6_demographics_bias.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "39460"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.special import logit\n",
    "import pandas as pd\n",
    "\n",
    "## Regression against the demographics:\n",
    "## DJ preprocessed the data using sql\n",
    "## 1 worker per row: count\n",
    "##    - count: number of identical rows\n",
    "##    - participation: number of submissions\n",
    "##  if count <> participation, worker changed his reponses (participation - count) times\n",
    "\n",
    "dem_df = pd.read_csv(\"demographics_preprocessed.csv\")\n",
    "\n",
    "dem_df[\"household_income\"]=dem_df[\"household_income\"].astype(\"category\")\n",
    "dem_df[\"household_size\"]=dem_df[\"household_size\"].astype(\"category\")\n",
    "dem_df[\"location_country\"]=dem_df[\"location_country\"].astype(\"category\")\n",
    "dem_df[\"marital_status\"]=dem_df[\"marital_status\"].astype(\"category\")\n",
    "dem_df[\"year_of_birth\"]=dem_df[\"year_of_birth\"].astype(int)\n",
    "\n",
    "dem_df['propensity'] = dem_df['participation']/29\n",
    "dem_df['life_event'] = dem_df['count']!= dem_df['participation']\n",
    "dem_df['life_event'] = dem_df['life_event'].apply(lambda x : 1 if x else 0)\n",
    "dem_df['location_country'] = dem_df['location_country'].apply(lambda x : x if x in ['US','IN','CA','GB','PH'] else 'OTHER')\n",
    "dem_df['age'] = 2017 - dem_df['year_of_birth']\n",
    "\n",
    "len(dem_df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>       <td>propensity</td>    <th>  R-squared:         </th>  <td>   0.284</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th>  <td>   0.283</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th>  <td>   578.3</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Fri, 15 Dec 2017</td> <th>  Prob (F-statistic):</th>   <td>  0.00</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>23:11:42</td>     <th>  Log-Likelihood:    </th>  <td>  43156.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td> 39460</td>      <th>  AIC:               </th> <td>-8.626e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td> 39432</td>      <th>  BIC:               </th> <td>-8.602e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>    27</td>      <th>                     </th>      <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>      <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "                      <td></td>                        <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>                                <td>    0.3227</td> <td>    0.115</td> <td>    2.812</td> <td> 0.005</td> <td>    0.098</td> <td>    0.548</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(location_country)[T.GB]</th>                <td>   -0.0050</td> <td>    0.005</td> <td>   -0.946</td> <td> 0.344</td> <td>   -0.015</td> <td>    0.005</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(location_country)[T.IN]</th>                <td>    0.0119</td> <td>    0.004</td> <td>    3.199</td> <td> 0.001</td> <td>    0.005</td> <td>    0.019</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(location_country)[T.OTHER]</th>             <td>   -0.0026</td> <td>    0.004</td> <td>   -0.687</td> <td> 0.492</td> <td>   -0.010</td> <td>    0.005</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(location_country)[T.PH]</th>                <td>   -0.0016</td> <td>    0.008</td> <td>   -0.212</td> <td> 0.832</td> <td>   -0.017</td> <td>    0.013</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(location_country)[T.US]</th>                <td>    0.0032</td> <td>    0.003</td> <td>    0.919</td> <td> 0.358</td> <td>   -0.004</td> <td>    0.010</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(gender)[T.female]</th>                      <td>    0.0065</td> <td>    0.081</td> <td>    0.080</td> <td> 0.936</td> <td>   -0.153</td> <td>    0.165</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(gender)[T.male]</th>                        <td>    0.0062</td> <td>    0.081</td> <td>    0.077</td> <td> 0.939</td> <td>   -0.153</td> <td>    0.165</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(household_income)[T.$100,000 or more]</th>  <td>    0.0053</td> <td>    0.002</td> <td>    2.630</td> <td> 0.009</td> <td>    0.001</td> <td>    0.009</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(household_income)[T.$15,000-$24,999]</th>   <td>    0.0040</td> <td>    0.002</td> <td>    2.066</td> <td> 0.039</td> <td>    0.000</td> <td>    0.008</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(household_income)[T.$25,000-$39,999]</th>   <td>    0.0047</td> <td>    0.002</td> <td>    2.561</td> <td> 0.010</td> <td>    0.001</td> <td>    0.008</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(household_income)[T.