{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Discrete Choice Models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fair's Affair data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A survey of women only was conducted in 1974 by *Redbook* asking about extramarital affairs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from scipy import stats\n",
    "import matplotlib.pyplot as plt\n",
    "import statsmodels.api as sm\n",
    "from statsmodels.formula.api import logit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Fair, Ray. 1978. \"A Theory of Extramarital Affairs,\" `Journal of Political\n",
      "Economy`, February, 45-61.\n",
      "\n",
      "The data is available at http://fairmodel.econ.yale.edu/rayfair/pdf/2011b.htm\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(sm.datasets.fair.SOURCE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "::\n",
      "\n",
      "    Number of observations: 6366\n",
      "    Number of variables: 9\n",
      "    Variable name definitions:\n",
      "\n",
      "        rate_marriage   : How rate marriage, 1 = very poor, 2 = poor, 3 = fair,\n",
      "                        4 = good, 5 = very good\n",
      "        age             : Age\n",
      "        yrs_married     : No. years married. Interval approximations. See\n",
      "                        original paper for detailed explanation.\n",
      "        children        : No. children\n",
      "        religious       : How relgious, 1 = not, 2 = mildly, 3 = fairly,\n",
      "                        4 = strongly\n",
      "        educ            : Level of education, 9 = grade school, 12 = high\n",
      "                        school, 14 = some college, 16 = college graduate,\n",
      "                        17 = some graduate school, 20 = advanced degree\n",
      "        occupation      : 1 = student, 2 = farming, agriculture; semi-skilled,\n",
      "                        or unskilled worker; 3 = white-colloar; 4 = teacher\n",
      "                        counselor social worker, nurse; artist, writers;\n",
      "                        technician, skilled worker, 5 = managerial,\n",
      "                        administrative, business, 6 = professional with\n",
      "                        advanced degree\n",
      "        occupation_husb : Husband's occupation. Same as occupation.\n",
      "        affairs         : measure of time spent in extramarital affairs\n",
      "\n",
      "    See the original paper for more details.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print( sm.datasets.fair.NOTE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "dta = sm.datasets.fair.load_pandas().data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   rate_marriage   age  yrs_married  children  religious  educ  occupation  \\\n",
      "0            3.0  32.0          9.0       3.0        3.0  17.0         2.0   \n",
      "1            3.0  27.0         13.0       3.0        1.0  14.0         3.0   \n",
      "2            4.0  22.0          2.5       0.0        1.0  16.0         3.0   \n",
      "3            4.0  37.0         16.5       4.0        3.0  16.0         5.0   \n",
      "4            5.0  27.0          9.0       1.0        1.0  14.0         3.0   \n",
      "5            4.0  27.0          9.0       0.0        2.0  14.0         3.0   \n",
      "6            5.0  37.0         23.0       5.5        2.0  12.0         5.0   \n",
      "7            5.0  37.0         23.0       5.5        2.0  12.0         2.0   \n",
      "8            3.0  22.0          2.5       0.0        2.0  12.0         3.0   \n",
      "9            3.0  27.0          6.0       0.0        1.0  16.0         3.0   \n",
      "\n",
      "   occupation_husb   affairs  affair  \n",
      "0              5.0  0.111111     1.0  \n",
      "1              4.0  3.230769     1.0  \n",
      "2              5.0  1.400000     1.0  \n",
      "3              5.0  0.727273     1.0  \n",
      "4              4.0  4.666666     1.0  \n",
      "5              4.0  4.666666     1.0  \n",
      "6              4.0  0.852174     1.0  \n",
      "7              3.0  1.826086     1.0  \n",
      "8              3.0  4.799999     1.0  \n",
      "9              5.0  1.333333     1.0  \n"
     ]
    }
   ],
   "source": [
    "dta['affair'] = (dta['affairs'] > 0).astype(float)\n",
    "print(dta.head(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "       rate_marriage          age  yrs_married     children    religious  \\\n",
      "count    6366.000000  6366.000000  6366.000000  6366.000000  6366.000000   \n",
      "mean        4.109645    29.082862     9.009425     1.396874     2.426170   \n",
      "std         0.961430     6.847882     7.280120     1.433471     0.878369   \n",
