{
 "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"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\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:                Mon, 24 Feb 2020   Pseudo R-squ.:                  0.1327\n",
      "Time:                        22:49:06   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:                  Mon, 24 Feb 2020   Deviance:                       4078.8\n",
      "Time:                          22:49:06   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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SnTU7k+l+AABiQgANoHRbN6/TzPTUivtmpqe0dfO6QCUCACA9BhECKF1noCCzcAAAqogAGkAQW9bPETADACqJFA4AAAAgAwJoAAAAIAMCaAAAACADAmgAAAAgAwJoAAAAIAMCaAAAACADAmgAAAAgAwJoAAAAIAMWUgEAAIWZX2ix6ihqhwAaAAAUYn6hpcuuvVlLy4clSa3FJV127c2SRBCNSiOABgAAQ43bi7xj54GjwXPH0vJh7dh5gAAalUYADQAABpqkF/nOxaVM9wNVEWwQoZmdbWafMLMvmNl+M3tpqLIAAID+hvUij3LW7Eym+4GqCDkLxyFJr3D3R0h6kqRfMbNHBiwPAADoMUkv8tbN6zQzPbXivpnpKW3dvC6XsgGhBAug3f0r7v655P/flvQFSSREAQAQkUl6kbesn9OVlz5ac7MzMklzszO68tJHk/+MyosiB9rMzpW0XtK/9nnsxZJeLEnnnHNOqeUC6oSppACMY+vmdStyoKVsvchb1s9xrEHtBF9IxcxOkfQ+SS9z92/1Pu7uV7v7BnffsGbNmvILCNRAZxBQa3FJrmODgOYXWqGLBiBy9CIDxwvaA21m02oHz+9092tDlgWoM6aSAjAJepGBlULOwmGS/lrSF9z99aHKATQBU0kBAJCfkCkcGyX9nKRNZrYvuf1EwPIAtcVUUgAA5CfkLByfcXdz98e4+wXJ7cOhygPUGVNJAQCQnyhm4QBQrE7uIrNwAAAwOQJooCEYBAQAQD4IoCPH3L0AgLRoM4ByEEBHrDN3b2f6sc7cvZI4IAIAVqDNAMoTfCEVDDZs7l4AGMf8Qksbt+/S2m3Xa+P2XSymUyO0GUB56IGOGHP3AsgTPZT1RpsBlIce6Igxdy+APNFDWW+0GUB5CKAjxty9APJED2W90WYA5SGFI2LM3QsgT2fNzqjVJ1imh7IeaDOA8pi7hy5Dahs2bPA9e/aELgYAVFJvDrTU7qG88tJHE2QBQA8z2+vuG/o9Rg80ADQEPZQAkI+RAbSZ/ZSkf3T3b5vZqyQ9TtIfuPvnCi8dACBXrEgJAJNLM4jw1Unw/L8kbZb0t5L+sthiAQAAAHFKE0B3kuUulvSX7v4BSfcrrkgAAABAvNLkQLfM7M2Sni7pdWa2Wkx/h5qYX2iRDwoAADJJE0D/tKSLJP2Ruy+a2fdL2lpssYDisSobgCJwYg7U