gokceneraslan/Untitled.ipynb

## Untitled.ipynb
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Loading required package: Formula\n",
      "\n",
      "Loading required package: rgl\n",
      "\n",
      "Warning message in rgl.init(initValue, onlyNULL):\n",
      "“RGL: unable to open X11 display”\n",
      "Warning message:\n",
      "“'rgl.init' failed, running with 'rgl.useNULL = TRUE'.”\n"
     ]
    }
   ],
   "source": [
    "library(DirichletReg)\n",
    "library(ggplot2)\n",
    "library(reshape2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = read.csv('https://gist.githubusercontent.com/gokceneraslan/15e20a1da9c2ec8c7ac74b4285a26ded/raw/95b5c21d9de43cfcb0ff8932bf0f00789a393556/dirichlet_test.csv')\n",
    "df.melt = melt(df, id.vars = c('chem', 'dis'), variable.name='m', value.name='proportions')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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I3t3fvixYsmJiZSpwPwTAsICAgICJA6BSBPnGOHmtiwYUNaWbZ431d4mApDpfAx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AwBG4eAIAAACAI3AoliWZTPbzzz8nJCTo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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      },
      "text/plain": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ggplot(data=df.melt, aes(x=m, y=proportions, fill=dis)) +  geom_dotplot(position='dodge', binaxis = \"y\", stackdir = \"center\", binwidth = 0.01) + \n",
    " theme_classic()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in DR_data(df[, 1:3]):\n",
      "“some entries are 0 or 1 => transformation forced”\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Call:\n",
      "DirichReg(formula = y ~ chem + dis, data = df)\n",
      "\n",
      "Standardized Residuals:\n",
      "        Min       1Q   Median      3Q     Max\n",
      "m1  -1.5026  -0.7038  -0.2209  0.5191  2.2051\n",
      "m2  -1.0351  -0.7366  -0.2784  0.1012  2.8222\n",
      "m3  -1.8685  -1.0478   0.1271  1.0657  1.7899\n",
      "\n",
      "------------------------------------------------------------------\n",
      "Beta-Coefficients for variable no. 1: m1\n",
      "            Estimate Std. Error z value Pr(>|z|)  \n",
      "(Intercept)   0.3862     0.7008   0.551   0.5816  \n",
      "chemv3        1.2732     0.5789   2.199   0.0279 *\n",
      "disl         -0.8534     0.5256  -1.624   0.1045  \n",
      "disnl        -1.5845     0.6656  -2.380   0.0173 *\n",
      "------------------------------------------------------------------\n",
      "Beta-Coefficients for variable no. 2: m2\n",
      "            Estimate Std. Error z value Pr(>|z|)    \n",
      "(Intercept)   1.1127     0.6138   1.813 0.069855 .  \n",
      "chemv3        0.8587     0.5784   1.484 0.137688    \n",
      "disl         -1.9920     0.5442  -3.660 0.000252 ***\n",
      "disnl        -1.4530     0.6943  -2.093 0.036374 *  \n",
      "------------------------------------------------------------------\n",
      "Beta-Coefficients for variable no. 3: m3\n",
      "            Estimate Std. Error z value Pr(>|z|)    \n",
      "(Intercept)   1.7268     0.9544   1.809   0.0704 .  \n",
      "chemv3        2.0083     0.7849   2.559   0.0105 *  \n",
      "disl         -2.3143     0.5353  -4.324 1.53e-05 ***\n",
      "disnl        -2.0078     0.8227  -2.440   0.0147 *  \n",
      "------------------------------------------------------------------\n",
      "Significance codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
      "\n",
      "Log-likelihood: 58.3 on 12 df (54 BFGS + 1 NR Iterations)\n",
      "AIC: -92.61, BIC: -76.2\n",
      "Number of Observations: 29\n",
      "Link: Log\n",
      "Parametrization: common\n"
     ]
    }
   ],
   "source": [
    "y = DR_data(df[,1:3])\n",
    "fit = DirichReg(y ~ chem + dis, df)\n",
    "summary(fit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Call:\n",
      "DirichReg(formula = y ~ chem + dis, data = df, model = \"alternative\", sub.comp\n",
      "= 1)\n",
      "\n",
      "Standardized Residuals:\n",
      "             Min       1Q   Median      3Q     Max\n",
      "m2 + m3  -2.0720  -0.3425   0.0689  0.7798  1.6014\n",
      "m1       -1.6014  -0.7798  -0.0689  0.3425  2.0720\n",
      "\n",
      "MEAN MODELS:\n",
      "------------------------------------------------------------------\n",
      "Coefficients for variable no. 1: m2 + m3\n",
      "- variable omitted (reference category) -\n",
      "------------------------------------------------------------------\n",
      "Coefficients for variable no. 2: m1\n",
      "            Estimate Std. Error z value Pr(>|z|)    \n",
      "(Intercept)  -2.0792     0.4602  -4.518 6.23e-06 ***\n",
      "chemv3        0.3660     0.3827   0.956   0.3389    \n",
      "disl          0.9703     0.3891   2.494   0.0126 *  \n",
