regression_blog4.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Logistic Regression for passing a test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>attempt</th>\n",
       "      <th>bukv</th>\n",
       "      <th>bukv0</th>\n",
       "      <th>host</th>\n",
       "      <th>kr</th>\n",
       "      <th>naextra</th>\n",
       "      <th>ncextra</th>\n",
       "      <th>nfscan</th>\n",
       "      <th>npause</th>\n",
       "      <th>nscan</th>\n",
       "      <th>...</th>\n",
       "      <th>tclast</th>\n",
       "      <th>texit</th>\n",
       "      <th>u</th>\n",
       "      <th>userid</th>\n",
       "      <th>var</th>\n",
       "      <th>vt</th>\n",
       "      <th>cmid</th>\n",
       "      <th>course</th>\n",
       "      <th>grade</th>\n",
       "      <th>result</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1795</td>\n",
       "      <td>257</td>\n",
       "      <td>147</td>\n",
       "      <td>up11</td>\n",
       "      <td>0.432422</td>\n",
       "      <td>-3</td>\n",
       "      <td>-2</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>64.556</td>\n",
       "      <td>66.461</td>\n",
       "      <td>UP11__4103478780151029</td>\n",
       "      <td>540</td>\n",
       "      <td>5</td>\n",
       "      <td>12.972669</td>\n",
       "      <td>1706</td>\n",
       "      <td>9</td>\n",
       "      <td>0.25</td>\n",
       "      <td>correct</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1795</td>\n",
       "      <td>283</td>\n",
       "      <td>49</td>\n",
       "      <td>up11</td>\n",
       "      <td>1.662998</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>158.545</td>\n",
       "      <td>159.532</td>\n",
       "      <td>UP11__4106285050151029</td>\n",
       "      <td>540</td>\n",
       "      <td>3</td>\n",
       "      <td>49.889946</td>\n",
       "      <td>1706</td>\n",
       "      <td>9</td>\n",
       "      <td>0.00</td>\n",
       "      <td>incorrect</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1795</td>\n",
       "      <td>81</td>\n",
       "      <td>27</td>\n",
       "      <td>up11</td>\n",
       "      <td>1.431508</td>\n",
       "      <td>-2</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>17.633</td>\n",
       "      <td>18.453</td>\n",
       "      <td>UP11__4106480830151029</td>\n",
       "      <td>540</td>\n",
       "      <td>4</td>\n",
       "      <td>42.945239</td>\n",
       "      <td>1706</td>\n",
       "      <td>9</td>\n",
       "      <td>0.00</td>\n",
       "      <td>incorrect</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1795</td>\n",
       "      <td>251</td>\n",
       "      <td>21</td>\n",
       "      <td>up11</td>\n",
       "      <td>1.870821</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>23.561</td>\n",
       "      <td>24.441</td>\n",
       "      <td>UP11__4107136770151029</td>\n",
       "      <td>540</td>\n",
       "      <td>4</td>\n",
       "      <td>56.124639</td>\n",
       "      <td>1706</td>\n",
       "      <td>9</td>\n",
       "      <td>0.25</td>\n",
       "      <td>correct</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1795</td>\n",
       "      <td>117</td>\n",
       "      <td>75</td>\n",
       "      <td>up11</td>\n",
       "      <td>0.275338</td>\n",
       "      <td>-1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>32.652</td>\n",
       "      <td>33.450</td>\n",
       "      <td>UP11__4107482870151029</td>\n",
       "      <td>540</td>\n",
       "      <td>3</td>\n",
       "      <td>8.260141</td>\n",
       "      <td>1706</td>\n",
       "      <td>9</td>\n",
       "      <td>0.25</td>\n",
       "      <td>correct</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 26 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   attempt  bukv  bukv0  host        kr  naextra  ncextra  nfscan  npause  \\\n",
       "0     1795   257    147  up11  0.432422       -3       -2       0       1   \n",
       "1     1795   283     49  up11  1.662998        4        0       0       2   \n",
       "2     1795    81     27  up11  1.431508       -2        0       0       0   \n",
       "3     1795   251     21  up11  1.870821        1        0       0       0   \n",
       "4     1795   117     75  up11  0.275338       -1        0       0       1   \n",
       "\n",
       "   nscan    ...       tclast    texit                       u userid  var  \\\n",
       "0      0    ...       64.556   66.461  UP11__4103478780151029    540    5   \n",
       "1      1    ...      158.545  159.532  UP11__4106285050151029    540    3   \n",
       "2      0    ...       17.633   18.453  UP11__4106480830151029    540    4   \n",
       "3      1    ...       23.561   24.441  UP11__4107136770151029    540    4   \n",
       "4      0    ...       32.652   33.450  UP11__4107482870151029    540    3   \n",
       "\n",
       "          vt  cmid  course grade     result  \n",
       "0  12.972669  1706       9  0.25    correct  \n",
       "1  49.889946  1706       9  0.00  incorrect  \n",
       "2  42.945239  1706       9  0.00  incorrect  \n",
