{
 "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:                Fri, 10 Jul 2020   Pseudo R-squ.:                  0.1327\n",
      "Time:                        05:46:36   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": [
       "0.07516159285059976"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "affair_mod.fittedvalues[1000]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5187815572121562"
      ]
     },
     "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:                  Fri, 10 Jul 2020   Deviance:                       4078.8\n",
      "Time:                          05:46:36   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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ALRCmAZRqbn5B51x0hZaWD0iSFhaXdM5FV0gSgRoAEB2GeQAo1bbte+8I0h1Lywe0bfveiloEAEB2hGkApbpucWmk2wEACBlhGkCpjl0zNdLtAACEjDANoFRbNq3X1OTEIbdNTU5oy6b1FbUIAIDsOAERQKk6JxkymwcAoA4I0wBKt3nDNOEZAFALDPMAAAAAMiJMAwAAABkRpgEAAICMCNMAAABARoRpAAAAICPCNAAAAJARYRoAAADIiDANAAAAZESYBgAAADLiCogAAKBwc/ML2rZ9r65bXNKxa6a0ZdN6roSKWiBMAwCAQs3NL+ici67Q0vIBSdLC4pLOuegKSSJQI3qEaQAAkErW6vK27XvvCNIdS8sHtG37XsI0okeYBgAAQ41TXb5ucWmk24GYVHYCopndx8w+b2bfNrMrzezPqmoLAAAYbFB1eZhj10yNdDsQkypn89gv6VXu/hBJj5H0J2b20ArbAwAAEoxTXd6yab2mJicOuW1qckJbNq3PpW1AlSoL0+5+vbt/o/3/n0v6tiQGTgEAEKBxqsubN0zr/DNO1PSaKZmk6TVTOv+MExkvjVoIYsy0mR0naYOkr/a570xJZ0rSunXrSm0XUAdMRwUgD1s2rT9kzLQ0WnV584Zptj2opcov2mJmR0n6iKSz3P1nvfe7+9vdfcbdZ9auXVt+A4GIdU4YWlhckuvgCUNz8wtVNw1AZKguA/1VWpk2s0m1gvQH3P2iKtsC1BHTUQHIE9VlYKUqZ/MwSe+S9G13/59VtQOoM6ajAgCgWFUO89go6YWSTjGzPe2fp1XYHqB2mI4KAIBiVTmbx5fc3dz94e5+cvvnk1W1B6gjpqMCAKBYQczmAaAYnbGNzOYBAEAxCNNAzXHCEAAAxSFMB4h5gQEA42A/ApSHMB2YzrzAnenMOvMCS2JDCAAYiv0IUK7KL9qCQw2aFxgAxjU3v6CNszt0/NZLtHF2BxfwqSH2I0C5qEwHhnmBARSFimUzsB8BykVlOjDMCwygKFQsm4H9CFAuwnRgmBcYQFGoWDYD+xGgXAzzCAzzAgMoyrFrprTQJzhTsawX9iNAuczdq25DajMzM75r166qmwEAUeodMy21Kpbnn3EiQQsAepjZbnefGfY4KtMA0BBULAEgf4RpAGgQrogJAPkaegKimf2Zmd3FWt5lZt8wsyeX0TgAAAAgZGlm83ipu/9M0pMlrZX0EkmzhbYKAAAAiECaYR7W/vdpkv7F3S8zMxv0B0Do5uYXGDcKAADGliZM7zazT0s6XtI5ZnZnSbcX2yygOFwFDkDROGAHmiPNMI/fl7RV0qPcfZ+kw9Qa6gFEiavAAShS54B9YXFJroMH7HPzC1U3DUABEivTZvaInpvux+gO1AFXgQNQpEEH7FSngfoZNMzj7wfc55JOybktQCm4ChzyQDc+knDADjRLYph29yeV2RCgLFs2re97Fbgtm9ZX2CrEhHH3B3FQsRIH7ECzpBkzLTN7mJn9tpm9qPNTdMOAomzeMK3zzzhR02umZJKm10xxOWWMhHH3LYwN7m/LpvWampw45DYO2IH6Gjqbh5mdK+mJkh4q6ZOSnirpS5LeV2jLgAJxFTiMg278FsYG98dl24FmSTM13rMlnSRp3t1fYmb3kPTOYpsFYBC61qtFN34LBxX98f0EmiXNMI8ld79d0n4zu4ukH0u6X7HNQpXm5he0cXaHjt96iTbO7mh8l21o6FqvHt34LUkHD007qOjG9xNonjRhepeZrZH0Dkm7JX1D0tcKbRUqw44gfIzXrR7j7ltCPKiouhjA9xNonqHDPNz95e3/vs3M/kPSXdz98mKbhaowBjJ8dK2HgXH34Y0NDmGWFb6fCAFDjcqV5gTEJ/S7zd2/WEyTUCV2BOFjvC5CEtJBRQjFAL6fqFoIB5VNk2aYx5aun9dK+rik8wpsEyrEGMjwhdi1DoSgX4iVyi0G8P1E1RhqVL6hYdrdT+v6+S1JD5P0o+KbhiqwIwgf