    
#############################################################################
+# EXAMPLE 1: ordered data - Partial credit model
+#############################################################################
+data( data.gpcm )
+
+# Model 1: partial credit model
+mod1 <- TAM::tam.mml( resp=data.gpcm,control=list( maxiter=200) )
+summary(mod1)
+  ##   Item Parameters -A*Xsi
+  ##        item   N     M AXsi_.Cat1 AXsi_.Cat2 AXsi_.Cat3 B.Cat1.Dim1 B.Cat2.Dim1 B.Cat3.Dim1
+  ##   1 Comfort 392 0.880     -1.302      1.154      3.881           1           2           3
+  ##   2    Work 392 1.278     -1.706     -0.847      0.833           1           2           3
+  ##   3 Benefit 392 1.163     -1.233     -0.404      1.806           1           2           3
+
+# Calculation of Thurstonian thresholds
+TAM::tam.threshold(mod1)
+  ##                Cat1      Cat2     Cat3
+  ##   Comfort -1.325226 2.0717468 3.139801
+  ##   Work    -1.777679 0.6459045 1.971222
+  ##   Benefit -1.343536 0.7491760 2.403168
+
+if (FALSE) {
+#############################################################################
+# EXAMPLE 2: Multidimensional model data.math
+#############################################################################
+
+library(sirt)
+data(data.math, package="sirt")
+dat <- data.math$data
+# select items
+items1 <- grep("M[A-D]", colnames(dat), value=TRUE)
+items2 <- grep("M[H-I]", colnames(dat), value=TRUE)
+# select dataset
+dat <- dat[ c(items1,items2)]
+# create Q-matrix
+Q <- matrix( 0, nrow=ncol(dat), ncol=2 )
+Q[ seq(1,length(items1) ), 1 ] <- 1
+Q[ length(items1) + seq(1,length(items2) ), 2 ] <- 1
+
+# fit two-dimensional model
+mod1 <- TAM::tam.mml( dat, Q=Q )
+# compute thresholds (specify a probability level of .625)
+tmod1 <- TAM::tam.threshold( mod1, prob.lvl=.625 )
+
+#############################################################################
+# EXAMPLE 3: Creating Wright maps with the WrightMap package
+#############################################################################
+
+library(WrightMap)
+# For conducting Wright maps in combination with TAM, see
+# http://wrightmap.org/post/100850738072/using-wrightmap-with-the-tam-package
+data(sim.rasch)
+dat <- sim.rasch
+
+# estimate Rasch model in TAM
+mod1 <- TAM::tam.mml(dat)
+summary(mod1)
+
+#--- A: creating a Wright map with WLEs
+
+# compute WLE
+wlemod1 <- TAM::tam.wle(mod1)$theta
+# extract thresholds
+tmod1 <- TAM::tam.threshold(mod1)
+# create Wright map
+WrightMap::wrightMap( thetas=wlemod1, thresholds=tmod1, label.items.srt=-90)
+
+#--- B: creating a Wright Map with population distribution
+
+# extract ability distribution and replicate observations
+uni.proficiency <- rep( mod1$theta[,1], round( mod1$pi.k * mod1$ic$n) )
+# draw WrightMap
+WrightMap::wrightMap( thetas=uni.proficiency, thresholds=tmod1, label.items.rows=3)
+}

+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/reference/tam.wle.html b/docs/reference/tam.wle.html
index 1529fbb..106f92e 100644
--- a/docs/reference/tam.wle.html
+++ b/docs/reference/tam.wle.html
@@ -1,71 +1,16 @@
-
 
-
-  
-  
-
-
-
-Weighted Likelihood Estimation and Maximum Likelihood Estimation of
-Person Parameters — tam.wle • TAM
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-Weighted Likelihood Estimation and Maximum Likelihood Estimation of
+Person Parameters — tam.wle • TAM
-
-
-
-
-
-
-
-
-
-
-
-
-  
+
+    
 
-  
     

-      

-      
 
       
 
-      

-
-

+      

   

     

     
Weighted Likelihood Estimation and Maximum Likelihood Estimation of
@@ -124,369 +56,370 @@ 
Weighted Likelihood Estimation and Maximum Likelihood Estimation of
 respectively.

     

 
-    
tam.wle(tamobj, ...)
-
-tam.mml.wle( tamobj, score.resp=NULL, WLE=TRUE, adj=.3, Msteps=20,
-       convM=.0001, progress=TRUE,    output.prob=FALSE )
-
-tam.mml.wle2(tamobj, score.resp=NULL, WLE=TRUE, adj=0.3, Msteps=20, convM=1e-04,
-        progress=TRUE, output.prob=FALSE, pid=NULL )
-
-tam_jml_wle(tamobj, resp, resp.ind, A, B, nstud, nitems, maxK, convM,
-    PersonScores, theta, xsi, Msteps, WLE=FALSE, theta.fixed=NULL, progress=FALSE,
-    output.prob=TRUE, damp=0, version=2)
-
-# S3 method for tam.wle
-summary(object, file=NULL, digits=3, ...)
-
-# S3 method for tam.wle
-print(x, digits=3, ...)

+    

+    
tam.wle(tamobj, ...)
+
+tam.mml.wle( tamobj, score.resp=NULL, WLE=TRUE, adj=.3, Msteps=20,
+       convM=.0001, progress=TRUE,    output.prob=FALSE )
+
+tam.mml.wle2(tamobj, score.resp=NULL, WLE=TRUE, adj=0.3, Msteps=20, convM=1e-04,
+        progress=TRUE, output.prob=FALSE, pid=NULL, theta_init=NULL )
+
+tam_jml_wle(tamobj, resp, resp.ind, A, B, nstud, nitems, maxK, convM,
+    PersonScores, theta, xsi, Msteps, WLE=FALSE, theta.fixed=NULL, progress=FALSE,
+    output.prob=TRUE, damp=0, version=2, theta_proc=NULL)
+
+# S3 method for tam.wle
+summary(object, file=NULL, digits=3, ...)
+
+# S3 method for tam.wle
+print(x, digits=3, ...)

+    

 
-    
Arguments

-    
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
tamobj
An object generated by tam.mml or tam.jml. The object can also
+    

+    
Arguments

+    
tamobj

+
An object generated by tam.mml or tam.jml. The object can also
      be a list containing (at least the) inputs AXsi, B and
      resp and therefore allows WLE estimation without fitting models
-     in TAM.
score.resp
An optional data frame for which WLEs or MLEs
+     in TAM.

+
+
score.resp

+
An optional data frame for which WLEs or MLEs
     should be calculated. In case of the default NULL,
     resp from tamobj (i.e. tamobj$resp) is chosen.
     Note that items in score.resp must be the same (and in the
-    same order) as in tamobj$resp.
WLE
A logical indicating whether the weighted likelihood estimate
+    same order) as in tamobj$resp.

+
+  
WLE

+
A logical indicating whether the weighted likelihood estimate
      (WLE, WLE=TRUE) or the maximum likelihood estimate (MLE, WLE=FALSE)
-     should be used.
adj
Adjustment in MLE estimation for extreme scores (i.e. all or none
+     should be used.

+
+  
adj

+
Adjustment in MLE estimation for extreme scores (i.e. all or none
      items were correctly solved). This argument is not used if
-     WLE=TRUE.
Msteps
Maximum number of iterations
convM
Convergence criterion
progress
Logical indicating whether progress should be displayed.
output.prob
Logical indicating whether evaluated probabilities should
-be included in the list of outputs.
pid
Optional vector of person identifiers
resp
Data frame with item responses (only for tam.jml.WLE)
resp.ind
Data frame with response indicators (only for tam.jml.WLE)
A
Design matrix \(A\) (applies only to tam.jml.WLE)
B
Design matrix \(B\) (applies only to tam.jml.WLE)
nstud
Number of persons (applies only to tam.jml.WLE)
nitems
Number of items (applies only to tam.jml.WLE)
maxK
Maximum item score (applies only to tam.jml.WLE)
PersonScores
A vector containing the sufficient statistics for the
-    person parameters (applies only to tam.jml.WLE)
theta
Initial \(\theta\) estimate (applies only to tam.jml.WLE)
xsi
Parameter vector \(\xi\) (applies only to tam.jml.WLE)
theta.fixed
Matrix for fixed person parameters \(\theta\). The first
+     WLE=TRUE.

+
+  
Msteps

+
Maximum number of iterations

+
+  
convM

+
Convergence criterion

+
+
progress

+
Logical indicating whether progress should be displayed.

+
+
output.prob

+
Logical indicating whether evaluated probabilities should
+be included in the list of outputs.

+
+
pid

+
Optional vector of person identifiers

+
+
theta_init

+
Initial theta values

+
+
resp

+
Data frame with item responses (only for tam.jml.WLE)

+
+
resp.ind

+
Data frame with response indicators (only for tam.jml.WLE)

+
+
A

+
Design matrix \(A\) (applies only to tam.jml.WLE)

+
+
B

+
Design matrix \(B\) (applies only to tam.jml.WLE)

+
+
nstud

+
Number of persons (applies only to tam.jml.WLE)

+
+
nitems

+
Number of items (applies only to tam.jml.WLE)

+
+
maxK

+
Maximum item score (applies only to tam.jml.WLE)

+
+
PersonScores

+
A vector containing the sufficient statistics for the
+    person parameters (applies only to tam.jml.WLE)

+
+
theta

+
Initial \(\theta\) estimate (applies only to tam.jml.WLE)

+
+
xsi

+
Parameter vector \(\xi\) (applies only to tam.jml.WLE)

+
+
theta.fixed

+
Matrix for fixed person parameters \(\theta\). The first
     column includes the index whereas the second column includes
-the fixed value.
damp
Numeric value between 0 and 1 indicating amount of dampening
-increments in \(\theta\) estimates during iterations
version
Integer with possible values 2 or 3. In case of missing item responses,
-version=3 will typically be more efficient.
...
Further arguments to be passed
object
Object of class tam.wle
x
Object of class tam.wle
file
Optional file name in which the object summary should be written.
digits
Number of digits for rounding

-
-    
Value

-
-    
For tam.wle.mml and tam.wle.mml2, it is a data frame with following
+the fixed value.

+
+
damp

+
Numeric value between 0 and 1 indicating amount of dampening
+increments in \(\theta\) estimates during iterations

+
+
version

+
Integer with possible values 2 or 3. In case of missing item responses,
+version=3 will typically be more efficient.

+
+
theta_proc

+
Function for processing theta within iterations.

+
+
...

+
Further arguments to be passed

+
+
object

+
Object of class tam.wle

+
+
x

+
Object of class tam.wle

+
+
file

+
Optional file name in which the object summary should be written.

+
+
digits

+
Number of digits for rounding

+
+

+    

+    
Value

+    
+
+
For tam.wle.mml and tam.wle.mml2, it is a data frame with following
 columns:

-
pid
Person identifier

-
PersonScores
Score of each person

-
PersonMax
Maximum score of each person

-
theta
Weighted likelihood estimate (WLE) or MLE

-
error
Standard error of the WLE or MLE

-
WLE.rel
WLE reliability (same value for all persons)
 
-
-For tam.jml.WLE, it is a list with following entries:
-
theta
Weighted likelihood estimate (WLE) or MLE

-
errorWLE
Standard error of the WLE or MLE

-
meanChangeWLE
Mean change between updated and previous ability
-    estimates from last iteration

+
pid

+
Person identifier

+
+
PersonScores

+
Score of each person

+
+
PersonMax

+
Maximum score of each person

+
+
theta

+
Weighted likelihood estimate (WLE) or MLE

+
+
error

+
Standard error of the WLE or MLE

+
+
WLE.rel

+
WLE reliability (same value for all persons)

+ 


+
+
 
-    
References

+
For tam.jml.WLE, it is a list with following entries:

+
theta

+
Weighted likelihood estimate (WLE) or MLE

 
+
errorWLE

+
Standard error of the WLE or MLE

+
+
meanChangeWLE

+
Mean change between updated and previous ability
+    estimates from last iteration

+
+

+    

+    
References

     
Penfield, R. D., & Bergeron, J. M. (2005). Applying a weighted maximum
 likelihood latent trait estimator to the generalized partial credit model.
 Applied Psychological Measurement, 29, 218-233.

 
Warm, T. A. (1989). Weighted likelihood estimation of ability in item
 response theory. Psychometrika, 54, 427-450.
-doi: 10.1007/BF02294627

-    
See also

-
-    
See the PP::PP_gpcm function
+doi:10.1007/BF02294627

+    

+    

+    
See also

+    
See the PP::PP_gpcm function
 in the PP package for more person
 parameter estimators for the partial credit model (Penfield & Bergeron, 2005).

-
See the S3 method IRT.factor.scores.tam.