      "min         1.000000    17.500000     0.500000     0.000000     1.000000   \n",
      "25%         4.000000    22.000000     2.500000     0.000000     2.000000   \n",
      "50%         4.000000    27.000000     6.000000     1.000000     2.000000   \n",
      "75%         5.000000    32.000000    16.500000     2.000000     3.000000   \n",
      "max         5.000000    42.000000    23.000000     5.500000     4.000000   \n",
      "\n",
      "              educ   occupation  occupation_husb      affairs       affair  \n",
      "count  6366.000000  6366.000000      6366.000000  6366.000000  6366.000000  \n",
      "mean     14.209865     3.424128         3.850141     0.705374     0.322495  \n",
      "std       2.178003     0.942399         1.346435     2.203374     0.467468  \n",
      "min       9.000000     1.000000         1.000000     0.000000     0.000000  \n",
      "25%      12.000000     3.000000         3.000000     0.000000     0.000000  \n",
      "50%      14.000000     3.000000         4.000000     0.000000     0.000000  \n",
      "75%      16.000000     4.000000         5.000000     0.484848     1.000000  \n",
      "max      20.000000     6.000000         6.000000    57.599991     1.000000  \n"
     ]
    }
   ],
   "source": [
    "print(dta.describe())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.545314\n",
      "         Iterations 6\n"
     ]
    }
   ],
   "source": [
    "affair_mod = logit(\"affair ~ occupation + educ + occupation_husb\"\n",
    "                   \"+ rate_marriage + age + yrs_married + children\"\n",
    "                   \" + religious\", dta).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                           Logit Regression Results                           \n",
      "==============================================================================\n",
      "Dep. Variable:                 affair   No. Observations:                 6366\n",
      "Model:                          Logit   Df Residuals:                     6357\n",
      "Method:                           MLE   Df Model:                            8\n",
      "Date:                Tue, 17 Dec 2019   Pseudo R-squ.:                  0.1327\n",
      "Time:                        23:41:26   Log-Likelihood:                -3471.5\n",
      "converged:                       True   LL-Null:                       -4002.5\n",
      "Covariance Type:            nonrobust   LLR p-value:                5.807e-224\n",
      "===================================================================================\n",
      "                      coef    std err          z      P>|z|      [0.025      0.975]\n",
      "-----------------------------------------------------------------------------------\n",
      "Intercept           3.7257      0.299     12.470      0.000       3.140       4.311\n",
      "occupation          0.1602      0.034      4.717      0.000       0.094       0.227\n",
      "educ               -0.0392      0.015     -2.533      0.011      -0.070      -0.009\n",
      "occupation_husb     0.0124      0.023      0.541      0.589      -0.033       0.057\n",
      "rate_marriage      -0.7161      0.031    -22.784      0.000      -0.778      -0.655\n",
      "age                -0.0605      0.010     -5.885      0.000      -0.081      -0.040\n",
      "yrs_married         0.1100      0.011     10.054      0.000       0.089       0.131\n",
      "children           -0.0042      0.032     -0.134      0.893      -0.066       0.058\n",
      "religious          -0.3752      0.035    -10.792      0.000      -0.443      -0.307\n",
      "===================================================================================\n"
     ]
    }
   ],
   "source": [
    "print(affair_mod.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How well are we predicting?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3882.,  431.],\n",
       "       [1326.,  727.]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "affair_mod.pred_table()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The coefficients of the discrete choice model do not tell us much. What we're after is marginal effects."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        Logit Marginal Effects       \n",
      "=====================================\n",
      "Dep. Variable:                 affair\n",
      "Method:                          dydx\n",
      "At:                           overall\n",
      "===================================================================================\n",
      "                     dy/dx    std err          z      P>|z|      [0.025      0.975]\n",
      "-----------------------------------------------------------------------------------\n",
      "occupation          0.0293      0.006      4.744      0.000       0.017       0.041\n",