43WBlebmF2QJ95VZDOD7iarRw1y+NFPj9bpWrUCNGuo3BvJJD16rbdv36uwL95Qy9oqxXsOF1LUOhGDb9r3yPrebVHoxgO8nqsRQo/KlGTP9FumObdQqSSdLuqzIRqFa3TuCssdeMdYLReEgrd6Sqm4uth1oli2b1h+yH5XoYS5amsr0rq7/75d0gbvvLKg9CEzZJ/SEcAIR6qeIgzTCeViSqnHTVOPQMKHNstMEaabGe28ZDUGYyh57xVgvFCHvgzR6UMJDNQ44iKFG5UoM02Z2hdR3CJokyd0fXkiLEJSyx14x1gtFyPsgjR6U8FCNA1CVQZXpp7f//ZP2v//a/vcFkvYV1iIEpexqD9UlFCHvgzR6UMJENQ5AFRLDtLv/QJLMbKO7b+y6a6uZ7ZT0V0U3DtUru9pDdQlFyPsgjR4UVIFx+kCY0pyAeKSZPd7dvyRJZvY4SUcW2yyEpOxqD9Ul5C3vg7Qm9KAQ3MaX5zJknH75+A4gLXNPHBbdeoDZIyW9W9Jd2zctSnqpu3+j4LatMDMz47t27Rr+QAAoWJ13tL3BTWodLHRffKTO7z8PaZbhKDbO7kicrWTn1lPGaitWyvvzQ5zMbLe7zwx7XJrZPHZLOsnM7qJW+P5pHg0EgJjVuQdl2AmWVEmHy/skVcbpl4uTjDGKQbN5/K67v9/M/r+e2yVJ7v4/C24bAKACw4IbQWO4vMMv4/TLxcELRrFqwH2dcdF3TvgBANRQUkDr3E7QGG7YMhzVlk3rNTU5cchteY7Tn5tf0MbZHTp+6yXaOLtDc/MLuTxvrPL+/FBvg2bz+Of2v68rrzkAgKoNO8GSKulweZ+kmudJtL3j3Z/04LX6yO4Fhu10acJJxshPmhMQ/07SGyQtSfoPSSdJOsvd31988w7FCYhAfDhRLU6DPjdOzkonxHW/32dn6n+Ftqaf3Bji54dypT0BMU2Y3uPuJ5vZMyVtlnS2pM+7+0n5NDU9wjQQh85OaGFxacWOmtBVDwSNOCXNCtKPSbp69tRiGwQELLfZPCRNtv99mqQL3P2mzkmIQF7YMddHb+Wr93CdE9Xqoc6zmdTZKOPaGbYDpDPoBMSOj5vZVZJmJH3OzNZK+kWxzUKTdMLXwuKSXAfH6zX9BJhY9ZvpoRcnqgHVSArIvSUyxgcD6Q0N0+6+VdJjJc24+7KkfZKeUXTD0ByDptlCfNIEZSpeQDWSZgV5wWPWaXrNlEytsdIMxQLSGzrMw8yOkPQnktZJOlPSsZLWS/pEsU1DUzDNVr0kzfTQQcWreAybQpI8ZwUB0JJmzPS/SNot6XHt36+V9CERppGTuk6z1dRA029Kqc5JiNMNWg5V4eqEGIbx7kC+0oTp+7v7c83sdyTJ3ZcspzMQzezdkp4u6cfu/rA8nhPxqeN8nk0ONFS+hivyQIurEwJAudKE6V+a2ZTaJ+Wb2f0l3ZbT679H0lslvS+n50OE6hi+mh5oqHwlK/pAi2FT6YXQexRCGwCMJ02YPleti7Xcx8w+IGmjpBfn8eLu/kUzOy6P50Lc6ha+CDRIUvSBVl2HTeUthN6jENoAYHxpZvP4jKQz1ArQF6g1Rd7VxTbrIDM708x2mdmuG264oayXBcaSFFwINEh7oDU3v6CNszt0/NZLtHF2R+qpIpNma4hx2FTWZZBGCLMIhdAGAOMbGKbN7LFm9mxJE+5+iaQfSvoHSV8qo3GS5O5vd/cZd59Zu3ZtWS8LjKVOgQb5SnOgNc7c65s3TOv8M06MfpqzouefD6H3KIQ2AFUr8qC5LInDPMxsm1onB+6R9Boz+4Skl0v6G0kvLad5QJzqNA6cMZ35SnPC7bhDQeowbKoJw2FCaEMTsA0LV12GOg0aM32qpA3u/gszO1rSdZIe7u7/VU7TgDgkbajrEGjqsqELSZoDraR5uptUsSy6ahvCLEIhtKHuYt2GNeUAoC4n6w8K00vu/gtJcvebzWxv3kHazC6Q9ERJx5jZtZLOdfd35fkaQJGK3lBXvUGty4YuNIMOtObmF+6Yl7tXkyqWRVdtQ+g9CqENdRfjNizWA4As6jLUaVCYvr+ZXdz1+3Hdv7v76eO+uLv/zrjPgYOqDl5NVOSGOoQNal02dDHZtn1v3yBtUqMqlmVUbUPoPQqhDXUW4zYsxgOArOoy1GlQmH5Gz+9/X2RDQhRTOA0heDVRkRvqEDaoddnQxSRp3XHV47ucdrtK1RZ5iHEbVvYBQJVZpy5DnRLDtLt/ocyGhCa2cBpC8CpTKAc6RW6oQ6io1GVDF5OkdWo64J1/WqNuV6naYlwxbsPKPACoOuvU5aB56DzTTRXb/J8hBK+yFD1l1iiKnAIvhLmq6zLNWkxCn1ZxnGmsYtuuIn4xbsPK3AaE8J3cvGFaO7eeoqtnT9XOracE/dkkSXMFxEaKLZzG2JWVtbqctgpfRvW6yKPqUCoqo1QHQ+kxKENR7zXkSs24VazYtquoh9h6OMrcBvCdzAdhOkFs4TSU4JVWv53y2Rfu0VkX7tH0kA1Hmi9/mV1XRW2oQw5V/VTdXVimot9rqDv/cYeTxbZdBapS1jaA72Q+hg7zMLMHmdk7zOzTZraj81NG46oUeldrr9i6svrtlDszGAwbtpFm+EPSTv91H79yxd+FfPWlmLq/QuguLEuT3mu3catYsW1XgbrjO5mPNJXpD0l6m6R3SDow5LG1EVtVUAq3mtXPsJ3voGpXmip80vPfvG9Zc/MLdzxvk6qpRWtSd2GT3mu3catYMW5XgTrjO5mPNGF6v7v/U+EtCVBM4TQ2STvlbknBJM2Xf9Dzd4f0ps2CUqQmdRc26b12y2M4WQjb1VjG9sfSTsQthO9k7NKE6Y+b2cslfVTSbZ0b3f2mwlqF2uu3U+41KJgM+/Jv2bReZ124p+993SG9qRXGIgwLWnUIBp33sLC4tOIqhU3oGq1DFSuW3qhY2gkgXZj+vfa/W7puc0n3y785aIrunfI4wSQpoG3eMK3zLr5Si0vLK/6mO6Q3tcJYhEFBqw7BoPc99F6l8PDV4c00WsQBTOxVrCp6o7J8DjH3mtXhwBkYxdAw7e7Hl9EQNE/3TjnLxndYQDvv9BOGdkmHNgtK7DuhpKAVczDo6Pceui0uLQd1gFCHA5giVHF1uSyfQ6y9Zqx3aKKhYdrMJiX9saQntG+6VNI/u/vKkh+QUZZq17CAlqZLOqRu6zrvhGINBt3StDWkA4Q6HMAUoezeqKyfQ6y9Zqx3aKI0wzz+SdKkpH9s//7C9m0vK6pRKF6eFdCqqqlpAlqakB5Kt3Wdd0KxBoNuaU6alcI5QKjDAUwRyu6Nyvo5hNZrllZI613sPX2IR5ow/Sh3P6nr9x1mdllRDULx8qyAVllNHTeghbahDWknlLdYg0G3NCfNSuEcIOR1ABPa9ySr7vdx16lJ3WlylRb3LRf+nrJ+DiH1mo0ilAPnOvf0ITxpzpg5YGb37/xiZvdTg+abrqM8LzhR5cUrxplsvrOhXVhckmv4hWLKkOZiNLGK7aJC/fS+h6OPmNTkKjvkMSEdIORxMYYQvydZ9L6PxaVl/WL5dr3puScXfjGkcT6HmC7a1BHKRUCaemElVCNNZXqLpM+b2fckmaT7SnpJoa1CofKsgFZZTR2nchPikIo6VG8HCWU4zTh630PIVds8KpuxzHwxTJXf91grzFmF8n7r3NOH8KSZzeNzZvZASevVCtNXufttQ/4MAcuzG67qLr2sAS3EDW0oOyGkF/oBwrjti2Xmi2Gq/r6Hvp7kLYT3W/W+Cc0ydJiHmT1H0mHufrmk0yRdYGaPKLxlKEye3XChdOmNKtQhFTF266K+yv6eFNU1H+r3HcWJdd+EOKUZM/1ad/+5mT1e0iZJ71VrNg9EKs/xq7GOhW3qhnZufkEbZ3fo+K2XaOPsjujGvqJcZX9PiqogN/X73mSx7psQ537K3Huv49XzALN5d99gZudLusLd/61zWzlNPGhmZsZ37dpV9ssiQHmMqwx5vGsRervQpVagYAcTtqrX0zJff+Psjr5d89NrprRz6yljPXfVyxHAcKHtp8xst7vPDH1cijD9CUkLkn5T0iMlLUn6Ws90eaUgTEMK78uWh8M8f7sAACAASURBVDJ29EUGFRSj6HU9tIBZx+82gPRC20+lDdNpZvP4bUlPkfRGd180s3upNcMHUIkQZ+IYR1nzoVZ9ElYoQguQgxS5roc4Dy8n4SKLmL7TGCzW/dTAMG1mq9SqQj+sc5u7Xy/p+qIbBiSJ9cuWpKyDA85uLzZAFrFDL3JdD/WgtOiZIAhe9RLiQSGyi3U/NfAERHe/XdJlZraupPYAQ9XtzPyyDg44Cau42SKKurhJket62vUuxpOBktTlIjQ4iIuz1Eus+6k0s3ncS9KVZvY5M7u481N0w4AksX7ZkpR1cMDZ7cUduOS9Q+8E2IXFJVnPfXmt62nWu7qFT4JX/dStp7LpYt1PpRkz/brCWwGMoG7jKsu88mEIF1MoQ1JXflFdiHnu0Hu7rV2tq2W5WjuWvNb1NOtdqENBsiJ41U+swwKQLMb9VJorIH6hjIYAo4jxy5YU8EI4OKjTONJBYyiLOnDJc4feL8B2gnT32ezjfmZp1ru6hU+CV/2UWYwAkgwN02b2GElvkfQQSYdJmpB0q7vfpeC2AbUx7CSZKg8O6nYCz6BqaieM5n3gkOcOPU2AzeszS1rvOkE9aeLUWMMnwat+QihGAGmGebxV0vMkfUjSjKQXSXpgkY0C6ibk7vKQ25bFsDCa94FLJ3guLR/QhJkOuI81HCNN9bTMKfN6TU5YtOGT4FVPMfZUol7ShGm5+3fMbMLdD0j6FzP7csHtAmol5O7ykNuWRZld+b3B84D7HZXOrDv3NNXTsqfM63bkYaszvbdQhhIRvADkLc1sHvvM7DBJe8zs78zsbElHFtwuoFZCns4v5LZlUeZsL0XMDpHmbPYqpszr+OnS8sjPWbdZQQAUL6ZpOdNUpl+oVuh+haSzJd1H0rOKbBRQNyGP1Qy5bVmU2ZVfVIV4WPV03M9sUJU4qbLfkddJlTEPJUKyUHogilL39xeK2M7lSTObxw/MbErSvdydafKADEIeqxly29Lqt4PrnvmiKFmGlOSxMx7nMxu2k+oX1DuKPKkS8YstAI2q7u8vJLEdgJt70vna7QeYnSbpjZIOc/fjzexkSX/l7qeX0cBuMzMzvmvXrrJfFkDA+p0wNzU5UcpE/6O+dpFtTRvSOxeD6dU99V7nuRYWlzKdVNnbln2/3K+b960cHpL3dH8YrshlnGbdilnd319Ijt96Sd/ZhEzS1bOnltYOM9vt7jPDHpdmmMd5kh4t6VJJcvc9ZnbcGG0DgNxUWcEYtUJcVFtHqZglDeHovj3LSXrdAbxzkZnO806uMk1OmJYPHNw99la5qfoVr+hlXPceiLq/v5DENid8mjC9391/atZ7UVvUEZUhxGRufiExHJa1gxsleFZxOfPetnUqzb0mxtjG97tqY7fl211rpiZ15OGrE7ctsXXrxqjoZRxbAOo1bP8X+/uLSWzn8qQJ0980s+dLmjCzB0r6U0lMjVdDVIYG40AjLJ31NUmIO7gQLmfeL0gPuj2NYdPpSa1ZQPac++TE+9NerIbvYHZFV1ZjC0Dd0uz/Yn5/sYntXJ40U+O9UtIJkm6T9G+SfirprCIbhWoUMc1XXTC1V3iGBbhbb9sf3OdT1LR9o0yVN53w2KTb00gTxoYdMAx7D3wHx1f0NJhppnUMVZr9X8zvL0abN0xr59ZTdPXsqdq59ZSgl3NiZdrM7iTpjyQ9QNIVkh7r7vvLahjKx3iwZHRBh2fYerm4tBxcz0pR1ZZRKmZFVNeGTaeX5vmHtYvv4PjKqKzGelGctPu/WN8fijVomMd7JS1L+j+SnirpIaIiXWuMB0vGgcahQuhuHxbgpDDDVhE741FCehGBvl9I65yEmHYWkGHtqtN3sKrvT2xd52Vi/4dxDArTD3X3EyXJzN4l6WvlNAlVYTxYslg3tEXstEMZWz9oPuRuSWFrlGUTwsHDMKOE9LwDfV4hbVC7Yv0O9qr6+0NltT/2fxjHoDB9x6Sg7r6f2Tzqj6pFshg3tEXttEPpbu9dX1clzFJx16nJFbeNsmyKWo6hBvSs7So6pMX4HewnlO9Pr1DXx7Kw/8M4Ei/aYmYHJN3a+VXSlKR97f+7u9+llBZ24aItKEqaHUlsO5uiLjAQymT6vebmF7TlQ5dp+fZDWzc5Ydr27JMO+axGWTZFLMcqLzQTY7s6YvsO9hPi9yf0zx2oytgXbXH3iaT7gJj17pCf9OC1+sjuhaGVx9i6R4saYxpqd/vmDdN63cevXHGlveUDvqLqN8qyKWI5hlqdDLVdHbF9B/sJ8ftT5OdehwMgYJg0U+MBtdFveq0PfOWHtZwSsKhpsIqa3i0Pi30uWS2tDL6jLJtRl+Pc/II2zu7Q8Vsv0cbZHX2nbgv1ZLpQ2zWuNJ9JWUL8/hT1uTOdIZqCMI1G6VeBSbpURewBoqiddshzraYNvqMsm1EemzY8FD3fb1ahtmscoQW6EL8/RX3uXLsATZHmCohAtHq7GIdNpdYt5gAhDT+hZpzu11C729OepFbUVHJpu8vHPZmuqK7zupzk1y3EoSuhfX+K+tzr2tMB9CJMI1rDAkW/WRg6c9/26r09tACR9wwLVU/PVZTNG6a16wc36YKvXqMD7pow07Me2X8ZFDGV3CgXfpCyzRyQ12c3aJ2q0xhXAt1wRX3uIY4PB4pAmEaU0gSKpCEd/YLzsx45rc9fdUOQAaKI4BtitS4Pc/ML+sjuhTumyDvgro/sXtDMfe9WyvsaJTxkrU7m8dkNW6diXgd6EejSKeJzr2NPB9BPpWHazJ4i6X9JmpD0TnefrbI9iEeaQJFUeepclS3E4NzPeRdfmXvwrWu1ruqDhDLCQx6fXdXLaRyj9tKEGuiaMMtFHXs6gH4qC9NmNiHpf0v6LUnXSvq6mV3s7t+qqk2IR5pAkVSRyjI/cBU7vrn5Bb3u41dqcSndDBWjqGu1ruqDhDLCQx6f3ajLKa/1f9zn6VdRP/vCPTrrwj2Jly0PMdDVdZhVP3Xr6QD6qbIy/WhJ33H370mSmX1Q0jMkEaYxVJpAkVdFqoodX7+LKPQaJ/iGWq0bVxkHCcMCYQxXAhxlOeU5Rnvc5xk0G8+g5wst0MXcM4CVmtDL0KuJ73mQxCsgFv7CZs+W9BR3f1n79xdK+lV3f0XS39z5znf2Rz7ykWU1EQG78Zbb9L0bbtXtXevvKjPdb+2ROuaoww953DU3Lem2/Qd0+OoJ3eduU4fcn8b8Dxd12/6Vofbw1RPasG5N9jeR4TW7PeDuR438XrrlsWxCk3a9CPX5R2nHOJ/dKO8jr/U/j+f5yvd+MvQxvc8X4no+6H085n6/UmJLqhfi5zOKULYJZWrSe/7CF74w3hUQS2B9bluR7M3sTElnStLhh9frQ0J2nS/ssI3wMUcdPvaXOynUDgu7Rbxmx+qJVWO/rzyWTWjSrhdZXXPT0iE7EEm63V3X3LRU6rIc97Mbtpy6A06SUdf/PL5Hh6+eGPr47vuvvvFW/ehnvzjkvu/dcKskVbruJ72Pw1c368LDvaEslM9nFKFsE8rUxPc8TJVh+lpJ9+n6/d6Srut9kLu/XdLbJWlmZsYvvfTSUhqH8aWZui6GbqKNszsSx15fOuLY63FfU2p16Vd9kYemOn7rJYlTK146e2rZzSlEZzjG0QOGGEmjr/95fI/SDH/qPN/c/ILOvnCP7tnnMXct8LubRr/30cTv9cbZHbp7n3Wi6s9nFE3YJvRq0ns261f3XanKKyB+XdIDzex4MztM0vMkXVxhe5CjYVcdK+uqZHlcRriKy//2e01JWjM12bgdblplXDK6iisEln0p7H7jeXtlWf/z+B51Xz1QWtm92f1827bvDfbqpiFeBbEog9bfqk8YzkMdrxo6TBPf8zCVVabdfb+ZvULSdrWmxnu3u19ZVXuKEkv1NW/DTrAp4wScvE6cGnc2gCzrQIgzEISsrJNEyz5xs4qTXwcFGZMyr4t5rdPdJxMO+m4Neh8h7PTLOCmy6v3PsPW3DrMK9dsmmKQnPXhtdY0qWF1PYB9HpfNMu/snJX2yyjYUqUnTH/UaVnEooyKRZ2DPuuMbZx0IbQaCkJU1O0LZBzlVzPqQ55SSvfJepwc9X9L7MKkRO/0Q9j/D1t86