{
 "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,
    "execution": {
     "iopub.execute_input": "2021-02-02T06:51:27.891387Z",
     "iopub.status.busy": "2021-02-02T06:51:27.890108Z",
     "iopub.status.idle": "2021-02-02T06:51:28.258743Z",
     "shell.execute_reply": "2021-02-02T06:51:28.259618Z"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:51:28.263972Z",
     "iopub.status.busy": "2021-02-02T06:51:28.263283Z",
     "iopub.status.idle": "2021-02-02T06:51:29.400420Z",
     "shell.execute_reply": "2021-02-02T06:51:29.401883Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:51:29.408292Z",
     "iopub.status.busy": "2021-02-02T06:51:29.406409Z",
     "iopub.status.idle": "2021-02-02T06:51:29.417013Z",
     "shell.execute_reply": "2021-02-02T06:51:29.418278Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:51:29.425023Z",
     "iopub.status.busy": "2021-02-02T06:51:29.422078Z",
     "iopub.status.idle": "2021-02-02T06:51:29.431350Z",
     "shell.execute_reply": "2021-02-02T06:51:29.432227Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:51:29.446055Z",
     "iopub.status.busy": "2021-02-02T06:51:29.444986Z",
     "iopub.status.idle": "2021-02-02T06:51:29.458603Z",
     "shell.execute_reply": "2021-02-02T06:51:29.459832Z"
    }
   },
   "outputs": [],
   "source": [
    "dta = sm.datasets.fair.load_pandas().data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:51:29.464897Z",
     "iopub.status.busy": "2021-02-02T06:51:29.463241Z",
     "iopub.status.idle": "2021-02-02T06:51:29.490221Z",
     "shell.execute_reply": "2021-02-02T06:51:29.491415Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:51:29.496645Z",
     "iopub.status.busy": "2021-02-02T06:51:29.494997Z",
     "iopub.status.idle": "2021-02-02T06:51:29.552342Z",
     "shell.execute_reply": "2021-02-02T06:51:29.553514Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:51:29.558717Z",
     "iopub.status.busy": "2021-02-02T06:51:29.557090Z",
     "iopub.status.idle": "2021-02-02T06:51:29.604372Z",
     "shell.execute_reply": "2021-02-02T06:51:29.604954Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:51:29.608952Z",
     "iopub.status.busy": "2021-02-02T06:51:29.608120Z",
     "iopub.status.idle": "2021-02-02T06:51:29.631788Z",
     "shell.execute_reply": "2021-02-02T06:51:29.632129Z"
    }
   },
   "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, 02 Feb 2021   Pseudo R-squ.:                  0.1327\n",
      "Time:                        06:51:29   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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:51:29.637877Z",
     "iopub.status.busy": "2021-02-02T06:51:29.635050Z",
     "iopub.status.idle": "2021-02-02T06:51:29.641779Z",
     "shell.execute_reply": "2021-02-02T06:51:29.642107Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3882.,  431.],\n",
       "       [1326.,  727.]])"
      ]
     },
     "execution_count": 1,
     "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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:51:29.645351Z",
     "iopub.status.busy": "2021-02-02T06:51:29.644938Z",
     "iopub.status.idle": "2021-02-02T06:51:29.667491Z",
     "shell.execute_reply": "2021-02-02T06:51:29.667120Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:51:29.671858Z",
     "iopub.status.busy": "2021-02-02T06:51:29.670845Z",
     "iopub.status.idle": "2021-02-02T06:51:29.674097Z",
     "shell.execute_reply": "2021-02-02T06:51:29.674412Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:51:29.678953Z",
     "iopub.status.busy": "2021-02-02T06:51:29.678527Z",
     "iopub.status.idle": "2021-02-02T06:51:29.681703Z",
     "shell.execute_reply": "2021-02-02T06:51:29.682050Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:51:29.685772Z",
     "iopub.status.busy": "2021-02-02T06:51:29.684897Z",
     "iopub.status.idle": "2021-02-02T06:51:29.710194Z",
     "shell.execute_reply": "2021-02-02T06:51:29.710995Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:51:29.714574Z",
     "iopub.status.busy": "2021-02-02T06:51:29.713467Z",
     "iopub.status.idle": "2021-02-02T06:51:29.732493Z",
     "shell.execute_reply": "2021-02-02T06:51:29.733321Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1000    0.518782\n",
       "dtype: float64"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "respondent1000 = dta.iloc[[1000]]\n",
    "affair_mod.predict(respondent1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:51:29.737189Z",