      "educ               -0.0072      0.003     -2.538      0.011      -0.013      -0.002\n",
      "occupation_husb     0.0023      0.004      0.541      0.589      -0.006       0.010\n",
      "rate_marriage      -0.1308      0.005    -26.891      0.000      -0.140      -0.121\n",
      "age                -0.0110      0.002     -5.937      0.000      -0.015      -0.007\n",
      "yrs_married         0.0201      0.002     10.327      0.000       0.016       0.024\n",
      "children           -0.0008      0.006     -0.134      0.893      -0.012       0.011\n",
      "religious          -0.0685      0.006    -11.119      0.000      -0.081      -0.056\n",
      "===================================================================================\n"
     ]
    }
   ],
   "source": [
    "mfx = affair_mod.get_margeff()\n",
    "print(mfx.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rate_marriage       4.000000\n",
      "age                37.000000\n",
      "yrs_married        23.000000\n",
      "children            3.000000\n",
      "religious           3.000000\n",
      "educ               12.000000\n",
      "occupation          3.000000\n",
      "occupation_husb     4.000000\n",
      "affairs             0.521739\n",
      "affair              1.000000\n",
      "Name: 1000, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "respondent1000 = dta.iloc[1000]\n",
    "print(respondent1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{1: 3.0, 2: 12.0, 3: 4.0, 4: 4.0, 5: 37.0, 6: 23.0, 7: 3.0, 8: 3.0, 0: 1}\n"
     ]
    }
   ],
   "source": [
    "resp = dict(zip(range(1,9), respondent1000[[\"occupation\", \"educ\",\n",
    "                                            \"occupation_husb\", \"rate_marriage\",\n",
    "                                            \"age\", \"yrs_married\", \"children\",\n",
    "                                            \"religious\"]].tolist()))\n",
    "resp.update({0 : 1})\n",
    "print(resp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        Logit Marginal Effects       \n",
      "=====================================\n",
      "Dep. Variable:                 affair\n",
      "Method:                          dydx\n",
      "At:                           overall\n",
      "===================================================================================\n",
      "                     dy/dx    std err          z      P>|z|      [0.025      0.975]\n",
      "-----------------------------------------------------------------------------------\n",
      "occupation          0.0400      0.008      4.711      0.000       0.023       0.057\n",
      "educ               -0.0098      0.004     -2.537      0.011      -0.017      -0.002\n",
      "occupation_husb     0.0031      0.006      0.541      0.589      -0.008       0.014\n",
      "rate_marriage      -0.1788      0.008    -22.743      0.000      -0.194      -0.163\n",
      "age                -0.0151      0.003     -5.928      0.000      -0.020      -0.010\n",
      "yrs_married         0.0275      0.003     10.256      0.000       0.022       0.033\n",
      "children           -0.0011      0.008     -0.134      0.893      -0.017       0.014\n",
      "religious          -0.0937      0.009    -10.722      0.000      -0.111      -0.077\n",
      "===================================================================================\n"
     ]
    }
   ],
   "source": [
    "mfx = affair_mod.get_margeff(atexog=resp)\n",
    "print(mfx.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`predict` expects a `DataFrame` since `patsy` is used to select columns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1000    0.518782\n",
       "dtype: float64"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "respondent1000 = dta.iloc[[1000]]\n",
    "affair_mod.predict(respondent1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0751615928505509"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "affair_mod.fittedvalues[1000]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.518781557212144"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "affair_mod.model.cdf(affair_mod.fittedvalues[1000])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The \"correct\" model here is likely the Tobit model. We have an work in progress branch \"tobit-model\" on github, if anyone is interested in censored regression models."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise: Logit vs Probit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12,8))\n",
    "ax = fig.add_subplot(111)\n",
    "support = np.linspace(-6, 6, 1000)\n",
    "ax.plot(support, stats.logistic.cdf(support), 'r-', label='Logistic')\n",
    "ax.plot(support, stats.norm.cdf(support), label='Probit')\n",