38CeZDM7w8zOkHSipBskfSP5+z5JzCWHymNVNgB565yYtxaX5Dp2Yj6/0ApdNAA5GtYDvVeSS7Kufztc0kMLLBdQOFZlA5C3YSfm9EID9TEwgHb3tWUWBCgbq7JhElymRz+cmAPNkGohFTM7XdIPqJ3OIUly908VVSigDFs3r+u7KtvWzesClgpVQP78MZxIrMSJOdAMI2fTMLNflvQpSTslvSb594piiwUUb8v6OV156aM1NzsjkzQ3O8OSxkiF/Pk28n2Pt3XzOs1MT624jxNzoH7S9EC/VNLjJd3o7k8zs/PUDqSBymNVNoyDy/Rt5Psej+XSgWZIE0B/192/a2Yys9XufouZcSoNRIDL52Fwmb6NE4njsU8CzZBmQZQ7zGxW0rykj5nZByTdWWyxEIv5hZY2bt+ltduu18btuxp9aTY2XD4Ph8v0bYNOGJp2ItHBPgk0x8gA2t2f4+6L7n6FpFdL+mtJW4ouGMKjMYgbebjhkD/fFtuJROgTfvZJoDlGpnCY2Tldf96a/PsgSbcVUiJEg/zGuHH5PCzy5+PK941hZhT2SYRE+lC50uRAX69jC6mcKGmtpAOSzi+wXIgAjUHcyMNFDGI5kYjhhJ99EqHEcALZNGlSOB7t7o9J/v0BSU+Q9Jnii4bQyG+MW2yXz4GQYjjhZ59EKKQPlS/NIMIV3P1zak9rh5qjMYgbebjAMbMnTWe6vwjskwglhhPIpkmTA/0bXX+ukvQ4SQcLKxGi0ZvfOHvStNyll1+zTzt2Higlv4qcruFiuXwOhOae7f6isE8iBNKHypemB/rUrttqtXOin11koRCPLevntHvbJr3heRfou8tHtLi0XNqMHMwCgryFnqUBxfnm0nKm+4E64Ypx+Ub2QLs7qw4iyACdGAYFoT6KGGTDFZJ40AOHJotpRpymGBhAm9kH1Z59oy93f1YhJUKUQuRXkdOFPOV9Qsao97hs3bxuxe8h0QOHZiF9qFzDUjj+SNIfqz3385Kkv0pu90j69+KLhpiEmJGDWUCQp7xPyBj1HhcG8AEo08AeaHf/pCSZ2e+7+490PfRBM/tU4SVDVEL07tCjhDzlfYmfKyTxoQcOQFnSDCJcY2YP7fxhZmslrSmuSIhRiN4depSQp7wH2XCFBGViACwQF/MRc/yY2UWSrpb0xeSucyX9H3ffWWzRjrdhwwbfs2dP2R8LoCbyHPTXmwMttQNyTvIgsa1VGYOD0WFme919Q9/HRgXQyRuslnRe8uct7n5fjuVLjQAaQEzq3NCO+m51/u6Tyjvg3bh9V9/0o7nZGe3etmmismIlTlbQbVgAPWwWjk3uvsvMLu156GFmJne/NtdSAkDF1DXndtQMI8xAMlzeM76Qb18epk9FWsNyoJ+S/HtJn9szCy4XACCQUTOMMAPJcHkHvOTbl4eTFaQ1bBaOy5N/X1hecQAAoY0KIggyhst7xhdmJCoPC/IgrZGzcJjZS83s/tb2FjP7nJk9o4zCAQDKN6rHkx7R4fKe8aXIGYmY3WMllsRGWiOX8pb0Inf/UzPbLOkBkl4o6W2SPlpoyQDUBgPOqmVUjyc9osMVsaxyHvn2vfvh085bo/ftbZHL3oUlsZFWmmnsPu/ujzGzP5V0g7u/38wW3H19OUU8hlk4gOroNNatxSWZpO4jDaPa48csHPXSb3aJ3v2yg9k9gLaJprEzs7dJmpO0VtJjJU2pHUhfmHdBRyGAbgYa5urr11j3opEGyjNoKrx+TNKt2y8utkBABYw1jV2XX5J0gaQvuvu9ZvZ9aqdxALljeqx66DdLQy8GnAHlybK/kcsOjJZmKW+X9EhJv578fbKkEwsrERqN6bHqIU1jTSMNlGfQ/mY9f5PLDqSTJoB+o6QnS/qZ5O9vS/qLwkqERmN6rHoYFRzTSBeLmRXQa9DsEi940jmFzO4B1F2aFI4nuvvjzGxBktz9bjO7X8HlQkPVcQ7OJuZ095uloTNgaa4hdRAKaVDoh9klgHylCaCXzWxKyWBdM1sj6UgeH25mb1V7VcOvufuj8nhPVFvdpsdqajBDYz1aUSdWLEWMQeq69DwQQpoA+s8kvV/SA8zstZKeK+lVOX3+30i6StLbc3o/VFzdAq8mBzM01oMVeWJFGlQ6oa8Mhf58AJMZGUC7+zvNbK+kH1X7KuwWd/9CHh/u7p8ys3PzeC/UR50CL4IZ9FPkiVUd06DyFvrKUOjPBzC5NIMI5e63uPtfuPtVkr5iZr9TcLmOMrMXm9keM9tz8ODBsj4WyAVLHqOfNCdW4w4ErMtSxEUOhAw920/ozwcwuYEBtJmdbWZXm9mHzOyXzewkM/tjSf+p9pLepXD3q919g7tvWLNmTVkfC+SiLsEM8jXqxKrTQ9laXJLrWA9lmiByy/o5XXnpoys9s8Ik3z+N0FeGQn8+EFJdZgkalsLxdkmflPQ+SRdJulHSfkmPcfevllA2oPLqktNNvma+Rg2WnTTFo+ppUEWPHQid5hL685uC41Z86pS+NCyAPsPdr0j+v9PM/kfS4939vuKLBVTPoIN11YOZOh3wYjHqxGrQkstN6aEsuoc29Gw/oT+/Cap43GpCwF+ngfVDBxGa2ek6tlDRVyWdZGYnS5K73zXph5vZuyQ9VdKZZnaHpMvd/a8nfV+gbEUerEMfVOt0wIvJoBOr+YXW0TmzezWlh7LoHtrQV4ZCf34TVO24VcWAfxx1Sl8aFkCfJmmvVq70+bnkX5f00Ek/3N1/ZvSzMI7QQVfTFHWwjuGgWqcDXhXs2Hmgb/BsUmN6KMvooQ19ZSj059dd1Y5bVQv4x1Wn9KWBAbS7n1tiOSqhKkFpDEFX0xR1sI7hoFqnA14VDNpmXNXff9MeQ+mhxaSqdtwqM+APGcvUKX0pzUIqULWC0hiCrrLEclJT1ME6hl6UOh3wqmDQtjQXacOfVtZjKD20mETVjltlBfyhY5k6nRynmgca1Zq3M4agqwxFT3WVRVHT1cUwj3QdpkWrktinPhx3CqoqHUNRfVU7bpW138ewH25ZP6fd2zbp1u0Xa/e2TdH+JqPQA51SlYLSql26GrcXOW1Pexm91EWdVcfSi5K1NzCWKwNFKuo7xtxDM0nvVZWOoaiHKl3FKGu/Zz/MT6oA2symJD2w+/nufltRhYpRlYLSWIKuNPo1yC+/Zp9eds0+zY04gKRdzS1Lgz9JUFTEwTrmYGqQ0JcIy1D0d4y14Z8kPaxKx1AghDL2e/bD/IxM4TCzX5P0P5I+Jun65PahgssVndgvq3ar0qWrfg1yZwaCUSkZadIbBjX4r/ng/uNeF1NKSLeqXe6K4RJh0ZrwHfuZpPeqSsdQoK7YD/OTpgf6pZLWufs3ii5MzKrWExhrD1avUQ3vsN6tND3tg97/7nuXNb/QWvG+TRp8WaQmXCJswnfsZ5Leq6odQ4E6Yj/MT5oA+nZJ3yy6IFVQlaC0SgY1yN0GBSVpDgTD3r83MG5qUJS3JlwibMJ37GfS9LBYjqFVyNGvQhlRTbHsh1WXJoD+oqQbzOx6SUeX8Xb31xdWKjRGvwa517CgZNSBYOvmdXrZNfv6PtYbGDc1KMrbsCCrDkHB/EJL937v0HH3N+EyaB16r6qQo1+FMgJNlyaAvi253S+5AbnpbpBbi0vHLWGcJSgZFJxdcd1+LS4tH/f83sC4SoMvYzYoyJJU+aCgN7DpMK3MgY7l+xRxwlL13quyU7XG+Q2qmk5WhxNkIK2RAbS7v0aSzOzU9p9+T+GlQqN0N8jjHoCH9dhc8azzUwXGMfWuVb0h6hdkbdy+q5JBQbd+gY10/MBXKXwQTS9mf2Wv+DbOb1DFdDK2NzTNyADazB4l6e8knZH8/XVJP+/ux09jAExo3N6tYT02u7dtOvqcNEsIhz7Y17UhqmJQ0CtNWWM5KahqL2bRykzVGvc3qGI6GdsbmiZNCsfVkn7D3T8hSWb2VEl/JemHCiwXSpRXb2fIXtNRwVkMgXFadW2IqhgU9Eoz6FWK46SgDicsRSgzVWvc36CK6WSxbG9Vv3qH6kizlPfJneBZktz9BkknF1YilCqvuY9Dz6E8yZLX4y5NXJRYGqK81WH+0X7foZ8YTgryWgY+tv1jXJ3v8fJr9mn1Cat0+knThc+TP+5vUKW5/Dvy2t4mEbodQrOkCaC/aGavNrNzk9urJN1adMFQjrwWhAi9sMS4wVmMB9wYGqIiVDEo6NX7HU4/aVrTq2zFc2I5KcjjhCXG/WMcvd9jcWlZ310+ojc874JCFyea5Deo2gJKMZwgh26H0CxpUjheJOk1kq5Ve7D5JyW9sMhCoTx59XaG7jUddwBgjOkSVbx8m1aVUmkG6f0OsV4yzmNQbIj9o4j6DLWfxzQwuWgxfNfQ7RCaJc0sHHdL+nVJMrMptVM6vlV0wVCOvPJSY8hvHSc4i/GAG0NDhPRiPimYtGxl7x9FDaANuZ/HvH3kLfR3jaEdQnOMTOEws783s/ub2cmS9ks6YGZbiy8aypDXZbcYLt+NI9Z0iapdvkU9lb1/FHUJPtb9HPmqajuEakqTA/3IpMd5i6QPSzpH0s8VWiqUJq+81Krmtzb1gFuXgWEoVtn7R1E9xU3dz5umqu0QqtkmpcmBnjazabUD6KvcfdnMfNSLUB15XXYLcflu0nzJJqZL1HWe6boKmWNd9v5R1CX4Ju7nTRU6jQTZVbVNMvfhsbCZ/ZqkbZJuknSx2j3Q73D3Hy6+eCtt2LDB9+zZU/bHIlL9llWemZ6qdI9DGcHSxu27+gYpc7MzRxedqbNYB/31U+Q2HmM91HGfBjBczG2Sme119w39HhvaA21mqyT9j7vPdd13m6Sn5VtEILsYZ9CYRFln4TEOnCxL1Xo6itrGY60HeoqRRYwngciuqm3S0ADa3Y+Y2a9Kek/XfTL6aTwAACAASURBVC7pUNEFA0ap6k43SFknBE0eqV50HefdoBe1jcd88lnkJXgCrvqI9SQQ2VW1TUoziPBjZvZKMzvbzM7o3AovGTBC3UbWl3VC0OQBVUXWcRGLjhS1jaethyoO7BmkLovCoI1FU+qjqm1SmgD6RZJ+RdKnJO1NbiQiI7iq7nSDlHVC0OSR6kXWcZ4NeidwbS0uyXoey2MbT1MPdQs4CbjqpW5XIJusqm1SmoVU1pZRECCruuVLlrkCYd1Hqg+6VF9kHefVoPdemna1l4B1tRuWPLbxNPUQc5rHOAi46qWql/3RXxXbpDTT2MnMHiXpkZJO7Nzn7m8vqlBAWlXb6YblYIY+IahLfmia3MgivmdeDXq/wLUTPHePSJ/k90pTD3ULOAm46qXMDgegn5EBtJldLumpagfQH5b045I+I4kAGsggTWAX6oSgTgNyRvWcFlXHeTXoaQLXPH6vYfUwv9DSKjMd7jPNaVUDTgKuegnd4QCk6YF+rqTHSlpw9xea2QMlvaXYYgH1E/Ml8ZjLllXZPafdPcGzJ01r9Qmr9M2l5bEb9DQ9pUX+Xp3gvF/wLElPO2/NRO8fCgFX/VTtCiTqJU0AvZRMZ3fIzO4v6WuSHlpwuYDaifmSeMxly6rMS/W9PcF337usmekpveF5F4zdsKfpKS3y9+oXnHf7xC0HM79nLOlBBFwA8pJmFo49ZjYr6a/UnoHjc5L+rdBSATUU87R7MZctqzJnZyliZoc0I9In/b2GTU83Kggfd1BkXWbzAFCcKk2dmWYWjv+b/PdNZvaPku7v7p8vtlhA/cScgxlz2bIq81J9UT3Bo3pKJ/m9RuVPD+rB78hjUGRV04MwWCxXGYpS9+8Xg6qNxUkziNAkvUDSQ93998zsHDN7grvTCw1kEHMOZsxlSytEAzdOukge5ez3ez3tvDXasfOAXn7NvqHve8V1+4cGtP2C846iBkWiHEXtI1ULfLKq+/eLRdVOttPkQL9R0hFJmyT9nqRvS3qfpMcXWC6glmLOwYy5bKOEauCy9gTnWc7u3yvt+84vtLS4tNz3/ToBbXdw3lpc0lQyG0faOah7g7TZk6Z1973Hf2bvSQY9fMUqch+pWuCTVd2/XyyqdrKdJoB+ors/zswWJMnd7zaz+xVcLgBILVQDl7Xnvqhypn3fYbnZ3QHtOCdT8wstveaD+1cEy63FJU2vMk1PmZYPH5vVo/ckgx6+4hW5j1Qt8Mmq7t8vFlWbqz1NAL1sZlNqz+UvM1ujdo80ao4eIVTB/EJrYM5uGQ1clmCzqIY47fsO+5xJ8t17A+Buy0dcszPTOnn1CQOPJfTwFa/IILBqgU+vUW1d1b9fVVRtLE6aAPrPJL1f0gPM7LVqzwv9qkJLheDoERqME4t4dLbTQWJr4IpqiNO+76DnnX7SdO494N2+ubSsfZc/Y+DjaRePYb8bX5FBYNUCn25p2roqf78qqdpYnJHT2Ln7OyX9pqQrJX1F0hZ3f2/RBUNYRUzPVQdMyRWXUYHbd+47FNVvU9QUe2nfd9DzLr/k/Ik+f1Qv5qggbdS0fOx3kytyesc0Uy/GKk1bV+XvVzVb1s9p97ZNunX7xdq9bVPUdTywB9rMTpT0EkkPl3SzpDe7+6GyCoawyPnqj0vNcRm1PS4uLUd15aSoHpa071vU5w+b+i5NkDaqh4/9bnJF9+5VdRBy2rauqt8PxRmWwvG3kpYlfVrSj0t6hKSXlVEohEfOV3+cWBwTwyX1UXMWS/EFWkU1xGnft4jPHzT13ezMtK541vkjP29UcFen/S7kfkMQeDzaOoxrWAD9SHd/tCSZ2V+L1QcbhZyv/qp6sM270Y4lR37YnMXdBgVaWeolhhOGWOXRuzksuKvqftcrlv0Gx9DWYVzDAuijcxG5+6H2eipoiqol85eligfbIhrtWC6p926nq5I5i3udNjN93H1Z6qWowCfGoHzcMhXZu1nF/a6fWPabbjFug2WircO4zPs0NpJkZoclfafzp6QZSfcm/3d3v38pJeyyYcMG37NnT9kfiwZJ05hUrcHZuH1X3967udkZ7d62aaz3XLvtevU7cpikW7dfPNZ75mF+oaWt771Jy0dWlm56yrTjuY9d8TtlqZci6rDf1G8z01NBByfFWKaOqu13/cS238T8ewMxMLO97r6h32MDe6DdfWrQY0Ad9DbITztvjd63tzWyl7FqeYRF5I/Gekl9y/q54xbzkKTlw35