-
-    
Examples

-    
#############################################################################
-# EXAMPLE 1: 1PL model, data.sim.rasch
-#############################################################################
-
-data(data.sim.rasch)
-# estimate Rasch model
-mod1 <- TAM::tam.mml(resp=data.sim.rasch)
-# WLE estimation
-wle1 <- TAM::tam.wle( mod1 )
-  ## WLE Reliability=0.894
-
-print(wle1)
-summary(wle1)
-
-# scoring for a different dataset containing same items (first 10 persons in sim.rasch)
-wle2 <- TAM::tam.wle( mod1, score.resp=data.sim.rasch[1:10,])
-
-#--- WLE estimation without using a TAM object
-
-#* create an input list
-input <- list( resp=data.sim.rasch, AXsi=mod1$AXsi, B=mod1$B )
-#* estimation
-wle2b <- TAM::tam.mml.wle2( input )
-
-if (FALSE) {
-#############################################################################
-# EXAMPLE 2: 3-dimensional Rasch model | data.read from sirt package
-#############################################################################
-
-data(data.read, package="sirt")
-# define Q-matrix
-Q <- matrix(0,12,3)
-Q[ cbind( 1:12, rep(1:3,each=4) ) ] <- 1
-# redefine data: create some missings for first three cases
-resp <- data.read
-resp[1:2, 5:12] <- NA
-resp[3,1:4] <- NA
-  ##   > head(resp)
-  ##      A1 A2 A3 A4 B1 B2 B3 B4 C1 C2 C3 C4
-  ##   2   1  1  1  1 NA NA NA NA NA NA NA NA
-  ##   22  1  1  0  0 NA NA NA NA NA NA NA NA
-  ##   23 NA NA NA NA  1  0  1  1  1  1  1  1
-  ##   41  1  1  1  1  1  1  1  1  1  1  1  1
-  ##   43  1  0  0  1  0  0  1  1  1  0  1  0
-  ##   63  1  1  0  0  1  0  1  1  1  1  1  1
-
-# estimate 3-dimensional Rasch model
-mod <- TAM::tam.mml( resp=resp, Q=Q, control=list(snodes=1000,maxiter=50) )
-summary(mod)
-
-# WLE estimates
-wmod <- TAM::tam.wle(mod, Msteps=3)
-summary(wmod)
-  ##   head(round(wmod,2))
-  ##      pid N.items PersonScores.Dim01 PersonScores.Dim02 PersonScores.Dim03
-  ##   2    1       4                3.7                0.3                0.3
-  ##   22   2       4                2.0                0.3                0.3
-  ##   23   3       8                0.3                3.0                3.7
-  ##   41   4      12                3.7                3.7                3.7
-  ##   43   5      12                2.0                2.0                2.0
-  ##   63   6      12                2.0                3.0                3.7
-  ##      PersonMax.Dim01 PersonMax.Dim02 PersonMax.Dim03 theta.Dim01 theta.Dim02
-  ##   2              4.0             0.6             0.6        1.06          NA
-  ##   22             4.0             0.6             0.6       -0.96          NA
-  ##   23             0.6             4.0             4.0          NA       -0.07
-  ##   41             4.0             4.0             4.0        1.06        0.82
-  ##   43             4.0             4.0             4.0       -0.96       -1.11
-  ##   63             4.0             4.0             4.0       -0.96       -0.07
-  ##      theta.Dim03 error.Dim01 error.Dim02 error.Dim03 WLE.rel.Dim01
-  ##   2           NA        1.50          NA          NA          -0.1
-  ##   22          NA        1.11          NA          NA          -0.1
-  ##   23        0.25          NA        1.17        1.92          -0.1
-  ##   41        0.25        1.50        1.48        1.92          -0.1
-  ##   43       -1.93        1.11        1.10        1.14          -0.1
-
-# (1) Note that estimated WLE reliabilities are not trustworthy in this example.
-# (2) If cases do not possess any observations on dimensions, then WLEs
-#     and their corresponding standard errors are set to NA.
-
-#############################################################################
-# EXAMPLE 3: Partial credit model | Comparison WLEs with PP package
-#############################################################################
-
-library(PP)
-data(data.gpcm)
-dat <- data.gpcm
-I <- ncol(dat)
-
-#****************************************
-#*** Model 1: Partial Credit Model
-
-# estimation in TAM
-mod1 <- TAM::tam.mml( dat )
-summary(mod1)
-
-#-- WLE estimation in TAM
-tamw1 <- TAM::tam.wle( mod1 )
-
-#-- WLE estimation with PP package
-# convert AXsi parameters into thres parameters for PP
-AXsi0 <- - mod1$AXsi[,-1]
-b <- AXsi0
-K <- ncol(AXsi0)
-for (cc in 2:K){
-    b[,cc] <- AXsi0[,cc] - AXsi0[,cc-1]
-}
-# WLE estimation in PP
-ppw1 <- PP::PP_gpcm( respm=as.matrix(dat),  thres=t(b), slopes=rep(1,I) )
-
-#-- compare results
-dfr <- cbind( tamw1[, c("theta","error") ], ppw1$resPP)
-head( round(dfr,3))
-  ##      theta error resPP.estimate resPP.SE nsteps
-  ##   1 -1.006 0.973         -1.006    0.973      8
-  ##   2 -0.122 0.904         -0.122    0.904      8
-  ##   3  0.640 0.836          0.640    0.836      8
-  ##   4  0.640 0.836          0.640    0.836      8
-  ##   5  0.640 0.836          0.640    0.836      8
-  ##   6 -1.941 1.106         -1.941    1.106      8
-plot( dfr$resPP.estimate, dfr$theta, pch=16, xlab="PP", ylab="TAM")
-lines( c(-10,10), c(-10,10) )
-
-#****************************************
-#*** Model 2: Generalized partial Credit Model
-
-# estimation in TAM
-mod2 <- TAM::tam.mml.2pl( dat, irtmodel="GPCM" )
-summary(mod2)
-
-#-- WLE estimation in TAM
-tamw2 <- TAM::tam.wle( mod2 )
-
-#-- WLE estimation in PP
-# convert AXsi parameters into thres and slopes parameters for PP
-AXsi0 <- - mod2$AXsi[,-1]
-slopes <- mod2$B[,2,1]
-K <- ncol(AXsi0)
-slopesM <- matrix( slopes, I, ncol=K )
-AXsi0 <- AXsi0 / slopesM
-b <- AXsi0
-for (cc in 2:K){
-    b[,cc] <- AXsi0[,cc] - AXsi0[,cc-1]
-}
-# estimation in PP
-ppw2 <- PP::PP_gpcm( respm=as.matrix(dat),  thres=t(b), slopes=slopes )
-
-#-- compare results
-dfr <- cbind( tamw2[, c("theta","error") ], ppw2$resPP)
-head( round(dfr,3))
-  ##      theta error resPP.estimate resPP.SE nsteps
-  ##   1 -0.476 0.971         -0.476    0.971     13
-  ##   2 -0.090 0.973         -0.090    0.973     13
-  ##   3  0.311 0.960          0.311    0.960     13
-  ##   4  0.311 0.960          0.311    0.960     13
-  ##   5  1.749 0.813          1.749    0.813     13
-  ##   6 -1.513 1.032         -1.513    1.032     13
-}

+
See the S3 method IRT.factor.scores.tam.

+    

+
+    

+    
Examples

+    
#############################################################################
+# EXAMPLE 1: 1PL model, data.sim.rasch
+#############################################################################
+
+data(data.sim.rasch)
+# estimate Rasch model
+mod1 <- TAM::tam.mml(resp=data.sim.rasch)
+# WLE estimation
+wle1 <- TAM::tam.wle( mod1 )
+  ## WLE Reliability=0.894
+
+print(wle1)
+summary(wle1)
+
+# scoring for a different dataset containing same items (first 10 persons in sim.rasch)
+wle2 <- TAM::tam.wle( mod1, score.resp=data.sim.rasch[1:10,])
+
+#--- WLE estimation without using a TAM object
+
+#* create an input list
+input <- list( resp=data.sim.rasch, AXsi=mod1$AXsi, B=mod1$B )
+#* estimation
+wle2b <- TAM::tam.mml.wle2( input )
+
+if (FALSE) {
+#############################################################################
+# EXAMPLE 2: 3-dimensional Rasch model | data.read from sirt package
+#############################################################################
+
+data(data.read, package="sirt")
+# define Q-matrix
+Q <- matrix(0,12,3)
+Q[ cbind( 1:12, rep(1:3,each=4) ) ] <- 1
+# redefine data: create some missings for first three cases
+resp <- data.read
+resp[1:2, 5:12] <- NA
+resp[3,1:4] <- NA
+  ##   > head(resp)
+  ##      A1 A2 A3 A4 B1 B2 B3 B4 C1 C2 C3 C4
+  ##   2   1  1  1  1 NA NA NA NA NA NA NA NA
+  ##   22  1  1  0  0 NA NA NA NA NA NA NA NA
+  ##   23 NA NA NA NA  1  0  1  1  1  1  1  1
+  ##   41  1  1  1  1  1  1  1  1  1  1  1  1
+  ##   43  1  0  0  1  0  0  1  1  1  0  1  0
+  ##   63  1  1  0  0  1  0  1  1  1  1  1  1
+
+# estimate 3-dimensional Rasch model
+mod <- TAM::tam.mml( resp=resp, Q=Q, control=list(snodes=1000,maxiter=50) )
+summary(mod)
+
+# WLE estimates
+wmod <- TAM::tam.wle(mod, Msteps=3)
+summary(wmod)
+  ##   head(round(wmod,2))
+  ##      pid N.items PersonScores.Dim01 PersonScores.Dim02 PersonScores.Dim03
+  ##   2    1       4                3.7                0.3                0.3
+  ##   22   2       4                2.0                0.3                0.3
+  ##   23   3       8                0.3                3.0                3.7
+  ##   41   4      12                3.7                3.7                3.7
+  ##   43   5      12                2.0                2.0                2.0
+  ##   63   6      12                2.0                3.0                3.7
+  ##      PersonMax.Dim01 PersonMax.Dim02 PersonMax.Dim03 theta.Dim01 theta.Dim02
+  ##   2              4.0             0.6             0.6        1.06          NA
+  ##   22             4.0             0.6             0.6       -0.96          NA
+  ##   23             0.6             4.0             4.0          NA       -0.07
+  ##   41             4.0             4.0             4.0        1.06        0.82
+  ##   43             4.0             4.0             4.0       -0.96       -1.11
+  ##   63             4.0             4.0             4.0       -0.96       -0.07
+  ##      theta.Dim03 error.Dim01 error.Dim02 error.Dim03 WLE.rel.Dim01
+  ##   2           NA        1.50          NA          NA          -0.1
+  ##   22          NA        1.11          NA          NA          -0.1
+  ##   23        0.25          NA        1.17        1.92          -0.1
+  ##   41        0.25        1.50        1.48        1.92          -0.1
+  ##   43       -1.93        1.11        1.10        1.14          -0.1
+
+# (1) Note that estimated WLE reliabilities are not trustworthy in this example.
+# (2) If cases do not possess any observations on dimensions, then WLEs
+#     and their corresponding standard errors are set to NA.
+
+#############################################################################
+# EXAMPLE 3: Partial credit model | Comparison WLEs with PP package
+#############################################################################
+
+library(PP)
+data(data.gpcm)
+dat <- data.gpcm
+I <- ncol(dat)
+
+#****************************************
+#*** Model 1: Partial Credit Model
+
+# estimation in TAM
+mod1 <- TAM::tam.mml( dat )
+summary(mod1)
+
+#-- WLE estimation in TAM
+tamw1 <- TAM::tam.wle( mod1 )
+
+#-- WLE estimation with PP package
+# convert AXsi parameters into thres parameters for PP
+AXsi0 <- - mod1$AXsi[,-1]
+b <- AXsi0
+K <- ncol(AXsi0)
+for (cc in 2:K){
+    b[,cc] <- AXsi0[,cc] - AXsi0[,cc-1]
+}
+# WLE estimation in PP
+ppw1 <- PP::PP_gpcm( respm=as.matrix(dat),  thres=t(b), slopes=rep(1,I) )
+
+#-- compare results
+dfr <- cbind( tamw1[, c("theta","error") ], ppw1$resPP)
+head( round(dfr,3))
+  ##      theta error resPP.estimate resPP.SE nsteps
+  ##   1 -1.006 0.973         -1.006    0.973      8
+  ##   2 -0.122 0.904         -0.122    0.904      8
+  ##   3  0.640 0.836          0.640    0.836      8
+  ##   4  0.640 0.836          0.640    0.836      8
+  ##   5  0.640 0.836          0.640    0.836      8
+  ##   6 -1.941 1.106         -1.941    1.106      8
+plot( dfr$resPP.estimate, dfr$theta, pch=16, xlab="PP", ylab="TAM")
+lines( c(-10,10), c(-10,10) )
+
+#****************************************
+#*** Model 2: Generalized partial Credit Model
+
+# estimation in TAM
+mod2 <- TAM::tam.mml.2pl( dat, irtmodel="GPCM" )
+summary(mod2)
+
+#-- WLE estimation in TAM
+tamw2 <- TAM::tam.wle( mod2 )
+
+#-- WLE estimation in PP
+# convert AXsi parameters into thres and slopes parameters for PP
+AXsi0 <- - mod2$AXsi[,-1]
+slopes <- mod2$B[,2,1]
+K <- ncol(AXsi0)
+slopesM <- matrix( slopes, I, ncol=K )
+AXsi0 <- AXsi0 / slopesM
+b <- AXsi0
+for (cc in 2:K){
+    b[,cc] <- AXsi0[,cc] - AXsi0[,cc-1]
+}
+# estimation in PP
+ppw2 <- PP::PP_gpcm( respm=as.matrix(dat),  thres=t(b), slopes=slopes )
+
+#-- compare results
+dfr <- cbind( tamw2[, c("theta","error") ], ppw2$resPP)
+head( round(dfr,3))
+  ##      theta error resPP.estimate resPP.SE nsteps
+  ##   1 -0.476 0.971         -0.476    0.971     13
+  ##   2 -0.090 0.973         -0.090    0.973     13
+  ##   3  0.311 0.960          0.311    0.960     13
+  ##   4  0.311 0.960          0.311    0.960     13
+  ##   5  1.749 0.813          1.749    0.813     13
+  ##   6 -1.513 1.032         -1.513    1.032     13
+}