    "ax.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12,8))\n",
    "ax = fig.add_subplot(111)\n",
    "support = np.linspace(-6, 6, 1000)\n",
    "ax.plot(support, stats.logistic.pdf(support), 'r-', label='Logistic')\n",
    "ax.plot(support, stats.norm.pdf(support), label='Probit')\n",
    "ax.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compare the estimates of the Logit Fair model above to a Probit model. Does the prediction table look better? Much difference in marginal effects?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generalized Linear Model Example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Jeff Gill's `Generalized Linear Models: A Unified Approach`\n",
      "\n",
      "http://jgill.wustl.edu/research/books.html\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(sm.datasets.star98.SOURCE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "This data is on the California education policy and outcomes (STAR program\n",
      "results for 1998.  The data measured standardized testing by the California\n",
      "Department of Education that required evaluation of 2nd - 11th grade students\n",
      "by the the Stanford 9 test on a variety of subjects.  This dataset is at\n",
      "the level of the unified school district and consists of 303 cases.  The\n",
      "binary response variable represents the number of 9th graders scoring\n",
      "over the national median value on the mathematics exam.\n",
      "\n",
      "The data used in this example is only a subset of the original source.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(sm.datasets.star98.DESCRLONG)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "::\n",
      "\n",
      "    Number of Observations - 303 (counties in California).\n",
      "\n",
      "    Number of Variables - 13 and 8 interaction terms.\n",
      "\n",
      "    Definition of variables names::\n",
      "\n",
      "        NABOVE   - Total number of students above the national median for the\n",
      "                   math section.\n",
      "        NBELOW   - Total number of students below the national median for the\n",
      "                   math section.\n",
      "        LOWINC   - Percentage of low income students\n",
      "        PERASIAN - Percentage of Asian student\n",
      "        PERBLACK - Percentage of black students\n",
      "        PERHISP  - Percentage of Hispanic students\n",
      "        PERMINTE - Percentage of minority teachers\n",
      "        AVYRSEXP - Sum of teachers' years in educational service divided by the\n",
      "                number of teachers.\n",
      "        AVSALK   - Total salary budget including benefits divided by the number\n",
      "                   of full-time teachers (in thousands)\n",
      "        PERSPENK - Per-pupil spending (in thousands)\n",
      "        PTRATIO  - Pupil-teacher ratio.\n",
      "        PCTAF    - Percentage of students taking UC/CSU prep courses\n",
      "        PCTCHRT  - Percentage of charter schools\n",
      "        PCTYRRND - Percentage of year-round schools\n",
      "\n",
      "        The below variables are interaction terms of the variables defined\n",
      "        above.\n",
      "\n",
      "        PERMINTE_AVYRSEXP\n",
      "        PEMINTE_AVSAL\n",
      "        AVYRSEXP_AVSAL\n",
      "        PERSPEN_PTRATIO\n",
      "        PERSPEN_PCTAF\n",
      "        PTRATIO_PCTAF\n",
      "        PERMINTE_AVTRSEXP_AVSAL\n",
      "        PERSPEN_PTRATIO_PCTAF\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(sm.datasets.star98.NOTE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Index(['NABOVE', 'NBELOW', 'LOWINC', 'PERASIAN', 'PERBLACK', 'PERHISP',\n",
      "       'PERMINTE', 'AVYRSEXP', 'AVSALK', 'PERSPENK', 'PTRATIO', 'PCTAF',\n",
      "       'PCTCHRT', 'PCTYRRND', 'PERMINTE_AVYRSEXP', 'PERMINTE_AVSAL',\n",
      "       'AVYRSEXP_AVSAL', 'PERSPEN_PTRATIO', 'PERSPEN_PCTAF', 'PTRATIO_PCTAF',\n",
      "       'PERMINTE_AVYRSEXP_AVSAL', 'PERSPEN_PTRATIO_PCTAF'],\n",
      "      dtype='object')\n"
     ]
    }
   ],
   "source": [
    "dta = sm.datasets.star98.load_pandas().data\n",
    "print(dta.columns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   NABOVE  NBELOW    LOWINC   PERASIAN   PERBLACK    PERHISP   PERMINTE\n",
      "0   452.0   355.0  34.39730  23.299300  14.235280  11.411120  15.918370\n",
      "1   144.0    40.0  17.36507  29.328380   8.234897   9.314884  13.636360\n",
      "2   337.0   234.0  32.64324   9.226386  42.406310  13.543720  28.834360\n",
      "3   395.0   178.0  11.90953  13.883090   3.796973  11.443110  11.111110\n",
      "4     8.0    57.0  36.88889  12.187500  76.875000   7.604167  43.589740\n",
      "5  1348.0   899.0  20.93149  28.023510   4.643221  13.808160  15.378490\n",