hLLOVVc/8JUf3tET4lKpF4sqG8WelbgCYoGaPP3RsIpDGRWJELoQk9aBsy7co23b9zZ+A5SXNJ91XlW6Mg9yqliH6xBwpOSK4Qsesy7671yadTmE/c+w9bcuoezzV92wYkhR3ff1FHsORZguUAhhrirDdshl7LBD6EIc9Fk3qaeiaMM+6xCqdFmMsw5nPXioS8Ap+n1UNYQi7bocwv4nzfpbh1AWwrJGtao8AbH2mjxIf9gJNmWcgFPFiYO9hn3WneoFxpN0wuatt+2/I/QkVelClnUdHvcE380bprVz6ym6evZU7dx6SrRhp6j3UdYJ1P2kXZdD2P+EsA0uQwjLGtWq7KItWczMzPiuXbuqbkZqTH9UvdBOwOnHJF1ds+mEqtC5/PrN+w69/PrU5MTQ5R9y9TXLOjxoGrph456r/s7EYJzlO65B05J1b0dC2f80YX0KZVkjf2YW/EVbaq8u3aUx6t2Av+m5J1ey3LvXgaR5o6le5KMzS0xvmF5aPqAJMx1IKBx0VxY7zxOSLN3gWbudYx0OM0wega77Oaqcci/t0J9Q9j91GMYxTCjLGtUhTBesCRuS0IQWCDrrQFL1Ik2XfREb6bTPO+rrV1mJSgozB9yHVqjrdMJQ1rHWIZy0lrc8tgdpepikcg6MRznfhP1PeVjWzcaYaVQu74tShDo+Nss48aLGZqZ93lFfv8qxpFJymOks686yT1KXE4ayjlWt44lUeWwPirqQTRZNuuALEAsq06hUEVXkOgWCoiqFaZ931NevurI5qGrXXTlKGvNalyE3WbudQ5gBJ29J3/uFxSVtnN2RavkUdSGbrKiCAmEhTKNSRYSvUANBlgOHog4M0j7vqK9f9YFM2hBZl7mUB8kSuOq4XAZdvKVz+7DvYpEXsgEQP4Z5oFJFhK9Qp2PK0t1c1JRLaZ931NcPYYqoNNOh0VXeXx2XS7/tgUmJF9lI+xxVb1PyHh4HIDsq06hUEVXkUM+sznLgUFSlMO3zjvL6c/ML2vfL/Sturzp0JKGrvL8QlkueJ7H22x4kzazT+13sbsddpyZ1p8lVWty3XPk2JbSTrIGmI0wjd6PsCLOExTTPn0cgyHtWiiwHDkUdGKR93rSPS5rtYM3UpM47/QR28D2KnvEk5rl9iwiKvduDNGPme9uxuLSsqcmJyqbZ7Fb1uQkADsVFW5BZvx22pJEnrx9lx1/W5PhFvE6dJ/av8iIWsSl6PYh9PStjXUqzjEJep9NeuAXAeLhoCwqVVD260+SqkSsmo1SRy6rIFPE6SVVeSalnFQjVoBkT5uYXons/RSp6HY69alnGSaxpelyqPpl2kFBPsgaaijCNTJJ22Elzsea1AyprB1fU6/QeONRl7OOgcahFvJ+YhzEUvQ6HHALTKCsoDjuIDzmw1nHWFSBmzOaBTEbdMee1AyprtoiyXifUC8yMqt9sBx15v5+qLwwzrqLXrRBmVBlHKDNnhNKOfuo460oHs5QgRlSma6royl1S1WbN1KRu2397YRWTsioyZb1O7FXEjs66ddaFe/ren+f7iX0YQ9K69aQHr81luM+wdTf0qn4os/GE0o4kIcy6kre69NSheQjTNVTGBilph33e6SdIyn8HVPYUVWXtSMvuSi4ySG3eMK1t2/cW/n5iPwDpt2496cFr9ZHdCwO/s2k/u0HrbixhJZSgGEo7miL2A2U0F2G6hpI2SOddfGWuwanzWv127nmG5zVHTOqWX+zX8u2t89fLmqKqjB1pmWMfqzzIyvP9hDyWNa1+U7UNChGjfnZJ626TwkoRB46hV/VjF/uBMpqLMF1DSRuexaXlXGdWKCps9gaHm/ctr3hMXQJAmV3JZQSpvN7PoNBSx5OvhoWIvD67poSVIg4cY6nqx6wOB8poJsJ0DQ2aWSGGANovOPRTlwBQVldyWUFq3PczLLSEPpY1i2EhIq/PrilhpYgDxyZV9atSxwNlNANhuoa2bFpfyolgRUnbxtADQGhdwrEEqTShJc8DkBA+p2EhIq/PLo+wUubyyvpaRRw4NqWqX6U6HiijGQjTNbR5w7Re9/Er+w6PCC049TOost4RerWi6i7hfiEklqpPmaGl6s+pY1iIyOuzGzeslLm8xnmtIg4cYzkYjR0nfSJGXE68pmK+pHC/tk9OmI48bLV+ulTcDB55qvJSxIM+eyn8qk+Zyy7kS0b3SqrSllkpjuWzKeI7EPM2FUA2XE68IZJ2pEV0l5W1065DV1+VXcKDhkns3HpK8MuxzAp6TF33/Sp2aau3eX13y1xe47xW0jZEUuZqdx22SwCKQZiOWJoTtfIcV7rlQ5fdMT3dwuKStnzosjteK2+xd/VV2SUcU0DsZ5zQMmpoLONzKvIgNM348jyHZpS5Xo/7Wv22IcOmIMzynADA5cQjVualqM+7+Mo7gnTH8u2u8y6+MvfXqoMqL0Uc++WkpVZo2bn1FF09e2rqanqWy4wX/TkVfenzNAdOeW4nylyvi3itYcurqZeybur7BvJCmI5YmRXIxaWVJzMOur3pNm+Y1vlnnKjpNVMytcZ5ljW2ssogX6UsobHoz6noA940B055bifKXK+LeK1By6voA59QNfV9A3limEfEOLs8bFV1CTd1bGfW0Fjk51TEAW/v1UEnV9khvUa9B055byfKXK/zfq1B4/HLmEc6hGkYezF/NjA+KtMRK7MCefQRkyPdjmplGSYRuxCHt+Tdpt4q4s37liWT1kxNJlZvm9