+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/reference/tam_NA_pattern.html b/docs/reference/tam_NA_pattern.html
index c43c372..5b666e8 100644
--- a/docs/reference/tam_NA_pattern.html
+++ b/docs/reference/tam_NA_pattern.html
@@ -1,68 +1,13 @@
-
 
-
-  
-  
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-Missing Data Patterns — tam_NA_pattern • TAM
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Missing Data Patterns

@@ -119,70 +51,70 @@ 
Missing Data Patterns

 responses.

     

 
-    
tam_NA_pattern(x)
-
-tam_01_pattern(x)

-
-    
Arguments

-    
-    
-    
-      
-      
-    
-    
x
Matrix or data frame

-
-    
Value

-
-    
List containing pattern identifiers and indices

-
-    
Examples

-    
#############################################################################
-# EXAMPLE 1: Missing data patterns
-#############################################################################
-
-data(data.sim.rasch.missing, package="TAM")
-dat <- data.sim.rasch.missing
+    

+    
tam_NA_pattern(x)
+
+tam_01_pattern(x)

+    

 
-res <- TAM::tam_NA_pattern(dat)
-str(res)
+    

+    
Arguments

+    
x

+
Matrix or data frame

 
-if (FALSE) {
-#############################################################################
-# EXAMPLE 2: Item response patterns
-#############################################################################
+

+    

+    
Value

+    
 
-data(data.read, package="sirt")
-dat <- data.read
+
List containing pattern identifiers and indices

+    

 
-res <- TAM::tam_01_pattern(dat)
-str(res)
-}

+    

+    
Examples

+    
#############################################################################
+# EXAMPLE 1: Missing data patterns
+#############################################################################
+
+data(data.sim.rasch.missing, package="TAM")
+dat <- data.sim.rasch.missing
+
+res <- TAM::tam_NA_pattern(dat)
+str(res)
+
+if (FALSE) {
+#############################################################################
+# EXAMPLE 2: Item response patterns
+#############################################################################
+
+data(data.read, package="sirt")
+dat <- data.read
+
+res <- TAM::tam_01_pattern(dat)
+str(res)
+}

+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
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+  
 
+  
 
diff --git a/docs/reference/tam_downcode.html b/docs/reference/tam_downcode.html
index 9576880..d06f82e 100644
--- a/docs/reference/tam_downcode.html
+++ b/docs/reference/tam_downcode.html
@@ -1,68 +1,13 @@
-
 
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-Downcoding an Item Response Dataset — tam_downcode • TAM
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Downcoding an Item Response Dataset

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Downcoding an Item Response Dataset

 \(0,1,\ldots,K_i\).

     

 
-    
tam_downcode(dat)

-
-    
Arguments

-    
-    
-    
-      
-      
-    
-    
dat
Data frame containing item responses

-
-    
Value

-
-    
List with following entries

-
dat
Recoded dataset

-
rec
Recoding table

-
-
-    
Examples

-    
#############################################################################
-# EXAMPLE 1: Downcoding in a toy example
-#############################################################################
-
-#-- simulate some toy data
-set.seed(989)
-# values to be sampled
-vals <- c(NA, 0:6)
-# number of persons and items
-N <- 10; I <- 5
-dat <- as.data.frame(matrix(NA, nrow=N, ncol=I))
-colnames(dat) <- paste0("I",1:I)
-for (ii in 1L:I){
-    dat[,ii] <- sample(vals, size=N, replace=TRUE)
-}
-
-#-- apply downcoding
-res <- TAM::tam_downcode(dat)
-dat <- res$dat   # extract downcoded dataset
-rec <- res$rec   # extract recoded table

+    

+    
tam_downcode(dat)

+    

+
+    

+    
Arguments

+    
dat

+
Data frame containing item responses

+
+

+    

+    
Value

+    
+
+
List with following entries

+
dat

+
Recoded dataset

+
+
rec

+
Recoding table

+
+

+
+    

+    
Examples

+    
#############################################################################
+# EXAMPLE 1: Downcoding in a toy example
+#############################################################################
+
+#-- simulate some toy data
+set.seed(989)
+# values to be sampled
+vals <- c(NA, 0:6)
+# number of persons and items
+N <- 10; I <- 5
+dat <- as.data.frame(matrix(NA, nrow=N, ncol=I))
+colnames(dat) <- paste0("I",1:I)
+for (ii in 1L:I){
+    dat[,ii] <- sample(vals, size=N, replace=TRUE)
+}
+
+#-- apply downcoding
+res <- TAM::tam_downcode(dat)
+dat <- res$dat   # extract downcoded dataset
+rec <- res$rec   # extract recoded table

+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/reference/tam_irf_3pl.html b/docs/reference/tam_irf_3pl.html
index 6fda230..4566813 100644
--- a/docs/reference/tam_irf_3pl.html
+++ b/docs/reference/tam_irf_3pl.html
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-
 
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Item Response Function for the 3PL Model

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Item Response Function for the 3PL Model

 package.

     

 
-    
tam_irf_3pl(theta, AXsi, B, guess=NULL, subtract_max=TRUE)

-
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Arguments

-    
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theta
Matrix or vector of \(\bold{\theta}\) values
AXsi
Matrix of item-category parameters
B
Array containing item-category loadings
guess
Optional parameter of guessing parameters
subtract_max
Logical indicating whether numerical underflow in
-probabilities should be explicitly avoided

-
-    
Value

-
-    
Array containing item response probabilities arranged by the dimensions
+    

+    
tam_irf_3pl(theta, AXsi, B, guess=NULL, subtract_max=TRUE)

+    

+
+    

+    
Arguments

+    
theta

+
Matrix or vector of \(\bold{\theta}\) values

+
+
AXsi

+
Matrix of item-category parameters

+
+
B

+
Array containing item-category loadings

+
+
guess

+
Optional parameter of guessing parameters

+
+
subtract_max

+
Logical indicating whether numerical underflow in
+probabilities should be explicitly avoided

+
+

+    

+    
Value

+    
+
+
Array containing item response probabilities arranged by the dimensions
 theta points \(\times\) items \(\times\) categories

+    

 
-    
Examples

-    
if (FALSE) {
-#############################################################################
-# EXAMPLE 1: 2PL example
-#############################################################################
-
-library(sirt)
-data(data.read, package="sirt")
-dat <- data.read
-
-#* estimate 2PL model
-mod <- TAM::tam.mml.2pl( resp=dat )
-#* define theta vector
-theta <- seq(-3,3, len=41)
-#* compute item response probabilities
-probs <- TAM::tam_irf_3pl( theta=theta, AXsi=mod$AXsi, B=mod$B )
-str(probs)
-}

+    

+    
Examples

+    
if (FALSE) {
+#############################################################################
+# EXAMPLE 1: 2PL example
+#############################################################################
+
+library(sirt)
+data(data.read, package="sirt")
+dat <- data.read
+
+#* estimate 2PL model
+mod <- TAM::tam.mml.2pl( resp=dat )
+#* define theta vector
+theta <- seq(-3,3, len=41)
+#* compute item response probabilities
+probs <- TAM::tam_irf_3pl( theta=theta, AXsi=mod$AXsi, B=mod$B )
+str(probs)
+}

+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/reference/tamaan.html b/docs/reference/tamaan.html
index a6be9bb..b9739c1 100644
--- a/docs/reference/tamaan.html
+++ b/docs/reference/tamaan.html
@@ -1,71 +1,16 @@
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Wrapper Function for TAM Language

@@ -120,514 +52,522 @@ 
Wrapper Function for TAM Language

     

     
This function is a convenience wrapper function for
 several item response models in TAM. Using the
-tamaanify framework, multidimensional item response models,
+tamaanify framework, multidimensional item response models,
 latent class models, located and ordered latent class models
 and mixture item response models can be estimated.

     

 
-    
tamaan(tammodel, resp, tam.method=NULL, control=list(), doparse=TRUE, ...)
-
-# S3 method for tamaan
-summary(object,file=NULL,...)
-
-# S3 method for tamaan
-print(x,...)

-
-    
Arguments

-    
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-      
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tammodel
String for specification in TAM, see also tamaanify.
resp
Dataset with item responses
tam.method
One of the TAM methods tam.mml, tam.mml.2pl
-or tam.mml.3pl.
control
List with control arguments. See tam.mml.
doparse
Optional logical indicating whether lavmodel
-should be parsed for DO statements, see doparse.
...
Further arguments to be passed to
+    

+    
tamaan(tammodel, resp, tam.method=NULL, control=list(), doparse=TRUE, ...)
+
+# S3 method for tamaan
+summary(object,file=NULL,...)
+
+# S3 method for tamaan
+print(x,...)

+    

+
+    

+    
Arguments

+    
tammodel

+
String for specification in TAM, see also tamaanify.

+
+  
resp

+
Dataset with item responses

+
+  
tam.method

+
One of the TAM methods tam.mml, tam.mml.2pl
+or tam.mml.3pl.

+
+  
control

+
List with control arguments. See tam.mml.

+
+
doparse

+
Optional logical indicating whether lavmodel
+should be parsed for DO statements, see doparse.

+
+  
...

+
Further arguments to be passed to
 tam.mml, tam.mml.2pl
-or tam.mml.3pl.
object
Object of class tamaan
file
A file name in which the summary output will be written
x
Object of class tamaan

-
-    
Value

-
-    
Values generated by tam.mml, tam.mml.2pl
-or tam.mml.3pl. In addition, the list also contains the (optional) entries

-
tamaanify
Output produced by tamaanify

-
lcaprobs
Matrix with probabilities for latent class models

-
locs
Matrix with cluster locations (for TYPE="LOCLCA")

-
probs_MIXTURE
Class probabilities (for TYPE="MIXTURE")

-
moments_MIXTURE
Distribution parameters (for TYPE="MIXTURE")

-
itempartable_MIXTURE
Item parameters (for TYPE="MIXTURE")

-
ind_classprobs
Individual posterior probabilities for
-  latent classes (for TYPE="MIXTURE")

+or tam.mml.3pl.

+
+  
object

+
Object of class tamaan

+
+
file

+
A file name in which the summary output will be written

+
+
x

+
Object of class tamaan

+
+

+    

+    
Value

+    
 
-    
See also

+
Values generated by tam.mml, tam.mml.2pl

 
-    
See tamaanify for more details about model specification
+
+
or tam.mml.3pl. In addition, the list also contains the (optional) entries

+
tamaanify

+
Output produced by tamaanify

+
+
lcaprobs

+
Matrix with probabilities for latent class models

+
+
locs

+
Matrix with cluster locations (for TYPE="LOCLCA")

+
+
probs_MIXTURE

+
Class probabilities (for TYPE="MIXTURE")

+
+
moments_MIXTURE

+
Distribution parameters (for TYPE="MIXTURE")

+
+
itempartable_MIXTURE

+
Item parameters (for TYPE="MIXTURE")

+
+
ind_classprobs

+
Individual posterior probabilities for
+  latent classes (for TYPE="MIXTURE")

+
+

+    

+    
See also

+    
See tamaanify for more details about model specification
 using tammodel.