$40,000-$59,999]</th>   <td>    0.0052</td> <td>    0.002</td> <td>    2.843</td> <td> 0.004</td> <td>    0.002</td> <td>    0.009</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(household_income)[T.$60,000-$74,999]</th>   <td>    0.0014</td> <td>    0.002</td> <td>    0.689</td> <td> 0.491</td> <td>   -0.003</td> <td>    0.005</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(household_income)[T.$75,000-$99,999]</th>   <td>    0.0040</td> <td>    0.002</td> <td>    1.977</td> <td> 0.048</td> <td> 3.44e-05</td> <td>    0.008</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(household_income)[T.Less than $10,000]</th> <td>    0.0074</td> <td>    0.002</td> <td>    3.906</td> <td> 0.000</td> <td>    0.004</td> <td>    0.011</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(household_size)[T.2]</th>                   <td>   -0.0026</td> <td>    0.001</td> <td>   -1.867</td> <td> 0.062</td> <td>   -0.005</td> <td>    0.000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(household_size)[T.3]</th>                   <td>   -0.0005</td> <td>    0.001</td> <td>   -0.347</td> <td> 0.729</td> <td>   -0.003</td> <td>    0.002</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(household_size)[T.4]</th>                   <td>   -0.0017</td> <td>    0.001</td> <td>   -1.117</td> <td> 0.264</td> <td>   -0.005</td> <td>    0.001</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(household_size)[T.5+]</th>                  <td>   -0.0005</td> <td>    0.002</td> <td>   -0.320</td> <td> 0.749</td> <td>   -0.004</td> <td>    0.003</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(marital_status)[T.cohabitating]</th>        <td>   -0.3186</td> <td>    0.081</td> <td>   -3.928</td> <td> 0.000</td> <td>   -0.478</td> <td>   -0.160</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(marital_status)[T.divorced]</th>            <td>   -0.3241</td> <td>    0.081</td> <td>   -3.996</td> <td> 0.000</td> <td>   -0.483</td> <td>   -0.165</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(marital_status)[T.engaged]</th>             <td>   -0.3208</td> <td>    0.081</td> <td>   -3.954</td> <td> 0.000</td> <td>   -0.480</td> <td>   -0.162</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(marital_status)[T.married]</th>             <td>   -0.3147</td> <td>    0.081</td> <td>   -3.880</td> <td> 0.000</td> <td>   -0.474</td> <td>   -0.156</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(marital_status)[T.separated]</th>           <td>   -0.3510</td> <td>    0.115</td> <td>   -3.060</td> <td> 0.002</td> <td>   -0.576</td> <td>   -0.126</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(marital_status)[T.single]</th>              <td>   -0.3161</td> <td>    0.081</td> <td>   -3.898</td> <td> 0.000</td> <td>   -0.475</td> <td>   -0.157</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(marital_status)[T.widowed]</th>             <td>   -0.2182</td> <td>    0.086</td> <td>   -2.537</td> <td> 0.011</td> <td>   -0.387</td> <td>   -0.050</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(life_event)[T.1]</th>                       <td>    0.1197</td> <td>    0.001</td> <td>  118.476</td> <td> 0.000</td> <td>    0.118</td> <td>    0.122</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>age</th>                                      <td>    0.0008</td> <td> 4.38e-05</td> <td>   18.711</td> <td> 0.000</td> <td>    0.001</td> <td>    0.001</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>35237.290</td> <th>  Durbin-Watson:     </th>  <td>   2.004</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th>  <td> 0.000</td>   <th>  Jarque-Bera (JB):  </th> <td>1292176.011</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>           <td> 4.303</td>   <th>  Prob(JB):          </th>  <td>    0.00</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>       <td>29.680</td>   <th>  Cond. No.          </th>  <td>2.07e+04</td>  \n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:             propensity   R-squared:                       0.284\n",
       "Model:                            OLS   Adj. R-squared:                  0.283\n",
       "Method:                 Least Squares   F-statistic:                     578.3\n",
       "Date:                Fri, 15 Dec 2017   Prob (F-statistic):               0.00\n",
       "Time:                        23:11:42   Log-Likelihood:                 43156.\n",
       "No. Observations:               39460   AIC:                        -8.626e+04\n",
       "Df Residuals:                   39432   BIC:                        -8.602e+04\n",
       "Df Model:                          27                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "============================================================================================================\n",
       "                                               coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------------------------------------\n",