pT0c+ganfRPX2hVoBjP8cCCAGV6YiVWYE897QTtOXDl2n5wMEK2OSE6dzTTsj9tYAksV1mPO829asiLh9wHXn4au0598l9/6apPRVJkqrdRff0hVoBpocTGB9hOnJldbmyQ0bVYrzMeN5tKmIoSxVDD0Ic7lD0wVioFeAQD0KB2BCmG2acnRjTQsUrxPAyqrIvM56XPNuUdxWxiitAhnLVyV5FH4yFWgEO8SAUiA1hukFC3YmhWCF87nmE+VAre2UqY9hIXkMPkj7zUIc7SMUejIVcAQ7xIBSICWG6QULeiaE4VX/ueYX5UCt7ZQpl2Mgwgz7zMk70C7HKSgUYqC/CdINQ2WumvD/3ufkFnXfxlXfMMX70EZM697QTEkNBXmE+5MpekiKCXcjDRjoGfeZFHhSF0AszCBVgoJ6YGq9BQpw6DMXL83PvXFa++2I9N+9b1pYPX5Y4xVdeYb7KC+Fk0W8qtC0fvkwnv+7TwVxprqhp8wZ95kVO1VfmVWEBoIPKdIMMquyF2jWaVVnvJ4bllmdFd9v2vSsuKy+1pmdLqjTnWYmMqbKXNI1d50AkhKppUUMPBn3mRQ53oPcNRYlhW4/qEKYbJGknJinortFRldXVG3qXckea8JJ2RzEolCTdN26Yj3UnlibAhXDOQhEHKMM+86IOimIdVx/rOt4UsWzrUR3CdMP024ltnN1RqxMTyzrhruoT+0YxbJ7htDuKpLDSuS/ptaVslciYd2KDllW3OlZNqzrZrl+In5ww3Xrbfh2/9ZIgg2rM63hTxLStRzUI06hd12hZ76cuy22UHcWWTeu15UOXrRjqMTlhAyvNWSuRMe/E+gW7fkKvmmbV/Zl3Kq9nX7in0EDbG+LXHDGpW36xP6ihNb1iXseboi7behSHMI1ou0aTlPV+6rLcRtlRdHbuw2bzyKvbOuadWFKw6z4QqXo2kjKGF5Rdee0O8Rtnd+jmfcuH3B9aUI15HW+KumzrURzCNKKccmyQst5PXZbbqDuKYVXmPMNT7Dux3mUV0tjYskJulZXXNEG16s8k9nW8CeqyrUdxCNOo3cUEyno/MS23QYEh5Kvqjdq2qoPRMCHNRlJWyK2y8josqI56QFHE+kVQC19M23pUgzANSWHt5PNQ1vuJYbkNCwwhX1VvlLZxItdoygq5VVReO6F3YXFJJql7hH93UB3lgKKo9YugFocYtvWoDmEaqLk0gSHPHcWaIyZXjFOVsoentG3jRK7RlBVyy6689oZel+4I1NM9QXWUA4oi168yg1rovTdAjAjTQM2V2c0+N7+gW36xf8Xtw2b7yENoJ3KFHlrKCrllV177hd5OkN659ZRDbh/lgCK09SsLem+AYhCmgZors5s96QqJRx62uvCddUgncuUZWooK5WWG3DIrr6OE3lEOKEJav7Ki9wYoxqqqGwCgWFs2rdfU5MQhtxXVzZ4UZH66tHLYR97KfJ/DDAoto+iE8oXFJbkOhvK5+YVc2rl5w7R2bj1FV8+eqp1bT6lFoEoKt/1u37xhWuefcaKm10zJ1Kpen3/GiX2XQ0jrV1Z1qK4DIaqkMm1mz5F0nqSHSHq0u++qoh1AE5RZgayyehfSiVx5hRYqiYdKU6UfdfhK2qp5SOtXVnWorgMhqmqYxzclnSHpnyt6faBRyupmr3qar1DOuM8rtFBJPCjt0JkiQ28o61dWVX8/gbqqJEy7+7clycyqeHkABalD9S4PeYUWKokHjVKljz30FoXvJ1AMTkAEkKsqg0woM2jkFVpCrCRWtYyp0ueDAw0gf4WFaTP7rKR79rnrL9z9YyM8z5mSzpSkdevW5dQ6AHUT2rRfeYSW0CqJVS5jqvQAQmXuK6exKu3FzS6V9Oq0JyDOzMz4rl2cqwikFUqltgwbZ3f0DVv95hdGet3r0CozHeizzyhjGfcGealVpU+afQMAxmVmu919ZtjjGOYB1FRoldqiMQwgWdaDqt51qF+QlspZxqFV6QGgo6qp8Z4p6S2S1kq6xMz2uPumKtqCg5pUxSxD1cuzadOqMQygv3EOqvqtQ/2UtYwZ7wsgRFXN5vFRSR+t4rXRX9OqmEULYXk2rVIb4sl6IRjnoCrNusIyboZxiwOD/r7qwgMwLoZ5QFLzqphFC2F5Nq1SW4dhAEWEinEOqpLWoY6jj5jUuaedENUyxujGLQ4M+ntJlRcegHERpmsoyw65aVXMooWwPJtYqY15GEBRvRnjHFT1W4e6/WL59sztQjzGLQ4M+vvO/7M+NxCCVVU3APnq7JAXFpfkOrhDnptfGPh3STvWulYxixbC8ty8YVrnn3GiptdMydSacYGZD8I1LHBktWXTek1NThxyW9qDqu51qJ882jc3v6CNszt0/NZLtHF2x9BtFco3bnFg0N+HUHgAxkWYrpmsO+RxdrhYacum9ZpcdegVPidXWenLc/OGae3ceoqunj1VO7eeQpAOWFGhYtyDqs46lHS92nHal/XgH+Uatzgw6O9DKDwA4yJM10zWHTJVzAL0po+kNAKo2N6MPA6qimhfUdV45GvcYsugv6eQgzpgzHTNjDM+MubxpqHZtn2vlg8cOifv8gFnHCAShT7GvYj20cUfh3FP7k3z9zGfOIzx1GE2F8J0zYS+Q24KQgJGFfpsJKO2L80OsmkzzsRs3GLLoL+nkNNcIUwjmwfCdM2EvkNuCkICsgg9VKRtX9odJAf/QLOFMI1sHgjTNRT6DrkJQgsJdehGQ/XSrkdpd5Ac/APNVpdeXMI0UICQQkJdutFQjqTAPMp6NMoOkoN/oLnq0otLmAYKEkpIqEs3WtmaWM0fFJhHWY/qsoMEUKzQenGzYmo8oObq0o1WpqbOfzwoMI+yHtVlujMuKAMUqy7T8lKZBmqOKuHomlrNHxSYR1mPQhrmlFUVw6Oa2BsChNKLOw7CNFBzdelGK1NTq/mDAvOo61HsO8iyD6g4twGIF8M8gJobpRuNbu2Wpl7ieNDwjLp0x6ZV9gEVV4ME4kVlGmiANFVCKmMHNbWaP2x4RuzV5lGUPTyqqb0hQB0QpgFIau444X5CG/Nb5ljaJgXmQco+oOLcBiBehGkAkqiM9QolVNJjUI2yD6ia2hsC1AFhGoAkKmOhosegOmUeUIXWGwIgPcI0AElUxkJFj0FzhNIbAmA0hGkgAmWMmaUyFiZ6DAAgbIRpIHBljpmlMhYeegwAIGzMMw0Ejvlnm61p8zsDQGyoTAOBY8ws6DGIB5cEB5qHMA0EjjGzzRBDCIuhjXka9f0yjSHQTAzzAAI36BLPZeNy48XohLCFxSW5DoawkJZvDG3MU5b3y5AsoJkI00DgQhkz27QwVaYYQlgMbcxTlvfLkCygmRjmAUQghDGzMV88JPThCTGEsBjamKcs75chWUAzUZkGkEqsYSqGinpS2AophMXQxjxleb/9hmRNrjLt++V+hkYBNUaYBjBQZ5y0J9wfepg67+Irgx+eENK4+CQxtDFPWd5v75CsNVOTkkk371sO9kAOwPgY5gEgUe/sBL1CD1Nz8wtaXFrue19IFfUYrj4ZQxvzlPX9dg/J2ji7Y8X6F8vQKADpEaYBJOo3TrpjOoIwNaj6HFpFPYRx8cPE0MY8jft+Yx0aBWA0hGkAiZJ2+iZp59ZTym1MBoNCS8gVddQDJyQCzcCYaQCJYj/pLKmdRx8x2agKK6rRtHHmQFMRpgH0NTe/oFtv27/i9pjCQFKYOfe0EypqEZoklDniARSLYR4AVkg68fDoIyZ17mknRBMGmnbSHMIT8jjz0OdfB2JBmAYiUeaOL+nEwyMOWx3dzjbkMANUpfeAuTNtnyS+L8CICNNABMre8TELAbKg0hmPmK9oCoSGMdNABAbt+IoQ+4mHKF8MV5rEQRwwA/khTAMRKHvHxywEGFXZB3wYDwfMQH4I00AEyt7xMQsBRkWlMy4cMAP5Ycw0EIEtm9avmF2j6B0fJ+5hFFygJC7MdAPkhzANRIAdX/44WS5fVRzwYTwcMAP5IEwDkWDHlx+mBcsfB3wAmoowDaBxmBasGBzwAWgiTkAE0DicLAcAyAthGkDjMC0YACAvcJL3kAAAC7ZJREFUhGkAjcO0YACAvDBmGkDjcLIcACAvlYRpM9sm6TRJv5T0XUkvcffFKtoCoJk4WQ4AkIeqhnl8RtLD3P3hkv5T0jkVtQMACjM3v6CNszt0/NZLtHF2h+bmF6puEgAgZ5WEaXf/tLvvb//6FUn3rqIdAFCUzlzWC4tLch2cy5pADQD1EsIJiC+V9KmqGwEAeRo0lzUAoD4KGzNtZp+VdM8+d/2Fu3+s/Zi/kLRf0gcGPM+Zks6UpHXr1hXQUgDIH3NZA0AzFBam3f03B91vZr8n6emSfsPdfcDzvF3S2yVpZmYm8XEAEJJj10xpoU9wZi5rAKiXSoZ5mNlTJL1G0unuvq+KNgBAkZjLGgCaoap5pt8q6XBJnzEzSfqKu/9RRW0BgNwxlzUANEMlYdrdH1DF6wJAmZjLGgDqL4TZPAAAAIAoEaYBAACAjAjTAAAAQEZVnYAIAEAtzM0vcKIp0GCEaQAAMupcNr5ztcvOZeMlEaiBhmCYBwAAGXHZeACEaQAAMuKy8QAI0wAAZJR0eXguGw80B2EaAICMuGw8AE5ABAAgIy4bD4AwDQDAGLhsPNBsDPMAAAAAMiJMAwAAABkRpgEAAICMGDMNAAAKw+XWUXeEaQDIiJAADMbl1tEEDPMAgAw6IWFhcUmugyFhbn6h6qYBweBy62gCwjQAZEBIAIbjcutoAoZ5ACOgWx8dhARguGPXTGmhz3eCy62jTqhMAynRrY9uSWGAkAAcxOXW0QSEaSAluvXRjZAADLd5w7TOP+NETa+ZkkmaXjOl8884kR491ArDPICU6NZHt04YYNgPMBiXW0fdEaaBlBj7h16EBAAAwzyAlOjWBwAAvahMAynRrQ8AAHoRpoER0K0PAAC6McwDAAAAyIgwDQAAAGREmAYAAAAyIkwDAAAAGRGmAQAAgIwI0wAAAEBGhGkAAAAgI8I0AAAAkBFhGgAAAMiIMA0AAABkRJgGAAAAMiJMAwAAABkRpgEAAICMCNMAAABARoRpAAAAICNz96rbkJqZ3SDpBxU34xhJN1bchlix7LJj2WXHssuOZZcdyy47lt14WH7Z9S67+7r72mF/FFWYDoGZ7XL3marbESOWXXYsu+xYdtmx7LJj2WXHshsPyy+7rMuOYR4AAABARoRpAAAAICPC9OjeXnUDIsayy45llx3LLjuWXXYsu+xYduNh+WWXadkxZhoAAADIiMo0AAAAkBFhug8ze4qZ7TWz75jZ1j73P9jM/q+Z3WZmr66ijaFKsexeYGaXt3++bGYnVdHOUKVYfs9oL7s9ZrbLzB5fRTtDNGzZdT3uUWZ2wMyeXWb7QpZivXuimf20vd7tMbO/rKKdIUqz3rWX3x4zu9LMvlB2G0OVYr3b0rXOfbP9vb1bFW0NTYpld