-
See tam.mml or tam.mml.3pl
+
See tam.mml or tam.mml.3pl
 for more examples.

+    

 
-    
Examples

-    
if (FALSE) {
-
-#############################################################################
-# EXAMPLE 1: Examples dichotomous data data.read
-#############################################################################
-
-library(sirt)
-data(data.read,package="sirt")
-dat <- data.read
-
-#*********************************************************************
-#*** Model 1: Rasch model
-
-tammodel <- "
-LAVAAN MODEL:
-  F1=~ A1__C4
-  F1 ~~ F1
-ITEM TYPE:
-  ALL(Rasch);
-    "
-# estimate model
-mod1 <- TAM::tamaan( tammodel, resp=dat)
-summary(mod1)
-
-#*********************************************************************
-#*** Model 2: 2PL model with some selected items
-
-tammodel <- "
-LAVAAN MODEL:
-  F1=~ A1__B1 + B3 + C1__C3
-  F1 ~~ F1
-    "
-mod2 <- TAM::tamaan( tammodel, resp=dat)
-summary(mod2)
-
-#*********************************************************************
-#*** Model 3: Multidimensional IRT model
-
-tammodel <- "
-LAVAAN MODEL:
-  G=~ A1__C4
-  F1=~ A1__B4
-  F2=~ C1__C4
-  F1 ~~ F2
-  # specify fixed entries in covariance matrix
-  F1 ~~ 1*F1
-  F2 ~~ 1*F2
-  G  ~~ 0*F1
-  G  ~~ 0.3*F2
-  G  ~~ 0.7*G
-    "
-mod3 <- TAM::tamaan( tammodel, resp=dat, control=list(maxiter=30))
-summary(mod3)
-
-#*********************************************************************
-#*** Model 4: Some linear constraints for item slopes and intercepts
-
-tammodel <- "
-LAVAAN MODEL:
-  F=~ lam1__lam10*A1__C2
-  F=~ 0.78*C3
-  F ~~ F
-  A1 | a1*t1
-  A2 | a2*t1
-  A3 | a3*t1
-  A4 | a4*t1
-  B1 | b1*t1
-  B2 | b2*t1
-  B3 | b3*t1
-  C1 | t1
-MODEL CONSTRAINT:
-  # defined parameters
-  # only linear combinations are permitted
-  b2==1.3*b1 + (-0.6)*b3
-  a1==q1
-  a2==q2 + t
-  a3==q1 + 2*t
-  a4==q2 + 3*t
-  # linear constraints for loadings
-  lam2==1.1*lam1
-  lam3==0.9*lam1 + (-.1)*lam0
-  lam8==lam0
-  lam9==lam0
-    "
-mod4 <- TAM::tamaan( tammodel, resp=dat, control=list(maxiter=5) )
-summary(mod4)
-
-#*********************************************************************
-#*** Model 5: Latent class analysis with three classes
-
-tammodel <- "
-ANALYSIS:
-  TYPE=LCA;
-  NCLASSES(3);   # 3 classes
-  NSTARTS(5,20); # 5 random starts with 20 iterations
-LAVAAN MODEL:
-  F=~ A1__C4
-    "
-mod5 <- TAM::tamaan( tammodel, resp=dat, control=list(maxiter=100)  )
-summary(mod5)
-
-#*********************************************************************
-#*** Model 6: Ordered latent class analysis with three classes
-
-tammodel <- "
-ANALYSIS:
-  TYPE=OLCA;
-  NCLASSES(3);    # 3 classes
-  NSTARTS(20,40); # 20 random starts with 40 iterations
-LAVAAN MODEL:
-  F=~ A1__C4
-    "
-mod6 <- TAM::tamaan( tammodel, dat )
-summary(mod6)
-
-#*********************************************************************
-#*** Model 7: Unidimensional located latent class model with three classes
-
-tammodel <- "
-ANALYSIS:
-  TYPE=LOCLCA;
-  NCLASSES(3)
-  NSTARTS(10,40)
-LAVAAN MODEL:
-  F=~ A1__C4
-  B2 | 0*t1
-    "
-mod7 <- TAM::tamaan( tammodel, resp=dat)
-summary(mod7)
-
-#*********************************************************************
-#*** Model 8: Two-dimensional located latent class analysis with some
-#             priors and equality constraints among thresholds
-
-tammodel <- "
-ANALYSIS:
-  TYPE=LOCLCA;
-  NCLASSES(4);
-  NSTARTS(10,20);
-LAVAAN MODEL:
-  AB=~ A1__B4
-  C=~ C1__C4
-  A1 | a1diff*t1
-  B2 | 0*t1
-  C2 | 0*t1
-  B1 | a1diff*t1
-MODEL PRIOR:
-  # prior distributions for cluster locations
-  DO2(1,4,1,1,2,1)
-    Cl%1_Dim%2 ~ N(0,2);
-  DOEND
-    "
-# estimate model
-mod8 <- TAM::tamaan( tammodel, resp=dat )
-summary(mod8)
-
-#*********************************************************************
-#*** Model 9: Two-dimensional model with constraints on parameters
-
-tammodel <- "
-LAVAAN MODEL:
-  FA=~ A1+b*A2+A3+d*A4
-  FB=~ B1+b*B2+B3+d*B4
-  FA ~~ 1*FA
-  FA ~~ FB
-  FB ~~ 1*FB
-  A1 | c*t1
-  B1 | c*t1
-  A2 | .7*t1
-    "
-# estimate model
-mod9 <- TAM::tamaan( tammodel, resp=dat, control=list(maxiter=30) )
-summary(mod9)
-
-#############################################################################
-# EXAMPLE 2: Examples polytomous data | data.Students
-#############################################################################
-
-library(CDM)
-data( data.Students, package="CDM")
-dat <- data.Students[,3:13]
-  ##   > colnames(dat)
-  ##    [1] "act1" "act2" "act3" "act4" "act5" "sc1"  "sc2"  "sc3"  "sc4"  "mj1"  "mj2"
-
-#*********************************************************************
-#*** Model 1: Two-dimensional generalized partial credit model
-
-tammodel <- "
-LAVAAN MODEL:
-  FA=~ act1__act5
-  FS=~ sc1__sc4
-  FA ~~ 1*FA
-  FS ~~ 1*FS
-  FA ~~ FS
-    "
-# estimate model
-mod1 <- TAM::tamaan( tammodel, dat, control=list(maxiter=10)  )
-summary(mod1)
-
-#*********************************************************************
-#*** Model 2: Two-dimensional model, some constraints
-
-tammodel <- "
-LAVAAN MODEL:
-  FA=~ a1__a4*act1__act4 + 0.89*act5
-  FS=~ 1*sc1 + sc2__sc4
-  FA ~~ FA
-  FS ~~ FS
-  FA ~~ FS
-  # some equality constraints
-  act1 + act3 | a13_t1 * t1
-  act1 + act3 | a13_t2 * t2
-    "
-# only create design matrices with tamaanify
-mod2 <- TAM::tamaanify( tammodel, dat  )
-mod2$lavpartable
-# estimate model (only few iterations as a test)
-mod2 <- TAM::tamaan( tammodel, dat, control=list(maxiter=10)  )
-summary(mod2)
-
-#*********************************************************************
-#*** Model 3: Two-dimensional model, some more linear constraints
-
-tammodel <- "
-LAVAAN MODEL:
-  FA=~ a1__a5*act1__act5
-  FS=~ b1__b4*sc1__sc4
-  FA ~~ 1*FA
-  FA ~~ FS
-  FS ~~ 1*FS
-  act1 + act3 | a13_t1 * t1
-  act1 + act3 | a13_t2 * t2
-MODEL CONSTRAINT:
-  a1==q0
-  a2==q0
-  a3==q0    + q1
-  a4==q2
-  a5==q2 + q1
-    "
-# estimate
-mod3 <- TAM::tamaan( tammodel, dat, control=list(maxiter=300 )  )
-summary(mod3)
-
-#*********************************************************************
-#*** Model 4: Latent class analysis with three latent classes
-
-tammodel <- "
-ANALYSIS:
-  TYPE=LCA;
-  NCLASSES(3);    # 3 classes
-  NSTARTS(10,30); # 10 random starts with 30 iterations
-LAVAAN MODEL:
-  F=~ act1__act5
-    "
-# estimate model
-mod4 <- TAM::tamaan( tammodel, resp=dat)
-summary(mod4)
-
-#*********************************************************************
-#*** Model 5: Partial credit model with "PCM2" parametrization
-
-# select data
-dat1 <- dat[, paste0("act",1:5) ]
-# specify tamaan model
-tammodel <- "
-  LAVAAN MODEL:
-    F=~ act1__act5
-    F ~~ F
-    # use DO statement as shortages
-    DO(1,5,1)
-      act% | b%_1 * t1
-      act% | b%_2 * t2
-    DOEND
-  MODEL CONSTRAINT:
-    DO(1,5,1)
-      b%_1==delta% + tau%_1
-      b%_2==2*delta%
-    DOEND
-  ITEM TYPE:
-    ALL(PCM)
-  "
-# estimate model
-mod5 <- TAM::tamaan( tammodel, dat1 )
-summary(mod5)
-# compare with PCM2 parametrization in tam.mml
-mod5b <- TAM::tam.mml( dat1, irtmodel="PCM2" )
-summary(mod5b)
-
-#*********************************************************************
-#*** Model 6: Rating scale model
-
-# select data
-dat1 <- dat[, paste0("sc",1:4) ]
-psych::describe(dat1)
-
-# specify tamaan model
-tammodel <- "
-  LAVAAN MODEL:
-    F=~ sc1__sc4
-    F ~~ F
-    # use DO statement as shortages
-    DO(1,4,1)
-      sc% | b%_1 * t1
-      sc% | b%_2 * t2
-      sc% | b%_3 * t3
-    DOEND
-  MODEL CONSTRAINT:
-    DO(1,4,1)
-      b%_1==delta% + step1
-      b%_2==2*delta% + step1 + step2
-      b%_3==3*delta%
-    DOEND
-  ITEM TYPE:
-    ALL(PCM)
-  "
-# estimate model
-mod6 <- TAM::tamaan( tammodel, dat1 )
-summary(mod6)
-# compare with RSM in tam.mml
-mod6b <- TAM::tam.mml( dat1, irtmodel="RSM" )
-summary(mod6b)
-
-#*********************************************************************
-#*** Model 7: Partial credit model with Fourier basis for
-#             item intercepts (Thissen, Cai & Bock, 2010)
-# see ?tamaanify manual
-
-# define tamaan model
-tammodel <- "
-LAVAAN MODEL:
-   mj=~ mj1__mj4
-   mj ~~ 1*mj
-ITEM TYPE:
-  mj1(PCM,2)
-  mj2(PCM,3)
-  mj3(PCM)
-  mj4(PCM,1)
-   "
-# estimate model
-mod7 <- TAM::tamaan( tammodel, dat )
-summary(mod7)
-# -> This function can also be applied for the generalized partial credit
-#    model (GPCM).
-
-#############################################################################
-# EXAMPLE 3: Rasch model and mixture Rasch model (Geiser & Eid, 2010)
-#############################################################################
-
-data(data.geiser, package="TAM")
-dat <- data.geiser
-
-#*********************************************************************
-#*** Model 1: Rasch model
-tammodel <- "
-LAVAAN MODEL:
-  F=~ mrt1__mrt6
-  F ~~ F
-ITEM TYPE:
-  ALL(Rasch);
-    "
-mod1 <- TAM::tamaan( tammodel, resp=dat  )
-summary(mod1)
-
-#*********************************************************************
-#*** Model 2: Mixed Rasch model with two classes
-tammodel <- "
-ANALYSIS:
-  TYPE=MIXTURE ;
-  NCLASSES(2);
-  NSTARTS(20,25);
-LAVAAN MODEL:
-  F=~ mrt1__mrt6
-  F ~~ F
-ITEM TYPE:
-  ALL(Rasch);
-    "
-mod2 <- TAM::tamaan( tammodel, resp=dat  )
-summary(mod2)
-
-# plot item parameters
-ipars <- mod2$itempartable_MIXTURE[ 1:6, ]
-plot( 1:6, ipars[,3], type="o", ylim=c(-3,2), pch=16,
-        xlab="Item", ylab="Item difficulty")
-lines( 1:6, ipars[,4], type="l", col=2, lty=2)
-points( 1:6, ipars[,4],  col=2, pch=2)
-
-# extract individual posterior distribution
-post2 <- IRT.posterior(mod2)
-str(post2)
-# num [1:519, 1:30] 0.000105 0.000105 0.000105 0.000105 0.000105 ...
-# - attr(*, "theta")=num [1:30, 1:30] 1 0 0 0 0 0 0 0 0 0 ...
-# - attr(*, "prob.theta")=num [1:30, 1] 1.21e-05 2.20e-04 2.29e-03 1.37e-02 4.68e-02 ...
-# - attr(*, "G")=num 1
-
-# There are 2 classes and 15 theta grid points for each class
-# The loadings of the theta grid on items are as follows
-mod2$E[1,2,,"mrt1_F_load_Cl1"]
-mod2$E[1,2,,"mrt1_F_load_Cl2"]
-
-# compute individual posterior probability for class 1 (first 15 columns)
-round( rowSums( post2[, 1:15] ), 3 )
-# columns 16 to 30 refer to class 2
-
-}