       "3  56.124639  1706       9  0.25    correct  \n",
       "4   8.260141  1706       9  0.25    correct  \n",
       "\n",
       "[5 rows x 26 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D=pandas.read_table('..\\StiReac\\D.tsv')\n",
    "D.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us use `statsmodel` module to test a logistic regression model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will test a logistic regression model for the association between explanatory variables - time of exit (`texit`) and a response variable - result (`result`), exposed as a binary categorical variable (`y`).\n",
    "\n",
    "The hypothesis is the more thouroughly reading (more time of exit) the more thinking and the less guessing.\n",
    "\n",
    "To exclude trials with cheating we use subsample without pauses (`npause<1`)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "D = D[D.npause<1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Make binary response variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PevTRR2e9hNYwi8IsCrOoZ83fzhkRbwT+MDPfERG/C3wwM7cf5bg2vC9KkjrnWN/O2cTg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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x8152a50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "D['y'] = 0\n",
    "D.ix[D.result == 'correct','y']=1\n",
    "D.y.hist();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.631916\n",
      "         Iterations 5\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Logit Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>         <td>y</td>        <th>  No. Observations:  </th>  <td>  2894</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>               <td>Logit</td>      <th>  Df Residuals:      </th>  <td>  2892</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>               <td>MLE</td>       <th>  Df Model:          </th>  <td>     1</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>          <td>Sun, 13 Mar 2016</td> <th>  Pseudo R-squ.:     </th>  <td>0.01634</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>              <td>20:08:13</td>     <th>  Log-Likelihood:    </th> <td> -1828.8</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>converged:</th>           <td>True</td>       <th>  LL-Null:           </th> <td> -1859.1</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th> </th>                      <td> </td>        <th>  LLR p-value:       </th> <td>6.508e-15</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th> <th>[95.0% Conf. Int.]</th> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th> <td>    0.1728</td> <td>    0.074</td> <td>    2.348</td> <td> 0.019</td> <td>    0.029     0.317</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>texit</th>     <td>    0.0263</td> <td>    0.004</td> <td>    7.446</td> <td> 0.000</td> <td>    0.019     0.033</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                           Logit Regression Results                           \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   No. Observations:                 2894\n",
       "Model:                          Logit   Df Residuals:                     2892\n",
       "Method:                           MLE   Df Model:                            1\n",
       "Date:                Sun, 13 Mar 2016   Pseudo R-squ.:                 0.01634\n",
       "Time:                        20:08:13   Log-Likelihood:                -1828.8\n",
       "converged:                       True   LL-Null:                       -1859.1\n",
       "                                        LLR p-value:                 6.508e-15\n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [95.0% Conf. Int.]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept      0.1728      0.074      2.348      0.019         0.029     0.317\n",
       "texit          0.0263      0.004      7.446      0.000         0.019     0.033\n",
       "==============================================================================\n",
       "\"\"\""
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg1 = smf.logit('y ~ texit ', data=D).fit()\n",
    "reg1.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intercept    1.188662\n",
      "texit        1.026676\n",
      "dtype: float64\n",
      "                  0         1\n",
      "Intercept  1.028999  1.373099\n",
      "texit      1.019585  1.033815\n"
     ]
    }
   ],
   "source": [
    "#odd ratio\n",
    "print(exp(reg1.params))\n",
    "print(exp(reg1.conf_int()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The results of the logistic regression model indicated that result of test is significantly better when time of exit is later (OR=1.03, 95% CI = 1.02-1.034, p<.001).\n",
    "\n",
    "   \n",
    "So the found model can be written \n",
    "$$ r =  \\frac{1}{1 + e^{-0.173 -0.026 t_{exit}}} $$\n",
    "where $r$ - result (0 - fail, 1 - success), $t_{exit}$ - time of exit\n",
    "\n",
    "\n",