      "6   477.0   887.0  53.26898   8.447858  19.374830  37.905330  25.525530\n",
      "7   565.0   347.0  15.19009   3.665781   2.649680  13.092070   6.203008\n",
      "8   205.0   320.0  28.21582  10.430420   6.786374  32.334300  13.461540\n",
      "9   469.0   598.0  32.77897  17.178310  12.484930  28.323290  27.259890\n"
     ]
    }
   ],
   "source": [
    "print(dta[['NABOVE', 'NBELOW', 'LOWINC', 'PERASIAN', 'PERBLACK', 'PERHISP', 'PERMINTE']].head(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   AVYRSEXP    AVSALK  PERSPENK   PTRATIO     PCTAF  PCTCHRT   PCTYRRND\n",
      "0  14.70646  59.15732  4.445207  21.71025  57.03276      0.0  22.222220\n",
      "1  16.08324  59.50397  5.267598  20.44278  64.62264      0.0   0.000000\n",
      "2  14.59559  60.56992  5.482922  18.95419  53.94191      0.0   0.000000\n",
      "3  14.38939  58.33411  4.165093  21.63539  49.06103      0.0   7.142857\n",
      "4  13.90568  63.15364  4.324902  18.77984  52.38095      0.0   0.000000\n",
      "5  14.97755  66.97055  3.916104  24.51914  44.91578      0.0   2.380952\n",
      "6  14.67829  57.62195  4.270903  22.21278  32.28916      0.0  12.121210\n",
      "7  13.66197  63.44740  4.309734  24.59026  30.45267      0.0   0.000000\n",
      "8  16.41760  57.84564  4.527603  21.74138  22.64574      0.0   0.000000\n",
      "9  12.51864  57.80141  4.648917  20.26010  26.07099      0.0   0.000000\n"
     ]
    }
   ],
   "source": [
    "print(dta[['AVYRSEXP', 'AVSALK', 'PERSPENK', 'PTRATIO', 'PCTAF', 'PCTCHRT', 'PCTYRRND']].head(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "formula = 'NABOVE + NBELOW ~ LOWINC + PERASIAN + PERBLACK + PERHISP + PCTCHRT '\n",
    "formula += '+ PCTYRRND + PERMINTE*AVYRSEXP*AVSALK + PERSPENK*PTRATIO*PCTAF'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Aside: Binomial distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Toss a six-sided die 5 times, what's the probability of exactly 2 fours?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.16075102880658435"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.binom(5, 1./6).pmf(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1607510288065844"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.special import comb\n",
    "comb(5,2) * (1/6.)**2 * (5/6.)**3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels.formula.api import glm\n",
    "glm_mod = glm(formula, dta, family=sm.families.Binomial()).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                  Generalized Linear Model Regression Results                   \n",
      "================================================================================\n",
      "Dep. Variable:     ['NABOVE', 'NBELOW']   No. Observations:                  303\n",
      "Model:                              GLM   Df Residuals:                      282\n",
      "Model Family:                  Binomial   Df Model:                           20\n",
      "Link Function:                    logit   Scale:                          1.0000\n",
      "Method:                            IRLS   Log-Likelihood:                -2998.6\n",
      "Date:                  Tue, 17 Dec 2019   Deviance:                       4078.8\n",
      "Time:                          23:41:27   Pearson chi2:                 4.05e+03\n",
      "No. Iterations:                       5                                         \n",
      "Covariance Type:              nonrobust                                         \n",
      "============================================================================================\n",
      "                               coef    std err          z      P>|z|      [0.025      0.975]\n",
      "--------------------------------------------------------------------------------------------\n",
      "Intercept                    2.9589      1.547      1.913      0.056      -0.073       5.990\n",
      "LOWINC                      -0.0168      0.000    -38.749      0.000      -0.018      -0.016\n",
      "PERASIAN                     0.0099      0.001     16.505      0.000       0.009       0.011\n",
      "PERBLACK                    -0.0187      0.001    -25.182      0.000      -0.020      -0.017\n",
      "PERHISP                     -0.0142      0.000    -32.818      0.000      -0.015      -0.013\n",
      "PCTCHRT                      0.0049      0.001      3.921      0.000       0.002       0.007\n",
      "PCTYRRND                    -0.0036      0.000    -15.878      0.000      -0.004      -0.003\n",
      "PERMINTE                     0.2545      0.030      8.498      0.000       0.196       0.313\n",
      "AVYRSEXP                     0.2407      0.057      4.212      0.000       0.129       0.353\n",
      "PERMINTE:AVYRSEXP           -0.0141      0.002     -7.391      0.000      -0.018      -0.010\n",