+    

+    
Examples

+    
if (FALSE) {
+
+#############################################################################
+# EXAMPLE 1: Examples dichotomous data data.read
+#############################################################################
+
+library(sirt)
+data(data.read,package="sirt")
+dat <- data.read
+
+#*********************************************************************
+#*** Model 1: Rasch model
+
+tammodel <- "
+LAVAAN MODEL:
+  F1=~ A1__C4
+  F1 ~~ F1
+ITEM TYPE:
+  ALL(Rasch);
+    "
+# estimate model
+mod1 <- TAM::tamaan( tammodel, resp=dat)
+summary(mod1)
+
+#*********************************************************************
+#*** Model 2: 2PL model with some selected items
+
+tammodel <- "
+LAVAAN MODEL:
+  F1=~ A1__B1 + B3 + C1__C3
+  F1 ~~ F1
+    "
+mod2 <- TAM::tamaan( tammodel, resp=dat)
+summary(mod2)
+
+#*********************************************************************
+#*** Model 3: Multidimensional IRT model
+
+tammodel <- "
+LAVAAN MODEL:
+  G=~ A1__C4
+  F1=~ A1__B4
+  F2=~ C1__C4
+  F1 ~~ F2
+  # specify fixed entries in covariance matrix
+  F1 ~~ 1*F1
+  F2 ~~ 1*F2
+  G  ~~ 0*F1
+  G  ~~ 0.3*F2
+  G  ~~ 0.7*G
+    "
+mod3 <- TAM::tamaan( tammodel, resp=dat, control=list(maxiter=30))
+summary(mod3)
+
+#*********************************************************************
+#*** Model 4: Some linear constraints for item slopes and intercepts
+
+tammodel <- "
+LAVAAN MODEL:
+  F=~ lam1__lam10*A1__C2
+  F=~ 0.78*C3
+  F ~~ F
+  A1 | a1*t1
+  A2 | a2*t1
+  A3 | a3*t1
+  A4 | a4*t1
+  B1 | b1*t1
+  B2 | b2*t1
+  B3 | b3*t1
+  C1 | t1
+MODEL CONSTRAINT:
+  # defined parameters
+  # only linear combinations are permitted
+  b2==1.3*b1 + (-0.6)*b3
+  a1==q1
+  a2==q2 + t
+  a3==q1 + 2*t
+  a4==q2 + 3*t
+  # linear constraints for loadings
+  lam2==1.1*lam1
+  lam3==0.9*lam1 + (-.1)*lam0
+  lam8==lam0
+  lam9==lam0
+    "
+mod4 <- TAM::tamaan( tammodel, resp=dat, control=list(maxiter=5) )
+summary(mod4)
+
+#*********************************************************************
+#*** Model 5: Latent class analysis with three classes
+
+tammodel <- "
+ANALYSIS:
+  TYPE=LCA;
+  NCLASSES(3);   # 3 classes
+  NSTARTS(5,20); # 5 random starts with 20 iterations
+LAVAAN MODEL:
+  F=~ A1__C4
+    "
+mod5 <- TAM::tamaan( tammodel, resp=dat, control=list(maxiter=100)  )
+summary(mod5)
+
+#*********************************************************************
+#*** Model 6: Ordered latent class analysis with three classes
+
+tammodel <- "
+ANALYSIS:
+  TYPE=OLCA;
+  NCLASSES(3);    # 3 classes
+  NSTARTS(20,40); # 20 random starts with 40 iterations
+LAVAAN MODEL:
+  F=~ A1__C4
+    "
+mod6 <- TAM::tamaan( tammodel, dat )
+summary(mod6)
+
+#*********************************************************************
+#*** Model 7: Unidimensional located latent class model with three classes
+
+tammodel <- "
+ANALYSIS:
+  TYPE=LOCLCA;
+  NCLASSES(3)
+  NSTARTS(10,40)
+LAVAAN MODEL:
+  F=~ A1__C4
+  B2 | 0*t1
+    "
+mod7 <- TAM::tamaan( tammodel, resp=dat)
+summary(mod7)
+
+#*********************************************************************
+#*** Model 8: Two-dimensional located latent class analysis with some
+#             priors and equality constraints among thresholds
+
+tammodel <- "
+ANALYSIS:
+  TYPE=LOCLCA;
+  NCLASSES(4);
+  NSTARTS(10,20);
+LAVAAN MODEL:
+  AB=~ A1__B4
+  C=~ C1__C4
+  A1 | a1diff*t1
+  B2 | 0*t1
+  C2 | 0*t1
+  B1 | a1diff*t1
+MODEL PRIOR:
+  # prior distributions for cluster locations
+  DO2(1,4,1,1,2,1)
+    Cl%1_Dim%2 ~ N(0,2);
+  DOEND
+    "
+# estimate model
+mod8 <- TAM::tamaan( tammodel, resp=dat )
+summary(mod8)
+
+#*********************************************************************
+#*** Model 9: Two-dimensional model with constraints on parameters
+
+tammodel <- "
+LAVAAN MODEL:
+  FA=~ A1+b*A2+A3+d*A4
+  FB=~ B1+b*B2+B3+d*B4
+  FA ~~ 1*FA
+  FA ~~ FB
+  FB ~~ 1*FB
+  A1 | c*t1
+  B1 | c*t1
+  A2 | .7*t1
+    "
+# estimate model
+mod9 <- TAM::tamaan( tammodel, resp=dat, control=list(maxiter=30) )
+summary(mod9)
+
+#############################################################################
+# EXAMPLE 2: Examples polytomous data | data.Students
+#############################################################################
+
+library(CDM)
+data( data.Students, package="CDM")
+dat <- data.Students[,3:13]
+  ##   > colnames(dat)
+  ##    [1] "act1" "act2" "act3" "act4" "act5" "sc1"  "sc2"  "sc3"  "sc4"  "mj1"  "mj2"
+
+#*********************************************************************
+#*** Model 1: Two-dimensional generalized partial credit model
+
+tammodel <- "
+LAVAAN MODEL:
+  FA=~ act1__act5
+  FS=~ sc1__sc4
+  FA ~~ 1*FA
+  FS ~~ 1*FS
+  FA ~~ FS
+    "
+# estimate model
+mod1 <- TAM::tamaan( tammodel, dat, control=list(maxiter=10)  )
+summary(mod1)
+
+#*********************************************************************
+#*** Model 2: Two-dimensional model, some constraints
+
+tammodel <- "
+LAVAAN MODEL:
+  FA=~ a1__a4*act1__act4 + 0.89*act5
+  FS=~ 1*sc1 + sc2__sc4
+  FA ~~ FA
+  FS ~~ FS
+  FA ~~ FS
+  # some equality constraints
+  act1 + act3 | a13_t1 * t1
+  act1 + act3 | a13_t2 * t2
+    "
+# only create design matrices with tamaanify
+mod2 <- TAM::tamaanify( tammodel, dat  )
+mod2$lavpartable
+# estimate model (only few iterations as a test)
+mod2 <- TAM::tamaan( tammodel, dat, control=list(maxiter=10)  )
+summary(mod2)
+
+#*********************************************************************
+#*** Model 3: Two-dimensional model, some more linear constraints
+
+tammodel <- "
+LAVAAN MODEL:
+  FA=~ a1__a5*act1__act5
+  FS=~ b1__b4*sc1__sc4
+  FA ~~ 1*FA
+  FA ~~ FS
+  FS ~~ 1*FS
+  act1 + act3 | a13_t1 * t1
+  act1 + act3 | a13_t2 * t2
+MODEL CONSTRAINT:
+  a1==q0
+  a2==q0
+  a3==q0    + q1
+  a4==q2
+  a5==q2 + q1
+    "
+# estimate
+mod3 <- TAM::tamaan( tammodel, dat, control=list(maxiter=300 )  )
+summary(mod3)
+
+#*********************************************************************
+#*** Model 4: Latent class analysis with three latent classes
+
+tammodel <- "
+ANALYSIS:
+  TYPE=LCA;
+  NCLASSES(3);    # 3 classes
+  NSTARTS(10,30); # 10 random starts with 30 iterations
+LAVAAN MODEL:
+  F=~ act1__act5
+    "
+# estimate model
+mod4 <- TAM::tamaan( tammodel, resp=dat)
+summary(mod4)
+
+#*********************************************************************
+#*** Model 5: Partial credit model with "PCM2" parametrization
+
+# select data
+dat1 <- dat[, paste0("act",1:5) ]
+# specify tamaan model
+tammodel <- "
+  LAVAAN MODEL:
+    F=~ act1__act5
+    F ~~ F
+    # use DO statement as shortages
+    DO(1,5,1)
+      act% | b%_1 * t1
+      act% | b%_2 * t2
+    DOEND
+  MODEL CONSTRAINT:
+    DO(1,5,1)
+      b%_1==delta% + tau%_1
+      b%_2==2*delta%
+    DOEND
+  ITEM TYPE:
+    ALL(PCM)
+  "
+# estimate model
+mod5 <- TAM::tamaan( tammodel, dat1 )
+summary(mod5)
+# compare with PCM2 parametrization in tam.mml
+mod5b <- TAM::tam.mml( dat1, irtmodel="PCM2" )
+summary(mod5b)
+
+#*********************************************************************
+#*** Model 6: Rating scale model
+
+# select data
+dat1 <- dat[, paste0("sc",1:4) ]
+psych::describe(dat1)
+
+# specify tamaan model
+tammodel <- "
+  LAVAAN MODEL:
+    F=~ sc1__sc4
+    F ~~ F
+    # use DO statement as shortages
+    DO(1,4,1)
+      sc% | b%_1 * t1
+      sc% | b%_2 * t2
+      sc% | b%_3 * t3
+    DOEND
+  MODEL CONSTRAINT:
+    DO(1,4,1)
+      b%_1==delta% + step1
+      b%_2==2*delta% + step1 + step2
+      b%_3==3*delta%
+    DOEND
+  ITEM TYPE:
+    ALL(PCM)
+  "
+# estimate model
+mod6 <- TAM::tamaan( tammodel, dat1 )
+summary(mod6)
+# compare with RSM in tam.mml
+mod6b <- TAM::tam.mml( dat1, irtmodel="RSM" )
+summary(mod6b)
+
+#*********************************************************************
+#*** Model 7: Partial credit model with Fourier basis for
+#             item intercepts (Thissen, Cai & Bock, 2010)
+# see ?tamaanify manual
+
+# define tamaan model
+tammodel <- "
+LAVAAN MODEL:
+   mj=~ mj1__mj4
+   mj ~~ 1*mj
+ITEM TYPE:
+  mj1(PCM,2)
+  mj2(PCM,3)
+  mj3(PCM)
+  mj4(PCM,1)
+   "
+# estimate model
+mod7 <- TAM::tamaan( tammodel, dat )
+summary(mod7)
+# -> This function can also be applied for the generalized partial credit
+#    model (GPCM).
+
+#############################################################################
+# EXAMPLE 3: Rasch model and mixture Rasch model (Geiser & Eid, 2010)
+#############################################################################
+
+data(data.geiser, package="TAM")
+dat <- data.geiser
+
+#*********************************************************************
+#*** Model 1: Rasch model
+tammodel <- "
+LAVAAN MODEL:
+  F=~ mrt1__mrt6
+  F ~~ F
+ITEM TYPE:
+  ALL(Rasch);
+    "
+mod1 <- TAM::tamaan( tammodel, resp=dat  )
+summary(mod1)
+
+#*********************************************************************
+#*** Model 2: Mixed Rasch model with two classes
+tammodel <- "
+ANALYSIS:
+  TYPE=MIXTURE ;
+  NCLASSES(2);
+  NSTARTS(20,25);
+LAVAAN MODEL:
+  F=~ mrt1__mrt6
+  F ~~ F
+ITEM TYPE:
+  ALL(Rasch);
+    "
+mod2 <- TAM::tamaan( tammodel, resp=dat  )
+summary(mod2)
+
+# plot item parameters
+ipars <- mod2$itempartable_MIXTURE[ 1:6, ]
+plot( 1:6, ipars[,3], type="o", ylim=c(-3,2), pch=16,
+        xlab="Item", ylab="Item difficulty")
+lines( 1:6, ipars[,4], type="l", col=2, lty=2)
+points( 1:6, ipars[,4],  col=2, pch=2)
+
+# extract individual posterior distribution
+post2 <- IRT.posterior(mod2)
+str(post2)
+# num [1:519, 1:30] 0.000105 0.000105 0.000105 0.000105 0.000105 ...
+# - attr(*, "theta")=num [1:30, 1:30] 1 0 0 0 0 0 0 0 0 0 ...
+# - attr(*, "prob.theta")=num [1:30, 1] 1.21e-05 2.20e-04 2.29e-03 1.37e-02 4.68e-02 ...
+# - attr(*, "G")=num 1
+
+# There are 2 classes and 15 theta grid points for each class
+# The loadings of the theta grid on items are as follows
+mod2$E[1,2,,"mrt1_F_load_Cl1"]
+mod2$E[1,2,,"mrt1_F_load_Cl2"]
+
+# compute individual posterior probability for class 1 (first 15 columns)
+round( rowSums( post2[, 1:15] ), 3 )
+# columns 16 to 30 refer to class 2
+
+}

+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/reference/tamaanify.html b/docs/reference/tamaanify.html
index 3301c1d..520c7c2 100644
--- a/docs/reference/tamaanify.html
+++ b/docs/reference/tamaanify.html
@@ -1,70 +1,15 @@
-
 
-
-  
-  
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-Function for Parsing <span class="pkg">TAM</span> Input — tamaanify • TAM
-
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-TAM Input — tamaanify" />
-Function for Parsing TAM Input — tamaanify • TAM
-
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+    
 
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Function for Parsing TAM Input

@@ -120,55 +52,51 @@ 
Function for Parsing TAM Input

     
This function parses a so called tammodel which is a
 string used for model estimation in TAM.
 The function is based on the lavaan syntax and operates
-at the extension lavaanify.IRT.