     "iopub.status.busy": "2021-02-02T06:51:29.735967Z",
     "iopub.status.idle": "2021-02-02T06:51:29.744274Z",
     "shell.execute_reply": "2021-02-02T06:51:29.745049Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.07516159285058333"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "affair_mod.fittedvalues[1000]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:51:29.748640Z",
     "iopub.status.busy": "2021-02-02T06:51:29.747513Z",
     "iopub.status.idle": "2021-02-02T06:51:29.754751Z",
     "shell.execute_reply": "2021-02-02T06:51:29.755588Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5187815572121521"
      ]
     },
     "execution_count": 1,
     "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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:51:29.759282Z",
     "iopub.status.busy": "2021-02-02T06:51:29.758153Z",
     "iopub.status.idle": "2021-02-02T06:51:30.008438Z",
     "shell.execute_reply": "2021-02-02T06:51:30.009028Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f6f574cf590>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:51:30.025007Z",
     "iopub.status.busy": "2021-02-02T06:51:30.023696Z",
     "iopub.status.idle": "2021-02-02T06:51:30.171498Z",
     "shell.execute_reply": "2021-02-02T06:51:30.171906Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f6f573d4310>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:51:30.175228Z",
     "iopub.status.busy": "2021-02-02T06:51:30.174802Z",
     "iopub.status.idle": "2021-02-02T06:51:30.179042Z",
     "shell.execute_reply": "2021-02-02T06:51:30.179397Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:51:30.182664Z",
     "iopub.status.busy": "2021-02-02T06:51:30.182261Z",
     "iopub.status.idle": "2021-02-02T06:51:30.185428Z",
     "shell.execute_reply": "2021-02-02T06:51:30.185772Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:51:30.189030Z",
     "iopub.status.busy": "2021-02-02T06:51:30.188612Z",
     "iopub.status.idle": "2021-02-02T06:51:30.192567Z",
     "shell.execute_reply": "2021-02-02T06:51:30.192203Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:51:30.196244Z",
     "iopub.status.busy": "2021-02-02T06:51:30.195537Z",
     "iopub.status.idle": "2021-02-02T06:51:30.203379Z",
     "shell.execute_reply": "2021-02-02T06:51:30.203693Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:51:30.212678Z",
     "iopub.status.busy": "2021-02-02T06:51:30.211635Z",
     "iopub.status.idle": "2021-02-02T06:51:30.214682Z",
     "shell.execute_reply": "2021-02-02T06:51:30.214117Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:51:30.223864Z",
     "iopub.status.busy": "2021-02-02T06:51:30.222570Z",
     "iopub.status.idle": "2021-02-02T06:51:30.225471Z",
     "shell.execute_reply": "2021-02-02T06:51:30.225096Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:51:30.229135Z",
     "iopub.status.busy": "2021-02-02T06:51:30.228153Z",
     "iopub.status.idle": "2021-02-02T06:51:30.230105Z",
     "shell.execute_reply": "2021-02-02T06:51:30.230463Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:51:30.236379Z",
     "iopub.status.busy": "2021-02-02T06:51:30.235881Z",
     "iopub.status.idle": "2021-02-02T06:51:30.238353Z",
     "shell.execute_reply": "2021-02-02T06:51:30.238706Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.16075102880658435"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.binom(5, 1./6).pmf(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:51:30.242960Z",
     "iopub.status.busy": "2021-02-02T06:51:30.242478Z",
     "iopub.status.idle": "2021-02-02T06:51:30.244964Z",
     "shell.execute_reply": "2021-02-02T06:51:30.245291Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1607510288065844"
      ]
     },
     "execution_count": 1,
     "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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:51:30.267368Z",
     "iopub.status.busy": "2021-02-02T06:51:30.266547Z",
     "iopub.status.idle": "2021-02-02T06:51:30.274473Z",
     "shell.execute_reply": "2021-02-02T06:51:30.274828Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:51:30.286366Z",
     "iopub.status.busy": "2021-02-02T06:51:30.283991Z",
     "iopub.status.idle": "2021-02-02T06:51:30.288384Z",
     "shell.execute_reply": "2021-02-02T06:51:30.288747Z"
    }
   },
   "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, 02 Feb 2021   Deviance:                       4078.8\n",