      "disnl        -0.2712     0.4275  -0.634   0.5259    \n",
      "------------------------------------------------------------------\n",
      "\n",
      "PRECISION MODEL:\n",
      "------------------------------------------------------------------\n",
      "            Estimate Std. Error z value Pr(>|z|)    \n",
      "(Intercept)   2.0105     0.2629   7.649 2.03e-14 ***\n",
      "------------------------------------------------------------------\n",
      "Significance codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
      "\n",
      "Log-likelihood: 24.84 on 5 df (30 BFGS + 1 NR Iterations)\n",
      "AIC: -39.69, BIC: -32.85\n",
      "Number of Observations: 29\n",
      "Links: Logit (Means) and Log (Precision)\n",
      "Parametrization: alternative\n"
     ]
    }
   ],
   "source": [
    "fit = DirichReg(y ~ chem + dis, df, model = 'alternative', sub.comp = 1)\n",
    "summary(fit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Call:\n",
      "DirichReg(formula = y ~ chem + dis, data = df, model = \"alternative\", sub.comp\n",
      "= 2)\n",
      "\n",
      "Standardized Residuals:\n",
      "             Min       1Q   Median      3Q     Max\n",
      "m1 + m3  -1.6672  -0.2930   0.3303  0.8385  1.4095\n",
      "m2       -1.4095  -0.8385  -0.3303  0.2930  1.6672\n",
      "\n",
      "MEAN MODELS:\n",
      "------------------------------------------------------------------\n",
      "Coefficients for variable no. 1: m1 + m3\n",
      "- variable omitted (reference category) -\n",
      "------------------------------------------------------------------\n",
      "Coefficients for variable no. 2: m2\n",
      "            Estimate Std. Error z value Pr(>|z|)    \n",
      "(Intercept)  -0.3558     0.4079  -0.872  0.38298    \n",
      "chemv3       -1.9760     0.3636  -5.435 5.48e-08 ***\n",
      "disl          0.1497     0.4864   0.308  0.75829    \n",
      "disnl         1.3220     0.4815   2.746  0.00603 ** \n",
      "------------------------------------------------------------------\n",
      "\n",
      "PRECISION MODEL:\n",
      "------------------------------------------------------------------\n",
      "            Estimate Std. Error z value Pr(>|z|)    \n",
      "(Intercept)   1.8823     0.2848   6.608 3.89e-11 ***\n",
      "------------------------------------------------------------------\n",
      "Significance codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
      "\n",
      "Log-likelihood: 22.67 on 5 df (30 BFGS + 1 NR Iterations)\n",
      "AIC: -35.34, BIC: -28.5\n",
      "Number of Observations: 29\n",
      "Links: Logit (Means) and Log (Precision)\n",
      "Parametrization: alternative\n"
     ]
    }
   ],
   "source": [
    "fit = DirichReg(y ~ chem + dis, df, model = 'alternative', sub.comp = 2)\n",
    "summary(fit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Call:\n",
      "DirichReg(formula = y ~ chem + dis, data = df, model = \"alternative\", sub.comp\n",
      "= 3)\n",
      "\n",
      "Standardized Residuals:\n",
      "             Min       1Q   Median      3Q     Max\n",
      "m1 + m2  -1.8135  -0.9328  -0.2562  0.5769  1.4859\n",
      "m3       -1.4859  -0.5769   0.2562  0.9328  1.8135\n",
      "\n",
      "MEAN MODELS:\n",
      "------------------------------------------------------------------\n",
      "Coefficients for variable no. 1: m1 + m2\n",
      "- variable omitted (reference category) -\n",
      "------------------------------------------------------------------\n",
      "Coefficients for variable no. 2: m3\n",
      "            Estimate Std. Error z value Pr(>|z|)    \n",
      "(Intercept)  -0.1215     0.4493  -0.270 0.786907    \n",
      "chemv3        1.5101     0.4053   3.726 0.000195 ***\n",
      "disl         -0.9476     0.4808  -1.971 0.048756 *  \n",
      "disnl        -1.0022     0.4552  -2.202 0.027678 *  \n",
      "------------------------------------------------------------------\n",
      "\n",
      "PRECISION MODEL:\n",
      "------------------------------------------------------------------\n",
      "            Estimate Std. Error z value Pr(>|z|)    \n",
      "(Intercept)   1.5191     0.2453   6.192 5.94e-10 ***\n",
      "------------------------------------------------------------------\n",
      "Significance codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
      "\n",
      "Log-likelihood: 8.812 on 5 df (25 BFGS + 1 NR Iterations)\n",
      "AIC: -7.624, BIC: -0.7877\n",
      "Number of Observations: 29\n",
      "Links: Logit (Means) and Log (Precision)\n",
      "Parametrization: alternative\n"
     ]
    }
   ],
   "source": [
    "fit = DirichReg(y ~ chem + dis, df, model = 'alternative', sub.comp = 3)\n",
    "summary(fit)"
   ]
  }
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