+at the extension lavaanify.IRT.

+    

+
+    

+    
tamaanify(tammodel, resp, tam.method=NULL, doparse=TRUE )

     

 
-    
tamaanify(tammodel, resp, tam.method=NULL, doparse=TRUE )

-
-    
Arguments

-    
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
tammodel
String for model definition following the rules described in Details and
-in Examples.
resp
Item response dataset
tam.method
One of the TAM methods tam.mml, tam.mml.2pl
-or tam.mml.3pl.
doparse
Optional logical indicating whether lavmodel
-should be parsed for DO statements.

-
-    
Details

+    

+    
Arguments

+    
tammodel

+
String for model definition following the rules described in Details and
+in Examples.

+
+  
resp

+
Item response dataset

 
+  
tam.method

+
One of the TAM methods tam.mml, tam.mml.2pl
+or tam.mml.3pl.

+
+
doparse

+
Optional logical indicating whether lavmodel
+should be parsed for DO statements.

+
+

+    

+    
Details

     
The model syntax tammodel consists of several sections.
-Some of them are optional. 

-
ANALYSIS: 

+Some of them are optional. 

+
ANALYSIS: 

 Possible model types are unidimensional and multidimensional
 item response models (TYPE="TRAIT"), latent class models
 ("LCA"), located latent class models ("LOCLCA";
 e.g. Formann, 1989; Bartolucci, 2007),
 ordered latent class models ("OLCA"; only works for
 dichotomous item responses; e.g. Hoijtink, 1997; Shojima, 2007) and
-mixture distribution models ("MIXTURE"; e.g. von Davier, 2007). 

-
LAVAAN MODEL: 

-For specification of the syntax, see lavaanify.IRT. 

-
MODEL CONSTRAINT: 

+mixture distribution models ("MIXTURE"; e.g. von Davier, 2007). 

+
LAVAAN MODEL: 

+For specification of the syntax, see lavaanify.IRT. 

+
MODEL CONSTRAINT: 

 Linear constraints can be specified by using conventional
 specification in R syntax. All terms must be combined
 with the + operator. Equality constraints are
-set by using the == operator as in lavaan. 

-
ITEM TYPE: 

+set by using the == operator as in lavaan. 

+
ITEM TYPE: 

 The following item types can be defined: Rasch model (Rasch),
 the 2PL model (2PL), partial credit model (PCM)
 and the generalized partial credit model (GPCM).

@@ -180,74 +108,137 @@ 
Details
 integer between 1 and \(K\). With kk=1, only a linear
 function is used. The subsequent integers correspond to
 Fourier functions with decreasing periods.
-See Example 2, Model 7 of the tamaan
-function. 

+See Example 2, Model 7 of the tamaan
+function. 

 
 
-
PRIOR: 

+
PRIOR: 

 Possible prior distributions: Normal distribution N(mu,sd),
 truncated normal distribution TN(mu,sd,low,upp) and
-Beta distribution Beta(a,b).
+Beta distribution Beta(a,b).
 Parameter labels and prior specification must be separated
-by ~.

+by ~.

 
 
-    
Value

+    

+    

+    
Value

+    
 
-    
A list with following (optional) entries
- which are used as input in one of the TAM functions
- tam.mml, tam.mml.2pl or
- tam.mml.3pl:

-
tammodel
Model input for TAM

-
tammodel.dfr
Processed tammodel input

-
ANALYSIS
Syntax specified in ANALYSIS

-
ANALYSIS.list
Parsed specifications in ANALYSIS

-
LAVAANMODEL
Syntax specified in LAVAAN MODEL

-
lavpartable
Parameter table processed by the
+
A list with following (optional) entries
+ which are used as input in one of the TAM functions

+

+
tam.mml, tam.mml.2pl or

+

+
tam.mml.3pl:

+
tammodel

+
Model input for TAM

+
+
tammodel.dfr

+
Processed tammodel input

+
+
ANALYSIS

+
Syntax specified in ANALYSIS

+
+
ANALYSIS.list

+
Parsed specifications in ANALYSIS

+
+
LAVAANMODEL

+
Syntax specified in LAVAAN MODEL

+
+
lavpartable

+
Parameter table processed by the
 syntax in LAVAAN MODEL

-
items
Informations about items: Number of categories,
+
+
items

+
Informations about items: Number of categories,
   specified item response function

-
maxcat
Maximum number of categories

-
ITEMTYPE
Syntax specified in ITEM TYPE

-
MODELCONSTRAINT
Syntax specified in MODEL CONSTRAINT

-
MODELCONSTRAINT.dfr
Processed syntax in MODEL CONSTRAINT

-
modelconstraint.thresh
Processed data frame for model constraint of thresholds

-
modelconstraint.loading
Processed data frame for loadings

-
resp
Data set for usage

-
method
Used TAM function

-
A
Design matrix A

-
Q
Design matrix for loadings

-
Q.fixed
Fixed values in \(Q\) matrix

-
B.fixed
Matrix with fixed item loadings
+
+
maxcat

+
Maximum number of categories

+
+
ITEMTYPE

+
Syntax specified in ITEM TYPE

+
+
MODELCONSTRAINT

+
Syntax specified in MODEL CONSTRAINT

+
+
MODELCONSTRAINT.dfr

+
Processed syntax in MODEL CONSTRAINT

+
+
modelconstraint.thresh

+
Processed data frame for model constraint of thresholds

+
+
modelconstraint.loading

+
Processed data frame for loadings

+
+
resp

+
Data set for usage

+
+
method

+
Used TAM function

+
+
A

+
Design matrix A

+
+
Q

+
Design matrix for loadings

+
+
Q.fixed

+
Fixed values in \(Q\) matrix

+
+
B.fixed

+
Matrix with fixed item loadings
       (used for tam.mml.2pl)

-
L
Processed design matrix for loadings when there
+
+
L

+
Processed design matrix for loadings when there
 are model constraints for loadings

-
variance.fixed
Matrix for specification of fixed values
+
+
variance.fixed

+
Matrix for specification of fixed values
 in covariance matrix

-
est.variance
Logical indicating whether variance should
-be estimated (tam.mml.2pl)

-
theta.k
Theta design matrix

-
E
Design matrix E

-
notA
Logical indicating whether \(A\) matrix is defined

-
gammaslope.fixed
Fixed gammaslope parameters

-
gammaslope.prior
Prior distributions for gammaslope parameters

-
xsi.fixed
Fixed \(\xi\) parameter

-
xsi.prior
Prior distributions for \(\xi\) parameters

-
-    
References

 
+
est.variance

+
Logical indicating whether variance should
+be estimated (tam.mml.2pl)

+
+
theta.k

+
Theta design matrix

+
+
E

+
Design matrix E

+
+
notA

+
Logical indicating whether \(A\) matrix is defined

+
+
gammaslope.fixed

+
Fixed gammaslope parameters

+
+
gammaslope.prior

+
Prior distributions for gammaslope parameters

+
+
xsi.fixed

+
Fixed \(\xi\) parameter

+
+
xsi.prior

+
Prior distributions for \(\xi\) parameters

+
+

+    

+    
References

     
Bartolucci, F. (2007). A class of multidimensional IRT models for testing
 unidimensionality and clustering items.
 Psychometrika, 72, 141-157.
-doi: 10.1007/s11336-005-1376-9

+doi:10.1007/s11336-005-1376-9

 
Formann, A. K. (1989). Constrained latent class models: Some further
 applications. British Journal of Mathematical and Statistical
 Psychology, 42, 37-54.
-doi: 10.1111/j.2044-8317.1989.tb01113.x

+doi:10.1111/j.2044-8317.1989.tb01113.x

 
Hojtink, H., & Molenaar, I. W. (1997). A multidimensional item response model:
 Constrained latent class analysis using the Gibbs sampler and posterior
 predictive checks. Psychometrika, 62(2), 171-189.
-doi: 10.1007/BF02295273

+doi:10.1007/BF02295273

 
Thissen, D., Cai, L., & Bock, R. D. (2010).
 The nominal categories item response model.
 In M. L. Nering & Ostini, R. (Eds.).
@@ -258,170 +249,170 @@ 
R
 DNC Research Note 07-12.

 
von Davier, M. (2007). Mixture distribution diagnostic models.
 ETS Research Report ETS RR-07-32. Princeton, ETS.
-doi: 10.1002/j.2333-8504.2007.tb02074.x

-    
See also

-
-    
See tamaan for more examples. Other examples
-are included in tam.mml and tam.mml.3pl.

-
lavaanify.IRT

-
-    
Examples

-    
if (FALSE) {
-
-#############################################################################
-# EXAMPLE 1: Examples dichotomous data data.read
-#############################################################################
-
-library(sirt)
-data(data.read,package="sirt")
-dat <- data.read
-
-#*********************************************************************
-#*** Model 1: 2PL estimation with some fixed parameters and
-#             equality constraints
-tammodel <- "
-LAVAAN MODEL:
-  F2=~ C1__C2 + 1.3*C3 + C4
-  F1=~ A1__B1
-  # fixed loading of 1.4 for item B2
-  F1=~ 1.4*B2
-  F1=~ B3
-  F1 ~~ F1
-  F2 ~~ F2
-  F1 ~~ F2
-  B1 | 1.23*t1 ; A3 | 0.679*t1
-  A2 | a*t1 ; C2 | a*t1 ; C4 | a*t1
-  C3 | x1*t1 ; C1 | x1*t1
-ITEM TYPE:
-  A1__A3 (Rasch) ;
-  A4 (2PL) ;
-  B1__C4 (Rasch) ;
-    "
-# process model
-out <- TAM::tamaanify( tammodel, resp=dat)
-# inspect some output
-out$method          # used TAM function
-out$lavpartable     # lavaan parameter table
-
-#*********************************************************************
-#*** Model 2: Latent class analysis with three classes
-tammodel <- "
-ANALYSIS:
-  TYPE=LCA;
-  NCLASSES(3);   # 3 classes
-  NSTARTS(5,20); # 5 random starts with 20 iterations
-LAVAAN MODEL:
-  F=~ A1__C4
-    "
-# process syntax
-out <- TAM::tamaanify( tammodel, resp=dat)
-str(out$E)     # E design matrix for estimation with tam.mml.3pl function
-
-#*********************************************************************
-#*** Model 3: Linear constraints for item intercepts and item loadings
-tammodel <- "
-LAVAAN MODEL:
-  F=~ lam1__lam10*A1__C2
-  F ~~ F
-  A1 | a1*t1
-  A2 | a2*t1
-  A3 | a3*t1
-  A4 | a4*t1
-  B1 | b1*t1
-  B2 | b2*t1
-  B3 | b3*t1
-  C1 | t1
-MODEL CONSTRAINT:
-  # defined parameters
-  # only linear combinations are permitted
-  b2==1.3*b1 + (-0.6)*b3
-  a1==q1
-  a2==q2 + t
-  a3==q1 + 2*t
-  a4==q2 + 3*t
-  # linear constraints for loadings
-  lam2==1.1*lam1
-  lam3==0.9*lam1 + (-.1)*lam0
-  lam8==lam0
-  lam9==lam0
-    "
-# parse syntax
-mod1 <- TAM::tamaanify( tammodel, resp=dat)
-mod1$A          # design matrix A for intercepts
-mod1$L[,1,]     # design matrix L for loadings
-}
-
-#############################################################################
-# EXAMPLE 2: Examples polytomous data data.Students
-#############################################################################
-
-library(CDM)
-data( data.Students, package="CDM")
-dat <- data.Students[,3:13]
-
-#*********************************************************************
-#*** Model 1: Two-dimensional generalized partial credit model
-tammodel <- "
-LAVAAN MODEL:
-  FA=~ act1__act5
-  FS=~ sc1__sc4
-  FA ~~ 1*FA
-  FS ~~ 1*FS
-  FA ~~ FS
-  act1__act3 | t1
-  sc2 | t2
-    "
-out <- TAM::tamaanify( tammodel, resp=dat)
-out$A    # design matrix for item intercepts
-out$Q    # loading matrix for items
-
-#*********************************************************************
-#*** Model 2: Linear constraints
-
-# In the following syntax, linear equations for multiple constraints
-# are arranged over multiple lines.
-tammodel <- "
-  LAVAAN MODEL:
-    F=~ a1__a5*act1__act5
-    F ~~ F
-  MODEL CONSTRAINT:
-      a1==delta +
-                tau1
-      a2==delta
-      a3==delta + z1
-      a4==1.1*delta +
-              2*tau1
-                + (-0.2)*z1
-  "
-# tamaanify model
-res <- TAM::tamaanify( tammodel, dat )
-res$MODELCONSTRAINT.dfr
-res$modelconstraint.loading

+doi:10.1002/j.2333-8504.2007.tb02074.x

+    

+    

+    
See also

+    
See tamaan for more examples. Other examples
+are included in tam.mml and tam.mml.3pl.

