check_emotikon_transform.qmd

---
title: Transformed and original metrics in Emotikon
---

In @Fuehner2021 the original metric of two tasks (Star, S20) is time, but they were transformed to speed scores in the publication prior to computing z-scores.
The critical result is the absence of evidence for the age x Sex x Test interaction.
Is this interaction significant if we analyse all tasks in their original metric?

Fitting the LMM of the publication takes time, roughly 1 hour.
However, if you save the model parameters (and other relevant information), you can restore the fitted model object very quickly.
The notebook also illustrates this procedure.

## Getting the packages and data

```{julia}
#| code-fold: true
using AlgebraOfGraphics
using Arrow
using CairoMakie
using DataFrames
using DataFrameMacros
using MixedModels
using MixedModelsMakie
using RCall
using Serialization
using StatsBase

CairoMakie.activate!(; type="svg")
datadir = joinpath(@__DIR__, "data");
```

### Data and figure in publication

```{julia}
dat = DataFrame(Arrow.Table(joinpath(datadir, "fggk21.arrow")))
@transform!(dat, :a1 = :age - 8.5);
select!(groupby(dat, :Test), :, :score => zscore => :zScore);
describe(dat)
```

### Data and figure with z-scores based on original metric

```{julia}
# dat_om = rcopy(R"readRDS('./data/fggk21_om.rds')");  #Don't know what the _om is
# @transform!(dat_om, :a1 = :age - 8.5);
# select!(groupby(dat_om, :Test), :, :score => zscore => :zScore);
# describe(dat_om)
```

## LMMs

### Contrasts

```{julia}
contrasts = Dict(
  :Test => SeqDiffCoding(),
  :Sex => HelmertCoding(),
  :School => Grouping(),
  :Child => Grouping(),
  :Cohort => Grouping(),
);
```

### Formula

```{julia}
f1 = @formula zScore ~
  1 +
  Test * a1 * Sex +
  (1 + Test + a1 + Sex | School) +
  (1 + Test | Child) +
  zerocorr(1 + Test | Cohort);
```

### Restore LMM m1 from publication

  - Command for fitting LMM m1 = fit(MixedModel, f1, dat, contrasts=contr)
  - Fit statistics for LMM m1: Minimizing 5179  Time: 0 Time: 1:00:38 ( 0.70  s/it)

```{julia}
m1x = LinearMixedModel(f1, dat; contrasts)
restoreoptsum!(m1x, "./fits/fggk21_m1_optsum.json")
```

```{julia}
VarCorr(m1x)
```

### Restore new LMM m1_om Star and S20 in original metric

  - Command for fitting LMM m1_om = fit(MixedModel, f1, dat_om, contrasts=contr)
  - Minimizing 10502 Time: 0 Time: 2:09:40 ( 0.74  s/it)
  - Store with: julia> saveoptsum("./fits/fggk21_m1_om_optsum.json", m1_om)
  - Only for short-term and when desperate: julia> serialize("./fits/m1_om.jls", m1_om);

#### ... restoreoptsum!()

```{julia}
#| eval: false
m1_om = LinearMixedModel(f1, dat; contrasts=contr);
restoreoptsum!(m1_om, "./fits/fggk21_m1_om_optsum.json");
```

#### ... deserialize()

```{julia}
#| eval: false
m1x_om = deserialize("./fits/m1_om.jls")
```

```{julia}
#| eval: false
VarCorr(m1x_om)
```

### Residual diagnostics for LMM m1

Residual plots for published LMM

```{julia}
#scatter(fitted(m1x), residuals(m1x)
```

```{julia}
#qqnorm(m1x)
```

### Residual diagnostics for LMM m1_om

Residual plots for LMM with Star and Speed in original metric.

```{julia}
#scatter(fitted(m1_om_v2), residuals(m1_om_v2)
```

```{julia}
#qqnorm(m1_om_v2)
```

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