       "Intercept                                    0.3227      0.115      2.812      0.005       0.098       0.548\n",
       "C(location_country)[T.GB]                   -0.0050      0.005     -0.946      0.344      -0.015       0.005\n",
       "C(location_country)[T.IN]                    0.0119      0.004      3.199      0.001       0.005       0.019\n",
       "C(location_country)[T.OTHER]                -0.0026      0.004     -0.687      0.492      -0.010       0.005\n",
       "C(location_country)[T.PH]                   -0.0016      0.008     -0.212      0.832      -0.017       0.013\n",
       "C(location_country)[T.US]                    0.0032      0.003      0.919      0.358      -0.004       0.010\n",
       "C(gender)[T.female]                          0.0065      0.081      0.080      0.936      -0.153       0.165\n",
       "C(gender)[T.male]                            0.0062      0.081      0.077      0.939      -0.153       0.165\n",
       "C(household_income)[T.$100,000 or more]      0.0053      0.002      2.630      0.009       0.001       0.009\n",
       "C(household_income)[T.$15,000-$24,999]       0.0040      0.002      2.066      0.039       0.000       0.008\n",
       "C(household_income)[T.$25,000-$39,999]       0.0047      0.002      2.561      0.010       0.001       0.008\n",
       "C(household_income)[T.$40,000-$59,999]       0.0052      0.002      2.843      0.004       0.002       0.009\n",
       "C(household_income)[T.$60,000-$74,999]       0.0014      0.002      0.689      0.491      -0.003       0.005\n",
       "C(household_income)[T.$75,000-$99,999]       0.0040      0.002      1.977      0.048    3.44e-05       0.008\n",
       "C(household_income)[T.Less than $10,000]     0.0074      0.002      3.906      0.000       0.004       0.011\n",
       "C(household_size)[T.2]                      -0.0026      0.001     -1.867      0.062      -0.005       0.000\n",
       "C(household_size)[T.3]                      -0.0005      0.001     -0.347      0.729      -0.003       0.002\n",
       "C(household_size)[T.4]                      -0.0017      0.001     -1.117      0.264      -0.005       0.001\n",
       "C(household_size)[T.5+]                     -0.0005      0.002     -0.320      0.749      -0.004       0.003\n",
       "C(marital_status)[T.cohabitating]           -0.3186      0.081     -3.928      0.000      -0.478      -0.160\n",
       "C(marital_status)[T.divorced]               -0.3241      0.081     -3.996      0.000      -0.483      -0.165\n",
       "C(marital_status)[T.engaged]                -0.3208      0.081     -3.954      0.000      -0.480      -0.162\n",
       "C(marital_status)[T.married]                -0.3147      0.081     -3.880      0.000      -0.474      -0.156\n",
       "C(marital_status)[T.separated]              -0.3510      0.115     -3.060      0.002      -0.576      -0.126\n",
       "C(marital_status)[T.single]                 -0.3161      0.081     -3.898      0.000      -0.475      -0.157\n",
       "C(marital_status)[T.widowed]                -0.2182      0.086     -2.537      0.011      -0.387      -0.050\n",
       "C(life_event)[T.1]                           0.1197      0.001    118.476      0.000       0.118       0.122\n",
       "age                                          0.0008   4.38e-05     18.711      0.000       0.001       0.001\n",
       "==============================================================================\n",
       "Omnibus:                    35237.290   Durbin-Watson:                   2.004\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):          1292176.011\n",
       "Skew:                           4.303   Prob(JB):                         0.00\n",
       "Kurtosis:                      29.680   Cond. No.                     2.07e+04\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 2.07e+04. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import math\n",
    "import statsmodels.formula.api as sm\n",
    "\n",
    "formula = \"propensity ~ C(location_country) + C(gender) +  C(household_income)+ C(household_size) + C(marital_status) + age + C(life_event)\"\n",
    "\n",
    "result = sm.ols(formula=formula, data=dem_df).fit()\n",
    "result.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "sns.set_style(\"whitegrid\")\n",
    "mpl.rc(\"figure\", figsize=(16, 8))\n",
    "mpl.rcParams.update({'font.size': 22})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fbae5369358>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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slW7IkCHx17/+NfLz8+N3v/udj6oCAABgO7npfsHZZ58dCxYsiLVr11bGPJXqyiuvjMce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\nMgAAACREMgAAACT+H9kh/eRnUpzIAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fbaf3926a58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dem_df.propensity.plot.hist(log=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}