    "So, results supported my hypothesis for the association between the explanatory variable and the response variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import seaborn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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lfwG+OloCJwcVHuH680RkgxjyJDut7Xq8uSMbWYX1GOjljEeTYzHQy1nqsoiI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\nEZFM/X/mlJTBe8cViAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12b317d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xx = arange(-20,100)\n",
    "yy= 1/(1+exp(-reg1.params['Intercept'] -reg1.params['texit']*xx))\n",
    "plot(xx, yy);\n",
    "xlabel('texit');\n",
    "ylabel('result');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regression plots\n",
    "\n",
    "seaborn can plot raw data together with regression line. Let us compare with a model plot above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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suI4FTfNa9vFIAKFQlGFPRHUx/ImugmEYyOSKKJkOVD0IWQ3WnZPfnynhYDnw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\nRURELOYfVB19NisqGNUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12b3c170>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "seaborn.regplot('texit','y', data=D, logistic=True)\n",
    "xlabel('texit');ylabel('result');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plots look the same. Our calculated model is like the built-in one in seaborn module.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Confounding "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Test problem contains texts of different length.\n",
    "So the text length can be confounding variable. To check this we add a variable `bukv` - number of letters in the question task and answer distractors.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.628807\n",
      "         Iterations 5\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Logit Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>         <td>y</td>        <th>  No. Observations:  </th>  <td>  2894</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>               <td>Logit</td>      <th>  Df Residuals:      </th>  <td>  2891</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>               <td>MLE</td>       <th>  Df Model:          </th>  <td>     2</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>          <td>Sun, 13 Mar 2016</td> <th>  Pseudo R-squ.:     </th>  <td>0.02118</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>              <td>21:40:20</td>     <th>  Log-Likelihood:    </th> <td> -1819.8</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>converged:</th>           <td>True</td>       <th>  LL-Null:           </th> <td> -1859.1</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th> </th>                      <td> </td>        <th>  LLR p-value:       </th> <td>7.994e-18</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th> <th>[95.0% Conf. Int.]</th> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th> <td>    0.5141</td> <td>    0.109</td> <td>    4.730</td> <td> 0.000</td> <td>    0.301     0.727</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>texit</th>     <td>    0.0284</td> <td>    0.004</td> <td>    7.920</td> <td> 0.000</td> <td>    0.021     0.035</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>bukv</th>      <td>   -0.0020</td> <td>    0.000</td> <td>   -4.256</td> <td> 0.000</td> <td>   -0.003    -0.001</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                           Logit Regression Results                           \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   No. Observations:                 2894\n",
       "Model:                          Logit   Df Residuals:                     2891\n",
       "Method:                           MLE   Df Model:                            2\n",
       "Date:                Sun, 13 Mar 2016   Pseudo R-squ.:                 0.02118\n",
       "Time:                        21:40:20   Log-Likelihood:                -1819.8\n",
       "converged:                       True   LL-Null:                       -1859.1\n",
       "                                        LLR p-value:                 7.994e-18\n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [95.0% Conf. Int.]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept      0.5141      0.109      4.730      0.000         0.301     0.727\n",
       "texit          0.0284      0.004      7.920      0.000         0.021     0.035\n",
       "bukv          -0.0020      0.000     -4.256      0.000        -0.003    -0.001\n",
       "==============================================================================\n",
       "\"\"\""
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg1 = smf.logit('y ~ texit + bukv', data=D).fit()\n",
    "reg1.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The confounding is not detected.\n",
    "\n",
    "No confounding for number of scans (`nscan`) and for reading rate (`kr`) also."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Successful result is more probable as the time of exit increases.\n",
    "The model supports my original hypothesis but can be improved."
   ]
  }
 ],
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