cL1+WeimiDmPsjYyxTB1V2+/6iW2/KfL3rsMJDzDMyGnsgDrqNy3WO2+8rZZT942aImwcRU6JNanFPstGS8cHu1nqJctz5xda2rh9l9Zuu14bt+8aONVajAPjYizTpNL+HmWIbb8p6vdm2kE0AQE0Gqlfz0v/ZKZqBw9SMY12zPOipg12s9RL2udmCRyKOLGZVIxlmkRsgVxs+01RvzfrCKAJ0qxECEQva+7yoGC5n6oGDx2jBsnEOGhsEmkHnGUZPJT2uVkuiU8yMK6oy+N1GazXEWNKSkz7TVG/dx2vZAC9CKBReWlmSOg3WKYf08qe6NiCh7yD3TpOq7Vl/Zz2fPkuvetfb9dhd02Z6Scv7P/9swQzaZ6bJXAYd/R/Xr/ZsG2pLrmrBHLDlb2wTtU7I4BuBNCovDS9TKOWfJbawfJPXjinT9xyMMrgoc7T0eVpfqGl9+1tHZ3O7rC73re3pQ0POaPw75Q1cBinNzKP32zUtlTV374XgdxoZS2sE1tnBDCpoAG0mV0k6U8lTUl6i7tvD1keVFOaXqZhPU4mRRcsd+v0FPYLBCYNduvYQxfypKCMwCGP3yxLHcU2m0KW8sQayMVWp3mr25UMoJ9gAbSZTUn6C0k/JukOSZ81s+vc/T9ClQnVlKaXadBzss7jW3bDlyb1pI7T0U0i5ElBGYFDHr9Z2jrK86pHHvtOv/K87Jp9es0H9+vyS45fMjzGQK6OaVP91OlKBtrqfuKX1cCFVAr/YLMnS7rC3Tcnf18mSe5+5aDXnHrqqX7hhReWVEJUxdfvuU9fPPgdHenalleZ6aFrTtaZp6xO/Zw8PidvC7ct6r5Dw1NPVp8wpfXnzI71/iG+U9EG1dkk9dTt6/fcp9vvWtJ9hw5r9QlTOvuMmVLrKo/fLG0d5VWXeW1nw/aHqmy3RW+fKE/oY0GZ6thWpPHJT34y+0IqJZiTdHvX33dIemLvk8zsxZJeLEmrV9f3R8L4OjvvsANZmueMcvtdSysOHpJ0xF2337VU2AFkVPAsSWefMX5vcR71Epuzz5jpe6CfpJ46ehuR+w4d1hcPthdsLavO8vjN0tbRoO0vzXbZLa99Z9jn9nu/GAOcvOq06mL8bbKI4VhQphDtX+xCBtDW577jusPd/WpJV0vtpbxvuOGGgosF9DdsGd4bClqGd9AS0h2nnzSthd99RiGfXWVFXWrcuH2XHtDn9zhtdkY3jLmkdyjD6qjz2IMGbHtzGb9vXvvOqP2h+/1eNX+z3nnjbTq96/HD01N6WeD5yoctC1+1bWhcnTSW07tS02L4bbKo07EgjRDtXwzM+oWqbSED6Dsknd3194Ml3RmoLChYmsY69ryqEPnC/QZBdcxMT+nyS84v7LOrrKj8yzoNukw7tWGvcQbh5bXvDNsfut9vfqGld95423ENfgwzzMQ6sLFMdZj9p07HgjTqOF5mUiED6M9K+gEzWyupJen5kn42YHlQkGGDZiSVMqAmjyA9RMPXPQiqtbikKTMddtdcxCcaoZRxIhaiESn7BHPYlI/jbnd57Tudz73iuv1aXFq5ZHv3++3YeSDalUVjHNhYhGHbbR2Cz6YFlJz4HS9YAO3uh8zsVyXtVHsau7e6+/5Q5SlDVXpa8zZqWdeieyLyGvU+ScM3yW/PaPbRyprZoOxGJMSMDYOCGJMyzVjTLc+gsbM/jBOgSXEEOGXs0yHbm1HbbR2Cz6edt0bvuPG2vvfXUVNO/LIIOg+0u39Y0odDlqEsTZm6qJ9xehvy7InI83LhOA1fk3/7spR