      "AVSALK                       0.0804      0.014      5.775      0.000       0.053       0.108\n",
      "PERMINTE:AVSALK             -0.0040      0.000     -8.450      0.000      -0.005      -0.003\n",
      "AVYRSEXP:AVSALK             -0.0039      0.001     -4.059      0.000      -0.006      -0.002\n",
      "PERMINTE:AVYRSEXP:AVSALK     0.0002   2.99e-05      7.428      0.000       0.000       0.000\n",
      "PERSPENK                    -1.9522      0.317     -6.162      0.000      -2.573      -1.331\n",
      "PTRATIO                     -0.3341      0.061     -5.453      0.000      -0.454      -0.214\n",
      "PERSPENK:PTRATIO             0.0917      0.015      6.321      0.000       0.063       0.120\n",
      "PCTAF                       -0.1690      0.033     -5.169      0.000      -0.233      -0.105\n",
      "PERSPENK:PCTAF               0.0490      0.007      6.574      0.000       0.034       0.064\n",
      "PTRATIO:PCTAF                0.0080      0.001      5.362      0.000       0.005       0.011\n",
      "PERSPENK:PTRATIO:PCTAF      -0.0022      0.000     -6.445      0.000      -0.003      -0.002\n",
      "============================================================================================\n"
     ]
    }
   ],
   "source": [
    "print(glm_mod.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The number of trials "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0      807.0\n",
       "1      184.0\n",
       "2      571.0\n",
       "3      573.0\n",
       "4       65.0\n",
       "       ...  \n",
       "298    342.0\n",
       "299    154.0\n",
       "300    595.0\n",
       "301    709.0\n",
       "302    156.0\n",
       "Length: 303, dtype: float64"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "glm_mod.model.data.orig_endog.sum(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0      470.732584\n",
       "1      138.266178\n",
       "2      285.832629\n",
       "3      392.702917\n",
       "4       20.963146\n",
       "          ...    \n",
       "298    111.464708\n",
       "299     61.037884\n",
       "300    235.517446\n",
       "301    290.952508\n",
       "302     53.312851\n",
       "Length: 303, dtype: float64"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "glm_mod.fittedvalues * glm_mod.model.data.orig_endog.sum(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First differences: We hold all explanatory variables constant at their means and manipulate the percentage of low income households to assess its impact\n",
    "on the response variables:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "exog = glm_mod.model.data.orig_exog # get the dataframe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intercept                       1.000000\n",
      "LOWINC                         41.409877\n",
      "PERASIAN                        5.896335\n",
      "PERBLACK                        5.636808\n",
      "PERHISP                        34.398080\n",
      "PCTCHRT                         1.175909\n",
      "PCTYRRND                       11.611905\n",
      "PERMINTE                       14.694747\n",
      "AVYRSEXP                       14.253875\n",
      "PERMINTE:AVYRSEXP             209.018700\n",
      "AVSALK                         58.640258\n",
      "PERMINTE:AVSALK               879.979883\n",
      "AVYRSEXP:AVSALK               839.718173\n",
      "PERMINTE:AVYRSEXP:AVSALK    12585.266464\n",
      "PERSPENK                        4.320310\n",
      "PTRATIO                        22.464250\n",
      "PERSPENK:PTRATIO               96.295756\n",
      "PCTAF                          33.630593\n",
      "PERSPENK:PCTAF                147.235740\n",
      "PTRATIO:PCTAF                 747.445536\n",
      "PERSPENK:PTRATIO:PCTAF       3243.607568\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "means25 = exog.mean()\n",
    "print(means25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intercept                       1.000000\n",
      "LOWINC                         26.683040\n",
      "PERASIAN                        5.896335\n",
      "PERBLACK                        5.636808\n",
      "PERHISP                        34.398080\n",
      "PCTCHRT                         1.175909\n",
      "PCTYRRND                       11.611905\n",
      "PERMINTE                       14.694747\n",
      "AVYRSEXP                       14.253875\n",
      "PERMINTE:AVYRSEXP             209.018700\n",
      "AVSALK                         58.640258\n",
      "PERMINTE:AVSALK               879.979883\n",
      "AVYRSEXP:AVSALK               839.718173\n",
      "PERMINTE:AVYRSEXP:AVSALK    12585.266464\n",
      "PERSPENK                        4.320310\n",
      "PTRATIO                        22.464250\n",