      "Time:                          06:51:30   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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:51:30.295160Z",
     "iopub.status.busy": "2021-02-02T06:51:30.294191Z",
     "iopub.status.idle": "2021-02-02T06:51:30.297186Z",
     "shell.execute_reply": "2021-02-02T06:51:30.297526Z"
    }
   },
   "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": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "glm_mod.model.data.orig_endog.sum(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:51:30.303341Z",
     "iopub.status.busy": "2021-02-02T06:51:30.300292Z",
     "iopub.status.idle": "2021-02-02T06:51:30.305819Z",
     "shell.execute_reply": "2021-02-02T06:51:30.305478Z"
    }
   },
   "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": 1,
     "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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:51:30.309542Z",
     "iopub.status.busy": "2021-02-02T06:51:30.308559Z",
     "iopub.status.idle": "2021-02-02T06:51:30.310926Z",
     "shell.execute_reply": "2021-02-02T06:51:30.310499Z"
    }
   },
   "outputs": [],
   "source": [
    "exog = glm_mod.model.data.orig_exog # get the dataframe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:51:30.316093Z",
     "iopub.status.busy": "2021-02-02T06:51:30.313667Z",
     "iopub.status.idle": "2021-02-02T06:51:30.318080Z",
     "shell.execute_reply": "2021-02-02T06:51:30.318409Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:51:30.324440Z",
     "iopub.status.busy": "2021-02-02T06:51:30.323451Z",
     "iopub.status.idle": "2021-02-02T06:51:30.325874Z",
     "shell.execute_reply": "2021-02-02T06:51:30.326222Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:51:30.332073Z",
     "iopub.status.busy": "2021-02-02T06:51:30.329917Z",
     "iopub.status.idle": "2021-02-02T06:51:30.334022Z",
     "shell.execute_reply": "2021-02-02T06:51:30.334354Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:51:30.365806Z",
     "iopub.status.busy": "2021-02-02T06:51:30.364822Z",
     "iopub.status.idle": "2021-02-02T06:51:30.366824Z",
     "shell.execute_reply": "2021-02-02T06:51:30.367251Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:51:30.371881Z",
     "iopub.status.busy": "2021-02-02T06:51:30.370756Z",
     "iopub.status.idle": "2021-02-02T06:51:30.373351Z",
     "shell.execute_reply": "2021-02-02T06:51:30.373696Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-11.8863%\n"
     ]
    }
   ],
   "source": [
    "print(\"%2.4f%%\" % (diff[0]*100))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:51:30.377500Z",
     "iopub.status.busy": "2021-02-02T06:51:30.376531Z",
     "iopub.status.idle": "2021-02-02T06:51:30.378889Z",
     "shell.execute_reply": "2021-02-02T06:51:30.378468Z"
    }
   },
   "outputs": [],
   "source": [
    "nobs = glm_mod.nobs\n",
    "y = glm_mod.model.endog\n",
    "yhat = glm_mod.mu"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:51:30.395201Z",
     "iopub.status.busy": "2021-02-02T06:51:30.394375Z",
     "iopub.status.idle": "2021-02-02T06:51:30.521414Z",
     "shell.execute_reply": "2021-02-02T06:51:30.521767Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:51:30.537902Z",
     "iopub.status.busy": "2021-02-02T06:51:30.537092Z",
     "iopub.status.idle": "2021-02-02T06:51:30.678671Z",
     "shell.execute_reply": "2021-02-02T06:51:30.679029Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f6f578b97d0>]"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:51:30.685326Z",
     "iopub.status.busy": "2021-02-02T06:51:30.684314Z",
     "iopub.status.idle": "2021-02-02T06:51:30.687412Z",
     "shell.execute_reply": "2021-02-02T06:51:30.687778Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<statsmodels.nonparametric.kde.KDEUnivariate at 0x7f6f578783d0>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:51:30.701875Z",
     "iopub.status.busy": "2021-02-02T06:51:30.696169Z",
     "iopub.status.idle": "2021-02-02T06:51:30.882635Z",
     "shell.execute_reply": "2021-02-02T06:51:30.883038Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f6f57865350>]"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:51:30.886107Z",
     "iopub.status.busy": "2021-02-02T06:51:30.885428Z",
     "iopub.status.idle": "2021-02-02T06:51:31.082146Z",
     "shell.execute_reply": "2021-02-02T06:51:31.082542Z"
    }
   },
   "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": "3.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}