1SbjsRiTEpe6igpu8g8Zh7zfoO5jUiB6z0MecUdttHXozP3HLwUz31wGdOSuxEmFJ6pDzNa5RDXLRPRGhLxcO+u1f8Z6b9PJr9nEmn4Ms8xpPGvyW2YiE2HbrENz0+w4m6QVPOqfy+1mabTh0ezNqu61Db2bodgXhEUCXpMk726gGuejGOvTlwkG/cWepaXqkJ5fmNw7dKzeOSbbdcU8W6hDcFP0dQqVHpN2GQ7c3abbbqvdmhm5XEN6q0AVoikE7VRN2ti3r53TlpY/W3OyMTO2BSFcm0xUNeywvWzev08z01Ir7yuxRS/Mbd+eEI7t+v7Ekfee+Q5pfaEkanYsfo3G33U6g1VpckutYoNWpi1G2rJ/T7m2bdOv2i7V726ZKBjpFfYdJ63YSabfh0O1N6GNuGZrwHTEcPdAlqcNl0UkM620ouicidI/aqKm3OppwNaIond/yNR/cr7vvPTY7w+LS8tEeukH121pc0tpt10fZ0zrutjvJJfymDnZOK2R6RNqe5dDtTehjbhma8B0xHAF0SdjZwugNBt7wvAtKr/Pe335VMhVdryZcjSjSlvVz2rHzwIoAWjoW3Ay65CppRU9i571iMc4J5riX8KuY5jJKHicE3e8Rcnq8tGkDMbQ3VU/RSKMJ3xGDEUCXiJ2tXDEFA92/fb+FKtJels+7QUz7nlk/O1Qv5rDA8Q3Pu2DklYC6DOwdNz8z9OCzvOVxDBi1sExHGSfAWXqWaW+AYpEDjWjML7S0cfsurd12vTZu3zVxTmGsOa/j5H0XkXeZ9j2zfnbIHNFhuZ+99T5IHVJpxs3PDD34LG95HAOGLSzTUVZ6RBljRgCkQw80olBEb3GdgoEiegbTvmfWzw7Zizmqh667V27j9l21HUU/7iX8us0sMOwYkPYqybDjhUmlp0fQswzEgQAaUSgi6Io1GBjnZKGIk4G075n1s0OeuGQJHEMPtCraOIFW3epk0DHgtJnp1PvgoPeYm50Ze2VGANVHCgeiUETQFes0Q+NcVi5iWqq075n1s0NPoZV2+jIuhx8vljrJK51r0DHATKn3wRiPI3mnuwHIjh5oRGGc3uJRl2DzGome94C4cU4WiugZTPueWT57fqGle7936Lj7Qwccg3A5/Hih6yTPdK5Bx4CXX7Ov7/O798Hu/f60mWmdOL1Ki/cuB59BKabB0UCTEUCjMFkCz6wBYtpGZNJgoIjGapyThSKmpUr7nmmfN2i2gtmZaV3xrPNp3LsUPUtJledyzjudq98xYMfOA0P3wd5teXFpWTPTU0GmwexVt5lSgKoigMbE+jXWkjIFnlkDxLIakSI+Z9ze5CJ6BtO+Z5rnDZqt4OTVJ9Cwdym6B7HqPZRl5NCP2gdjDlLrNDgaqDICaExkUGN94vSqzA1QlgCxrEakiM8ZdLIgtWeGqGKvoTR8pb/5hValvkuRig7OYg7+0ihj8O+oE/aYg9RYB0cDTUMAjYkMaqwHzZuaVwNUViNS1Of0nixUvddQGlxXkgr5LlVNUyg6OIs5+EujrJlAhp2wxxyk1m2mFKCqmIWjAYocsZ21Uc6rASprZHxZnxProi9Z9Kurjry/S8jFWiZV9CwloWdBmVQMM4HEOPNGRwz1UwRmFkHV0ANdc0X3bA7qqZmdmdZ9h44U1ktSxKC6kJ9T9V5D6VhdvSzFDAeTqnKawrAexDx61Uf1UFah5z70TCBl7ffjCl0/eavDFTg0DwF0zRUdaAxqrK941vlHPz/PBihE419GY1X2JeOi6nHL+rmRMxzkoconHMNy