      "PERSPENK:PTRATIO               96.295756\n",
      "PCTAF                          33.630593\n",
      "PERSPENK:PCTAF                147.235740\n",
      "PTRATIO:PCTAF                 747.445536\n",
      "PERSPENK:PTRATIO:PCTAF       3243.607568\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "means25['LOWINC'] = exog['LOWINC'].quantile(.25)\n",
    "print(means25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intercept                       1.000000\n",
      "LOWINC                         55.460075\n",
      "PERASIAN                        5.896335\n",
      "PERBLACK                        5.636808\n",
      "PERHISP                        34.398080\n",
      "PCTCHRT                         1.175909\n",
      "PCTYRRND                       11.611905\n",
      "PERMINTE                       14.694747\n",
      "AVYRSEXP                       14.253875\n",
      "PERMINTE:AVYRSEXP             209.018700\n",
      "AVSALK                         58.640258\n",
      "PERMINTE:AVSALK               879.979883\n",
      "AVYRSEXP:AVSALK               839.718173\n",
      "PERMINTE:AVYRSEXP:AVSALK    12585.266464\n",
      "PERSPENK                        4.320310\n",
      "PTRATIO                        22.464250\n",
      "PERSPENK:PTRATIO               96.295756\n",
      "PCTAF                          33.630593\n",
      "PERSPENK:PCTAF                147.235740\n",
      "PTRATIO:PCTAF                 747.445536\n",
      "PERSPENK:PTRATIO:PCTAF       3243.607568\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "means75 = exog.mean()\n",
    "means75['LOWINC'] = exog['LOWINC'].quantile(.75)\n",
    "print(means75)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, `predict` expects a `DataFrame` since `patsy` is used to select columns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "resp25 = glm_mod.predict(pd.DataFrame(means25).T)\n",
    "resp75 = glm_mod.predict(pd.DataFrame(means75).T)\n",
    "diff = resp75 - resp25"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The interquartile first difference for the percentage of low income households in a school district is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-11.8863%\n"
     ]
    }
   ],
   "source": [
    "print(\"%2.4f%%\" % (diff[0]*100))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "nobs = glm_mod.nobs\n",
    "y = glm_mod.model.endog\n",
    "yhat = glm_mod.mu"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from statsmodels.graphics.api import abline_plot\n",
    "fig = plt.figure(figsize=(12,8))\n",
    "ax = fig.add_subplot(111, ylabel='Observed Values', xlabel='Fitted Values')\n",
    "ax.scatter(yhat, y)\n",
    "y_vs_yhat = sm.OLS(y, sm.add_constant(yhat, prepend=True)).fit()\n",
    "fig = abline_plot(model_results=y_vs_yhat, ax=ax)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plot fitted values vs Pearson residuals"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pearson residuals are defined to be\n",
    "\n",
    "$$\\frac{(y - \\mu)}{\\sqrt{(var(\\mu))}}$$\n",
    "\n",
    "where var is typically determined by the family. E.g., binomial variance is $np(1 - p)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12,8))\n",
    "ax = fig.add_subplot(111, title='Residual Dependence Plot', xlabel='Fitted Values',\n",
    "                          ylabel='Pearson Residuals')\n",
    "ax.scatter(yhat, stats.zscore(glm_mod.resid_pearson))\n",
    "ax.axis('tight')\n",
    "ax.plot([0.0, 1.0],[0.0, 0.0], 'k-');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Histogram of standardized deviance residuals with Kernel Density Estimate overlaid"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The definition of the deviance residuals depends on the family. For the Binomial distribution this is\n",
    "\n",
    "$$r_{dev} = sign\\left(Y-\\mu\\right)*\\sqrt{2n(Y\\log\\frac{Y}{\\mu}+(1-Y)\\log\\frac{(1-Y)}{(1-\\mu)}}$$\n",
    "\n",
    "They can be used to detect ill-fitting covariates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "resid = glm_mod.resid_deviance\n",
    "resid_std = stats.zscore(resid)\n",
    "kde_resid = sm.nonparametric.KDEUnivariate(resid_std)\n",
    "kde_resid.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12,8))\n",
    "ax = fig.add_subplot(111, title=\"Standardized Deviance Residuals\")\n",
    "ax.hist(resid_std, bins=25, density=True);\n",
    "ax.plot(kde_resid.support, kde_resid.density, 'r');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### QQ-plot of deviance residuals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12,8))\n",
    "ax = fig.add_subplot(111)\n",
    "fig = sm.graphics.qqplot(resid, line='r', ax=ax)"
   ]
  }
 ],
 "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": "3.7.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}