+
lavaanify.IRT

+    

+
+    

+    
Examples

+    
if (FALSE) {
+
+#############################################################################
+# EXAMPLE 1: Examples dichotomous data data.read
+#############################################################################
+
+library(sirt)
+data(data.read,package="sirt")
+dat <- data.read
+
+#*********************************************************************
+#*** Model 1: 2PL estimation with some fixed parameters and
+#             equality constraints
+tammodel <- "
+LAVAAN MODEL:
+  F2=~ C1__C2 + 1.3*C3 + C4
+  F1=~ A1__B1
+  # fixed loading of 1.4 for item B2
+  F1=~ 1.4*B2
+  F1=~ B3
+  F1 ~~ F1
+  F2 ~~ F2
+  F1 ~~ F2
+  B1 | 1.23*t1 ; A3 | 0.679*t1
+  A2 | a*t1 ; C2 | a*t1 ; C4 | a*t1
+  C3 | x1*t1 ; C1 | x1*t1
+ITEM TYPE:
+  A1__A3 (Rasch) ;
+  A4 (2PL) ;
+  B1__C4 (Rasch) ;
+    "
+# process model
+out <- TAM::tamaanify( tammodel, resp=dat)
+# inspect some output
+out$method          # used TAM function
+out$lavpartable     # lavaan parameter table
+
+#*********************************************************************
+#*** Model 2: Latent class analysis with three classes
+tammodel <- "
+ANALYSIS:
+  TYPE=LCA;
+  NCLASSES(3);   # 3 classes
+  NSTARTS(5,20); # 5 random starts with 20 iterations
+LAVAAN MODEL:
+  F=~ A1__C4
+    "
+# process syntax
+out <- TAM::tamaanify( tammodel, resp=dat)
+str(out$E)     # E design matrix for estimation with tam.mml.3pl function
+
+#*********************************************************************
+#*** Model 3: Linear constraints for item intercepts and item loadings
+tammodel <- "
+LAVAAN MODEL:
+  F=~ lam1__lam10*A1__C2
+  F ~~ F
+  A1 | a1*t1
+  A2 | a2*t1
+  A3 | a3*t1
+  A4 | a4*t1
+  B1 | b1*t1
+  B2 | b2*t1
+  B3 | b3*t1
+  C1 | t1
+MODEL CONSTRAINT:
+  # defined parameters
+  # only linear combinations are permitted
+  b2==1.3*b1 + (-0.6)*b3
+  a1==q1
+  a2==q2 + t
+  a3==q1 + 2*t
+  a4==q2 + 3*t
+  # linear constraints for loadings
+  lam2==1.1*lam1
+  lam3==0.9*lam1 + (-.1)*lam0
+  lam8==lam0
+  lam9==lam0
+    "
+# parse syntax
+mod1 <- TAM::tamaanify( tammodel, resp=dat)
+mod1$A          # design matrix A for intercepts
+mod1$L[,1,]     # design matrix L for loadings
+}
+
+#############################################################################
+# EXAMPLE 2: Examples polytomous data data.Students
+#############################################################################
+
+library(CDM)
+data( data.Students, package="CDM")
+dat <- data.Students[,3:13]
+
+#*********************************************************************
+#*** Model 1: Two-dimensional generalized partial credit model
+tammodel <- "
+LAVAAN MODEL:
+  FA=~ act1__act5
+  FS=~ sc1__sc4
+  FA ~~ 1*FA
+  FS ~~ 1*FS
+  FA ~~ FS
+  act1__act3 | t1
+  sc2 | t2
+    "
+out <- TAM::tamaanify( tammodel, resp=dat)
+out$A    # design matrix for item intercepts
+out$Q    # loading matrix for items
+
+#*********************************************************************
+#*** Model 2: Linear constraints
+
+# In the following syntax, linear equations for multiple constraints
+# are arranged over multiple lines.
+tammodel <- "
+  LAVAAN MODEL:
+    F=~ a1__a5*act1__act5
+    F ~~ F
+  MODEL CONSTRAINT:
+      a1==delta +
+                tau1
+      a2==delta
+      a3==delta + z1
+      a4==1.1*delta +
+              2*tau1
+                + (-0.2)*z1
+  "
+# tamaanify model
+res <- TAM::tamaanify( tammodel, dat )
+res$MODELCONSTRAINT.dfr
+res$modelconstraint.loading

+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/reference/tampv2datalist.html b/docs/reference/tampv2datalist.html
index b7d99f3..c8ef9c9 100644
--- a/docs/reference/tampv2datalist.html
+++ b/docs/reference/tampv2datalist.html
@@ -1,70 +1,15 @@
-
 
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-  
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-Conversion of Plausible Value Object into Datalist — tampv2datalist • TAM
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Conversion of Plausible Value Object into Datalist

@@ -117,82 +49,76 @@ 
Conversion of Plausible Value Object into Datalist

     

 
     

-    
Converts a tam.pv object and a matrix of covariates
+    
Converts a tam.pv object and a matrix of covariates
 into a list of multiply imputed datasets. This list can be conveniently
 analyzed by R packages such as semTools, Zelig, mice
 or BIFIEsurvey.

     

 
-    
tampv2datalist(tam.pv.object, pvnames=NULL, Y=NULL, Y.pid="pid",
-      as_mids=FALSE, stringsAsFactors=FALSE)

-
-    
Arguments

-    
-    
-    
-      
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-      
-      
-    
-    
tam.pv.object
Generated tam.pv object
pvnames
Variable names of generated plausible values
Y
Matrix with covariates
Y.pid
Person identifier in Y matrix. It is not required that a person
+    

+    
tampv2datalist(tam.pv.object, pvnames=NULL, Y=NULL, Y.pid="pid",
+      as_mids=FALSE, stringsAsFactors=FALSE)

+    

+
+    

+    
Arguments

+    
tam.pv.object

+
Generated tam.pv object

+
+  
pvnames

+
Variable names of generated plausible values

+
+  
Y

+
Matrix with covariates

+
+  
Y.pid

+
Person identifier in Y matrix. It is not required that a person
 identifier is provided. In this case, the merge of the datasets will
-be conducted as for rbind.
as_mids
Logical indicating whether the datalist
+be conducted as for rbind.

+
+
as_mids

+
Logical indicating whether the datalist
   should be converted into an object of class mids for
   analysis in the mice package. This functionality uses the
-  the function miceadds::datalist2mids.
stringsAsFactors
Logical indicating whether strings in the data frame
-should be converted into factors

+  the function miceadds::datalist2mids.

 
-    
Value

+
stringsAsFactors

+
Logical indicating whether strings in the data frame
+should be converted into factors

 
-    
List of multiply imputed datasets or an mids object

-    
See also

+

+    

+    
Value

+    
 
-    
For examples see tam.pv.

+
List of multiply imputed datasets or an mids object

+    

+    

+    
See also

+    
For examples see tam.pv.

+    

 
   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/reference/weighted_Stats.html b/docs/reference/weighted_Stats.html
index 12f923c..ffe4167 100644
--- a/docs/reference/weighted_Stats.html
+++ b/docs/reference/weighted_Stats.html
@@ -1,70 +1,15 @@
-
 
-
-  
-  
-
-
-
-Descriptive Statistics for Weighted Data — weighted_Stats • TAM
-
-
-
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-
-Descriptive Statistics for Weighted Data — weighted_Stats • TAM
-
-
-
-
-
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-
-
-
-
-  
+
+    
 
-  
     

-      

-      
 
       
 
-      

-
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+      

   

     

     
Descriptive Statistics for Weighted Data

@@ -123,99 +55,94 @@ 
Descriptive Statistics for Weighted Data

 the data.

     

 
-    
weighted_mean(x, w=rep(1, length(x)), select=NULL  )
-
-weighted_var(x, w=rep(1, length(x)), method="unbiased", select=NULL )
-
-weighted_sd(x, w=rep(1, length(x)), method="unbiased", select=NULL )
-
-weighted_skewness( x, w=rep(1,length(x)), select=NULL  )
-
-weighted_kurtosis( x, w=rep(1,length(x)), select=NULL  )
-
-weighted_quantile( x, w=rep(1,length(x)), probs=seq(0,1,.25), type=NULL, select=NULL )
-
-weighted_table( x, w=NULL, props=FALSE )

-
-    
Arguments

-    
-    
-    
-      
-      
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-    
-    
x
A numeric vector. For weighted_table, a matrix with
-two columns can be used as input for cross-tabulation.
w
Optional vector of sample weights
select
Vector referring to selected cases
method
Computation method (can be "unbiased" or "ML")), see
-stats::cov.wt
probs
Vector with probabilities
type
Quantile type. For unweighted data, quantile types 6 and
+    

+    
weighted_mean(x, w=rep(1, length(x)), select=NULL  )
+
+weighted_var(x, w=rep(1, length(x)), method="unbiased", select=NULL )
+
+weighted_sd(x, w=rep(1, length(x)), method="unbiased", select=NULL )
+
+weighted_skewness( x, w=rep(1,length(x)), select=NULL  )
+
+weighted_kurtosis( x, w=rep(1,length(x)), select=NULL  )
+
+weighted_quantile( x, w=rep(1,length(x)), probs=seq(0,1,.25), type=NULL, select=NULL )
+
+weighted_table( x, w=NULL, props=FALSE )

+    

+
+    

+    
Arguments

+    
x

+
A numeric vector. For weighted_table, a matrix with
+two columns can be used as input for cross-tabulation.

+
+  
w

+
Optional vector of sample weights

+
+
select

+
Vector referring to selected cases

+
+  
method

+
Computation method (can be "unbiased" or "ML")), see
+stats::cov.wt

+
+
probs

+
Vector with probabilities

+
+
type

+
Quantile type. For unweighted data, quantile types 6 and
 7 can be used (see
-stats::quantile).
+stats::quantile).
 For weighted data, the quantile type "i/n"
-is used (see Hmisc::wtd.quantile)).
props
Logical indicating whether relative or absolute
-frequencies should be calculated.

+is used (see Hmisc::wtd.quantile)).

 
-    
Value

+
props

+
Logical indicating whether relative or absolute
+frequencies should be calculated.

 
-    
Numeric value

-    
See also

+

+    

+    
Value

+    
 
-    
See stats::weighted.mean for
+
Numeric value

+    

+    

+    
See also

+    
See stats::weighted.mean for
 computing a weighted mean.

-
See stats::var for computing
+
See stats::var for computing
 unweighted variances.

-
See stats::quantile and
-Hmisc::wtd.quantile) for quantiles.

+
See stats::quantile and
+Hmisc::wtd.quantile) for quantiles.

+    

 
-    
Examples

-    

+    

+    
Examples

+    
+    

   

   
+    

 

 
 
-      

-      

-  
Developed by Alexander Robitzsch.

+      

+  
Developed by Alexander Robitzsch.

 

 
 

-  
Site built with pkgdown 1.5.1.

+  
Site built with pkgdown 2.0.7.