1cz+7iZXdZe715SRTtDlGLZHW1mH23va79mZg8b+qTuzk/Xj6QJSd+VdD9Jh0m6TNJDex5zd0mPkvTXkl5ddZtD+Um57B4n6ej2/58q6atVtzuUn5TL7ygdHJ71cElXVd3uEH7SLLuux+2Q9ElJz6663SH8pFzvnijpE1W3NbSflMtujaRvSVrX/v3uVbc7hJ+039mux58maUfV7Q7hJ+V69z8k/W37/2sl3STpsKrbXvVPymW3TdK57f8/WNLnhj0vlemVHi3pO+7+PXf/paQPSnpG9wPc/cfu/nVJy1U0MGBplt2X3f3m9q9fkXTvktsYsjTL7xZvf8MlHSmJkx5ahi67tldK+oikH5fZuMClXXZYKc2ye76ki9z9h1Jr/1FyG0M16nr3O5IuKKVl4Uuz7FzSnc3M1CrC3CRpf7nNDFKaZfdQSZ+TJHe/StJxZnaPQU9KmF5pWtI1Xb9f274Nw4267H5f0qcKbVFcUi0/M3ummV0l6RJJLy2pbaEbuuzMbFrSMyW9rcR2xSDt9/ax7S7jT5nZCeU0LXhplt2DJB1tZpea2W4ze1FprQtb6v2FmR0h6SlqHQgj3bJ7q6SHSLpO0hWS/szdby+neUFLs+wuk3SGJJnZoyXdV0MKf4TplazPbVT/0km97MzsSWqF6dcU2qK4pFp+7v5Rd3+wpM2SXl94q+KQZtm9WdJr3P1ACe2JSZpl9w21Lqt7kqS3SJorvFVxSLPsVkt6pKRTJW2S9Foze1DRDYvAKPva0yTtdPebCmxPTNIsu02S9kg6VtLJkt5qZncpumERSLPsZtU6AN6jVm/mvIZU9Vfn07ZauVbSfbp+v7daR3YYLtWyM7OHS3qnpKe6+09KalsMRlr33P2LZnZ/MzvG3W8svHVhS7PsZiR9sNXrqWMkPc3M9rt704Ph0GXn7j/r+v8nzewfWe8kpVvvrpV0o7vfKulWM/uipJMk/Wc5TQzWKNu754khHt3SLLuXSJptDwv8jpldrdb436+V08Rgpd3evUSS2sNkrm7/JKIyvdLXJT3QzI43s8PU+hJfXHGbYjF02ZnZOkkXSXqhuzd9Z9IrzfJ7QPvLLTN7hFonUHBAkmLZufvx7n6cux8n6cOSXk6QlpRuvbtn13r3aLX2Hax36fYXH5P0a2a2uj1c4VclfbvkdoYo1b7WzO4q6dfVWo5oSbPsfijpNySpPd53vaTvldrKMKXZ3q1p3ydJL5P0xe6CQj9Upnu4+34ze4Wk7Wqd9flud7/SzP6off/bzOyeknZJuouk283sLLXOBh24sOsuzbKT9JeSfkXSP7b3zfvdfaaqNock5fJ7lqQXmdmypCVJz+06IbGxUi479JFy2T1b0h+b2X611rvnsd6lW3bu/m0z+w9Jl0u6XdI73f2b1bU6DCN8Z58p6dPtyj6Uetm9XtJ7zOwKtYY2vIaepNTL7iGS3mdmB9Saief3hz0vV0AEAAAAMmKYBwAAAJARYRoAAADIiDANAAAAZESYBgAAADIiTAMAAAAZEaYBoARmdsDM9nT9HGdmX27fd5yZPb/rsSeb2dMyvMalZjbTc9t5ZnZ+z20nm1niXMftv3n1qK8PAE1EmAaAciy5+8ldP99398e17ztO0vO7HnuypJHDdIILJD2357bnSfq3nJ4fABqNMA0AFTGzW9r/nVXrKnl7zOw1kv5K0nPbvz/XzI40s3eb2dfNbN7MntH++ykz+6CZXW5mF0qa6n0Nd98radHMfrXr5t9W69Lqf9B+zsvM7CPtK/T1tvGOareZHWNm32//f8LMtrX//nIz+8P27fcysy+22/5NM/u13BYYAASIKyACQDmmzGxP+/9Xu/szu+7bKunV7v50STKzH0macfdXtH//G0k73P2lZrZG0tfM7LOS/lDSPnd/uJk9XNI3El77ArWq0V81s8dI+om7/5eZ3eTu72i/xhvUutLXW1K+n9+X9FN3f5SZHS5pp5l9WtIZkra7+1+b2YSkFQEdAOqEMA0A5Vhy95Mz/u2TJZ3eNY75TpLWSXqCpH+QJHe/3MwuT/j7D0r6spm9Sq1QfUH79oe1Q/QaSUepdYndUdr0cDN7dvv3u0p6oKSvS3q3mU1KmnP3PUlPAAB1QJgGgPCZpGe1h2wcvNFMknzYH7v7Ne3hGb8u6VmSHtu+6z2SNrv7ZWb2YklP7PPn+3VwSOCdetr0SndfEcDN7AmSTpX0r2a2zd3fN6yNABArxkwDQPV+LunOA37fLumV1k7PZrahffsXJb2gfdvDJD18wGtcIOlNkr7r7te2b7uzpOvbVeQXJPzd9yU9sv3/Z3fdvl3SH7f/Vmb2oPbY7vtK+nF7+Mi7JD1iQJsAIHqEaQCo3uWS9rdPBDxb0uclPbRzAqKk10ualHS5mX2z/bsk/ZOko9rDO/5c0tcGvMaHJJ2g1pCPjtdK+qqkz0i6KuHv3qhWaP6ypGO6bn+npG9J+ka7Tf+sVm/nEyXtMbN5targ/yvF+weAaJn70B5CAAAAAH1QmQYAAAAyIkwDAAAAGRGmAQAAgIwI0wAAAEBGhGkAAAAgI8I0AAAAkBFhGgAAAMiIMA0AAABk9P8AvVmlwuabplAAAAAASUVORK5CYII=\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": "3.8.4rc1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
