6_chemometrics_correlationDependance.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chemometrics\n",
    "<br>\n",
    "**Julien Wist / 2017 / Universidad del Valle**\n",
    "<br>\n",
    "**Andrés Bernal / 2017 / ???**\n",
    "\n",
    "An up-to-date version of this notebook can be found here: https://github.com/jwist/chemometrics/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "options(repr.plot.width=4, repr.plot.height=4) # change these setting to plot larger figures"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## dependance and correlation and orthogonality\n",
    "\n",
    "We should try to explain the difference in results we obtained by scaling the data in this simple example. The main question we want to answer with this example is precisely about the importance of the IVs (temperature, pH, concentration and the intereaction terms). The fact that such a difference, not only in magnitude but also in trends (the ranking of importance is not maintained) call for a more thorough explanation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider the following function: $y=x^2$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "-0.0853006355036285"
      ],
      "text/latex": [
       "-0.0853006355036285"
      ],
      "text/markdown": [
       "-0.0853006355036285"
      ],
      "text/plain": [
       "[1] -0.08530064"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "\tPearson's Chi-squared test with simulated p-value (based on 2000\n",
       "\treplicates)\n",
       "\n",
       "data:  x and y\n",
       "X-squared = 39800, df = NA, p-value = 0.0004998\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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758r5mZmZOnp6dzYFUoTU1NnTA7O3tO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\nBCAAgRoiUOsDpLt0r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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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0kVDvXLerWdk+67CNs2dv4z+7PkxM6+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\nRK5CYII=",
      "text/plain": [
       "Plot with title “Histogram of y”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x <- runif(200, min = -1, max = 1)\n",
    "y <- x^2 + rnorm(200, sd = 0.002)\n",
    "plot(x,y,pch=16)\n",
    "rug(x,side=1,col=\"grey\")\n",
    "rug(y,side=2,col=\"grey\")\n",
    "cor(x,y)\n",
    "chisq.test(x,y, simulate.p.value = TRUE)\n",
    "d1 <- hist(y, breaks = 200, right=FALSE, plot = FALSE)\n",
    "plot(d1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and compare it with $y=x$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "1"
      ],
      "text/latex": [
       "1"
      ],
      "text/markdown": [
       "1"
      ],
      "text/plain": [
       "[1] 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "\tPearson's Chi-squared test with simulated p-value (based on 2000\n",
       "\treplicates)\n",
       "\n",
       "data:  x and y\n",
       "X-squared = 39800, df = NA, p-value = 0.0004998\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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KwnwABpPZLabDj99NO9ESNG/FgPim1zbYEWeviK6rjbtR7KI4AAAggggAACNRA4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\nQar27lh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F562Zid/4Jvvt6SEOgk8FG9s763tNPcdwdJueb7smXeflr/Wt6jci1k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\nAAIIJEPg/wNWtK8blk+ysgAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x <- runif(200,min=-1,max=1)\n",
    "y <- x\n",
    "plot(x,y,pch=16)\n",
    "rug(x,side=1,col=\"grey\")\n",
    "rug(y,side=2,col=\"grey\")\n",
    "cor(x,y)\n",
    "chisq.test(x,y, simulate.p.value = TRUE) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Despite in both cases $x$ and $y$ are dependent, in the left case they are completely uncorrelated. So being uncorrelated is not the same as being independent, but independant variables are uncorrelated. Two variables are considered independent when their joint probability distribution is equal to the product of their individual marginal probability distributions: $$P_{X,Y}(x,y)=P_X(x)P_Y(y)$$\n",
    "\n",
    "Two variables are uncorrelated when their correlation coefficient is zero or when their covariance is equal to zero."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### correlations in experimental design\n",
    "\n",
    "Experimental design is all about designing an experiment where the IV are uncorrelated so that effect of each IV can be studied separately. Then, by definition we can assume that IV are uncorrelated. You can check this for our chemical data. For example the correlation between pH and temperature is `r cor(datas$ph, datas$temp)`, while the correlation between ph and pH$\\times$T is `r cor(datas$ph,datas$phTemp)`, non zero as expected.\n",
    "\n",
    "if we look at the data for example for example for temperature and concentration we might have `r d[2,2:3]` and `r d[3,2:3]` for second and third point. If we represent them as vectors, we can see that both vectors are somehow collinear and that the product of both vectors is even more collinear."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      ],