 

 
-      

-   

+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/sitemap.xml b/docs/sitemap.xml
new file mode 100644
index 0000000..cae1a4b
--- /dev/null
+++ b/docs/sitemap.xml
@@ -0,0 +1,216 @@
+
+
+  
+    /404.html
+  
+  
+    /authors.html
+  
+  
+    /index.html
+  
+  
+    /reference/anova.tam.html
+  
+  
+    /reference/cfa.extract.itempars.html
+  
+  
+    /reference/data.cqc.html
+  
+  
+    /reference/data.ctest.html
+  
+  
+    /reference/data.examples.html
+  
+  
+    /reference/data.fims.Aus.Jpn.html
+  
+  
+    /reference/data.geiser.html
+  
+  
+    /reference/data.gpcm.html
+  
+  
+    /reference/data.janssen.html
+  
+  
+    /reference/data.mc.html
+  
+  
+    /reference/data.numeracy.html
+  
+  
+    /reference/data.sim.mfr.html
+  
+  
+    /reference/data.sim.rasch.html
+  
+  
+    /reference/data.timssAusTwn.html
+  
+  
+    /reference/DescribeBy.html
+  
+  
+    /reference/designMatrices.html
+  
+  
+    /reference/doparse.html
+  
+  
+    /reference/index.html
+  
+  
+    /reference/IRT.cv.html
+  
+  
+    /reference/IRT.data.tam.html
+  
+  
+    /reference/IRT.drawPV.html
+  
+  
+    /reference/IRT.expectedCounts.tam.html
+  
+  
+    /reference/IRT.factor.scores.tam.html
+  
+  
+    /reference/IRT.frequencies.tam.html
+  
+  
+    /reference/IRT.informationCurves.html
+  
+  
+    /reference/IRT.irfprob.tam.html
+  
+  
+    /reference/IRT.itemfit.html
+  
+  
+    /reference/IRT.likelihood.tam.html
+  
+  
+    /reference/IRT.linearCFA.html
+  
+  
+    /reference/IRT.residuals.html
+  
+  
+    /reference/IRT.simulate.html
+  
+  
+    /reference/IRT.threshold.html
+  
+  
+    /reference/IRT.truescore.html
+  
+  
+    /reference/IRT.WrightMap.html
+  
+  
+    /reference/IRTLikelihood.cfa.html
+  
+  
+    /reference/IRTLikelihood.ctt.html
+  
+  
+    /reference/lavaanify.IRT.html
+  
+  
+    /reference/msq.itemfit.html
+  
+  
+    /reference/plot.tam.html
+  
+  
+    /reference/plotDevianceTAM.html
+  
+  
+    /reference/predict.html
+  
+  
+    /reference/Scale.html
+  
+  
+    /reference/TAM-defunct.html
+  
+  
+    /reference/TAM-package.html
+  
+  
+    /reference/TAM-utilities.html
+  
+  
+    /reference/tam.ctt.html
+  
+  
+    /reference/tam.fa.html
+  
+  
+    /reference/tam.fit.html
+  
+  
+    /reference/tam.jml.html
+  
+  
+    /reference/tam.latreg.html
+  
+  
+    /reference/tam.linking.html
+  
+  
+    /reference/tam.mml.3pl.html
+  
+  
+    /reference/tam.mml.html
+  
+  
+    /reference/tam.modelfit.html
+  
+  
+    /reference/tam.np.html
+  
+  
+    /reference/tam.personfit.html
+  
+  
+    /reference/tam.pv.html
+  
+  
+    /reference/tam.se.html
+  
+  
+    /reference/tam.threshold.html
+  
+  
+    /reference/tam.wle.html
+  
+  
+    /reference/tamaan.html
+  
+  
+    /reference/tamaanify.html
+  
+  
+    /reference/tampv2datalist.html
+  
+  
+    /reference/tam_downcode.html
+  
+  
+    /reference/tam_irf_3pl.html
+  
+  
+    /reference/tam_NA_pattern.html
+  
+  
+    /reference/weighted_Stats.html
+  
+  
+    /reference/WLErel.html
+  
+
diff --git a/inst/NEWS b/inst/NEWS
index 8d43c08..5bef10a 100644
--- a/inst/NEWS
+++ b/inst/NEWS
@@ -42,16 +42,15 @@ http://www.edmeasurementsurveys.com/TAM/Tutorials/
 
 
 -------------------------------------------------------------
-VERSIONS TAM 4.3  |  2024-02-20  |  Last: TAM 4.3-2
+VERSIONS TAM 4.3  |  2024-09-09  |  Last: TAM 4.3-4
 -------------------------------------------------------------
 
-xxx   * ...
+ADDED * included processing function for theta within iterations
+        in tam.jml() (thanks to a discussion with Stefanie Wind)
 
 
 DATA  * included/modified datasets: ---
-EXAMP * included/modified examples: ---
-
-
+EXAMP * included/modified examples: tam.jml (5)
 
 
 -------------------------------------------------------------
diff --git a/man/IRT.residuals.Rd b/man/IRT.residuals.Rd
index dc01711..ee6462a 100644
--- a/man/IRT.residuals.Rd
+++ b/man/IRT.residuals.Rd
@@ -1,5 +1,5 @@
 %% File Name: IRT.residuals.Rd
-%% File Version: 0.183
+%% File Version: 0.185
 
 \name{IRT.residuals}
 \alias{IRT.residuals}
@@ -83,9 +83,8 @@ factor analysis (see Example 1).
 %% ~Make other sections like Warning with \section{Warning }{....} ~
 
 \seealso{
-See also the \code{eRm::residuals} (\bold{eRm}) or
-\code{\link[mirt:residuals-method]{residuals}} (\bold{mirt})
-functions.
+See also the \code{eRm::residuals} (\bold{eRm}) function or the
+\code{mirt:residuals-method} in the \bold{mirt} package.
 
 See also \code{\link[TAM:predict.tam.mml]{predict.tam.mml}}.
 }
diff --git a/man/IRT.threshold.Rd b/man/IRT.threshold.Rd
index 7b359ac..5df7db9 100644
--- a/man/IRT.threshold.Rd
+++ b/man/IRT.threshold.Rd
@@ -1,5 +1,5 @@
 %% File Name: IRT.threshold.Rd
-%% File Version: 1.441
+%% File Version: 1.444
 
 \name{IRT.threshold}
 \alias{IRT.threshold}
@@ -12,10 +12,12 @@
 Thurstonian Thresholds and Wright Map for Item Response Models
 }
 
+%% \code{\link[lavaan:cfa]{lavaan::cfa}}
+
 \description{
 The function \code{IRT.threshold} computes Thurstonian thresholds
 for item response models. It is only based on fitted models
-for which the \code{\link{IRT.irfprob}} does exist.
+for which the \code{\link{[CDM:IRT.irfprob]CDM::IRT.irfprob}} class does exist.
 
 The function \code{IRT.WrightMap} creates a Wright map and works as a wrapper to the
 \code{\link[WrightMap:wrightMap]{WrightMap::wrightMap}} function in
@@ -42,7 +44,8 @@ IRT.WrightMap(object, \dots)
 
 \arguments{
 \item{object}{
-Object of fitted models for which \code{\link{IRT.irfprob}} exists.
+Object of fitted models for which \code{\link{[CDM:IRT.irfprob]CDM::IRT.irfprob}}
+ exists.
 }
 \item{prob.lvl}{Requested probability level of thresholds.}
 \item{type}{Type of thresholds to be calculated. The default is
diff --git a/man/tam.jml.Rd b/man/tam.jml.Rd
index 4cc9db5..e1ba5ec 100644
--- a/man/tam.jml.Rd
+++ b/man/tam.jml.Rd
@@ -1,5 +1,5 @@
 %% File Name: tam.jml.Rd
-%% File Version: 2.405
+%% File Version: 2.408
 
 \name{tam.jml}
 
@@ -20,7 +20,8 @@ item response models with joint maximum likelihood (JML,
 \usage{
 tam.jml(resp, group=NULL, adj=.3, disattenuate=FALSE, bias=TRUE,
     xsi.fixed=NULL, xsi.inits=NULL, theta.fixed=NULL, A=NULL, B=NULL, Q=NULL,
-    ndim=1, pweights=NULL, constraint="cases", verbose=TRUE, control=list(), version=3)
+    ndim=1, pweights=NULL, constraint="cases", verbose=TRUE, control=list(), version=3,
+    theta_proc=NULL)
 
 \method{summary}{tam.jml}(object, file=NULL, \dots)
 
@@ -103,6 +104,8 @@ is the former \code{tam.jml2} function in \pkg{TAM} (<2.0).
 The default \code{version=3} allows efficient handling in case of missing
 data.
 }
+\item{theta_proc}{Function for processing \code{theta} within iterations. Can only
+be applied for \code{version=1}.}
   \item{object}{
 Object of class \code{tam.jml} (only for \code{summary.tam}
 function)
@@ -346,6 +349,39 @@ mod2 <- TAM::tam.jml( resp=resp1, A=A1, xsi.fixed=xsi.fixed, theta.fixed=theta.f
             control=list( Msteps=4, maxiter=100) )
 summary(mod2)
 cbind( mod2$WLE, mod2$errorWLE )
+
+#############################################################################
+# EXAMPLE 5: Disconnected item design
+#############################################################################
+
+# define a disconnected design with two item sets,
+# bit random allocation of persons to item sets
+
+set.seed(878)
+ind1 <- 1:1000      # indices persons group 1
+ind2 <- 1001:3000   # indices persons group 2
+
+I <- 10   # number of items
+# simulate item responses
+dat1 <- sirt::sim.raschtype( rnorm( length(ind1)), b=seq(-2,2,len=I) )
+colnames(dat1) <- paste0("A", 100+1:I)
+dat2 <- sirt::sim.raschtype( rnorm( length(ind2)), b=seq(-1,3,len=I) )
+colnames(dat2) <- paste0("B", 100+1:I)
+# merge datasets
+dat <- plyr::rbind.fill(dat1, dat2)
+summary(dat)
+
+# define theta processing function
+theta_proc <- function(theta){
+    theta[ind1,1] <- theta[ind1,1] - mean( theta[ind1,1] )
+    theta[ind2,1] <- theta[ind2,1] - mean( theta[ind2,1] )
+    return(theta)
+}
+
+# JML estimation
+res <- TAM::tam.jml( dat, theta_proc=theta_proc )
+# check means
+stats::aggregate( res$theta, list(1:3000 %in% ind2), mean )
 }
 }
 
diff --git a/man/tam.wle.Rd b/man/tam.wle.Rd
index 9f4f577..880273a 100644
--- a/man/tam.wle.Rd
+++ b/man/tam.wle.Rd
@@ -1,5 +1,5 @@
 %% File Name: tam.wle.Rd
-%% File Version: 2.507
+%% File Version: 2.509
 
 \name{tam.wle}
 
@@ -33,7 +33,7 @@ tam.mml.wle2(tamobj, score.resp=NULL, WLE=TRUE, adj=0.3, Msteps=20, convM=1e-04,
 
 tam_jml_wle(tamobj, resp, resp.ind, A, B, nstud, nitems, maxK, convM,
     PersonScores, theta, xsi, Msteps, WLE=FALSE, theta.fixed=NULL, progress=FALSE,
-    output.prob=TRUE, damp=0, version=2)
+    output.prob=TRUE, damp=0, version=2, theta_proc=NULL)
 
 \method{summary}{tam.wle}(object, file=NULL, digits=3, \dots)
 
@@ -102,6 +102,7 @@ the fixed value.}
 increments in \eqn{\theta} estimates during iterations}
 \item{version}{Integer with possible values 2 or 3. In case of missing item responses,
 \code{version=3} will typically be more efficient.}
+\item{theta_proc}{Function for processing \code{theta} within iterations.}
 \item{\dots}{Further arguments to be passed}
 \item{object}{Object of class \code{tam.wle}}
 \item{x}{Object of class \code{tam.wle}}
diff --git a/src/RcppExports.cpp b/src/RcppExports.cpp
index ce31d18..187b523 100644
--- a/src/RcppExports.cpp
+++ b/src/RcppExports.cpp
@@ -1,5 +1,5 @@
 //// File Name: RcppExports.cpp
-//// File Version: 4.003002
+//// File Version: 4.003004
 // Generated by using Rcpp::compileAttributes() -> do not edit by hand
 // Generator token: 10BE3573-1514-4C36-9D1C-5A225CD40393
 
diff --git a/src/init.c b/src/init.c
index 344f9c8..948f755 100644
--- a/src/init.c
+++ b/src/init.c
@@ -1,5 +1,5 @@
 //// File Name: init.c
-//// File Version: 4.003002
+//// File Version: 4.003004
 #include 
 #include 
 #include  // for NULL