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/svg+xml": {
       "isolated": true
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "d <- c(6,60,4,34.841,6,60,2,16.567,6,20,4,45.396,6,20,2,27.939,4,60,4,19.825,4,60,2,1.444,4,20,4,37.673,4,20,2,23.131,6,40,3,23.088,4,40,3,12.325,5,60,3,16.461,5,20,3,33.489,5,40,4,26.189,5,40,2,8.337,5,40,3,19.192,5,40,3,16.579,5,40,3,17.794,5,40,3,16.65,5,40,3,16.799,5,40,3,16.635)\n",
    "dim(d) <- c(4,20) # we force the data into a mtrix of dimension 4 x 20\n",
    "# we create the data frame\n",
    "\n",
    "plot(d[1,],d[2,], ylim=c(0,80), xlim=c(0,120),type='n')\n",
    "for (i in 2) {\n",
    "  arrows(x0=0, y0=0, x1=d[2,i], y1=d[2,i+1])\n",
    "  arrows(x0=0, y0=0, x1=d[3,i], y1=d[3,i+1],col=2)\n",
    "  arrows(x0=0, y0=0, x1=d[3,i]*d[2,i], y1=d[3,i+1]*d[2,i+1],col=3)\n",
    "}\n",
    "abline(0,0)\n",
    "abline(v=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, if we scale / encode these data and draw again their vector we observe that they became orthogonal. So the collinearity has been reduced by proper scaling.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "plot without title"
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      "image/svg+xml": {
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   ],
   "source": [
    "# scale with y <- (2*x - max(x) - min(x)) / (max(x)-min(x))\n",
    "maxs <- apply(d[1:3,],1,max); mins <- apply(d[1:3,],1,min)\n",
    "d[1:3,] <- t( scale(t(d)[,1:3],center = (mins + maxs)/2, scale = (maxs - mins)/2) )\n",
    "\n",
    "plot(d[1,],d[2,], ylim=c(-1,1), xlim=c(-1,1),type='n')\n",
    "for (i in 2) {\n",
    "  arrows(x0=0, y0=0, x1=d[2,i], y1=d[2,i+1])\n",
    "  arrows(x0=0, y0=0, x1=d[3,i], y1=d[3,i+1],col=2)\n",
    "  arrows(x0=0, y0=0, x1=d[3,i]*d[2,i], y1=d[3,i+1]*d[2,i+1],col=3)\n",
    "}\n",
    "abline(0,0)\n",
    "abline(v=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Collinearity should be avoided because it causes overfitting. The goal of a regression is to find the best variables (IVs) than explain most of the variance in the dependent variable (DV). This is usually measured by the explained variance, $R^2$, parameter. Too many collinear predictors may lead to high values of $R^2$ without the resulting model being necessarily useful. Collinear predictors are poor at describing the whole variable space. For example, we can find a best line that passes close to three points in space. If points are close, the error may be much larger, without incrementing the residuals, than if the three points are spread over a large distance. \n",
    "\n",
    "In addition, in the case of collinear variable, it will be difficult to rank them according to their importance to explain variance. Indeed the importance of a variable will depend on the order in which the variable are taken into account. If one vector explains a lot of variance, a collinear predictor that follow will not be able to explain anymore variance and will thus be discarded, although it contains important information.\n",
    "\n",
    "<div class=\"ref\">\n",
    "http://creative-wisdom.com/computer/sas/collinear.html\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"https://raw.githubusercontent.com/jwist/chemometrics/master/img/stepwise1.gif\" width=\"200\"><img src=\"https://raw.githubusercontent.com/jwist/chemometrics/master/img/stepwise2.gif\" width=\"200\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is best illustrated by the above figures. In one case, each variable will explain its part of variance, while in the second case, several variable explain \"the same\" bit of variance."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### high number of variable\n",
    "\n",
    "Imagine for a moment that the number of available variables (predictors) is much higher that the number of observation. In this case, the degree of freedom will become negative, that is the system lacks degrees of freedom, a situation which is referred to as overfitting. It is thus necessary to reduce the number of variables a task that is achieved by step-wise regression, etc. The general principles behind these methods consists in performing regressions with different combinations of variables in order to find out the ones to keep. \n",
    "\n",
    "However there are others and more robust alternatives to these methods that aknowledge the redundancy of information spanned by collinear predictors and try to convert collinearity of predictors (an issue) into reliability (a plusvalue). Such methods, as PLS (Projection to Latent Structure, a.k.a Partial Least Square), seek projecting predictors into composit variables to better explain the structure of the response. Moreover, PLS focuses on prediction, rather than fit, and is inherently weak at posterior interpretation of the relevant variables (this is also known as soft-modeling). Such methods also forms the domain of multivariate analysis, which should not be confused with multiple regression or multiple variable analysis. "
   ]
  }
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