4IcFEWl/s2HBH4FKev3SrKo8RiFmVT4hRnMRQNfcsIFdeRjVU5PXrAKdoMwkeXJ/nRr/MvMaiw6i8vouwwLGmHNU0+h3UrZx+66haTxZZ7Xpd3+TApU8TxI58ShWlU+I0VzkQNfcoIDCpNxyzNKu/DaO7lxX6Vjw3FG1POFBysxrLDrfOo/vMirHOeYc1XENCyLy+s2aEqjknSNfhzEKMat63j6aiR7omuusutUbeLpUiV6nQXMLd6tL419WXmMZQdSk32VUT2nsOarjGNarntdvVrWe+3F7kfPuaW/KiUcozCyCKiKArrkt6+dKGdRVlDRljLXx74ht0FYVgqg0AUueJxwx/EbDgoi88srzCFTKqqtJ0ibyDnirsM9UWR1PiFF/BNANMFfhg/+wuYWl+HspQuZODgp0qtDbU2bAEkt+66ggIo/fbNJApcy6mqQXOe/tpwr7TNXVbWYR1B8BdI1UOWAapF/ZOwMJ5yrQSxFq0FaaQCfm3p4yt9mYBtYNCiJGzayR5becJFAps64m6UXOe6rAKuwzAMpFAF0TZQZM8wstveaD+3X3vcuS2nM+X/Gs8wtpTKrecIXKnUyTQxxzHZb5u1clv7Xfb5a2RzivtIsy62qSXuRxpwoc9Z4x7zMAykUAXRNlBUzzCy1t/YebtHz42LDExaVlbX3vTZKKueRd5YYrVO5kVYLCYcb93bMGi0X/RkXmDKfpEc4z7aLM7XnSqxBZpwqs6jEGQBhMY1cTZQVMO3YeWBE8dywfcaZ06iPUdGtNnRZqnOnLivyNil5yPM1+n+cUbGVuz0VM7Tiqvpq2nHTTvi+QJ3qga6KsnqFhAXmVejfLEioFpcp575MYJ0e3yN+o6JzhNPt9nifXZW/PeV99GlZfRQ+QjGGml97yxDB4FqgqAuiaKCtgGjYrRt17N8cVIgWl6rnj4xo3WCzqNyriylB3IDZ70rSmV5mWjxy7KtS73+d9cl3llKpRUwUWdbITY7Aa0+BZoIoIoGuirIBp6+Z1x+VAS9L0Kqt972bVVDnQGaZKS3znXZ7eQOzue5c1PWWanZnWN5eW++73Tb0a0c+w4+TLC5wvP8ZgtQ7jJICQCKBrpIyAqfP+Zc3CAXQb1ZMXW7CYd3n6BWLLh10nrz5B+y5/Rt/XxHY1InQqw6DjZJEnXzEGq7GdbAJVQwCNzOras4n4VW2J77zLU0SKSpkBbYypDB1FnnzFGKzGdrIJVA0BdIOF7glCuerwe5e9xHce8ixP0SkheQa0/ba3GFMZOoo8+YoxWI3tZBOoGgLohoq5Jwj5i+H3ziOAj7Enr0xlpITkEdAO2t56P6sjlrzbok6+Yg1WYzvZBKqEALqhYu4JQv5C/955BfAx9uSNkmfPfywpIaMM2t6mzHTYj59HPs8ToFivtBCsAvVCAN1QMQ5qQXHy/r3nF1q64rr9WlxqDyQ9/aRpXX7J4IGkeQXwsfbkDVJEz3/MKSEdg7arw+6amZ4q7AQohistAJqBlQgbqqkr1TVVnr/3/EJLW99709HgWWpPp7b1H24auJJZ3ot57N62Sbduv1i7t22KOjAadOLwivfcFMXqb0WtLDhou+qsJpjn6oLd8lx1EQCGoQe6oYZdCo/1Eug4yvousddZnqkPO3YeWLFwR8fyYR/Yo9zU3OVhPbFS+B7Sonr0h21vRaYycGUNeYr9uI6wCKAbalDDKak2l0DLupxbhcvGaQOlNA3GOMu5TxLAV7kRG7ZyZ0fosQdFBLShUm2qeKJW5e27zqpwXEdY5n0GdMRqw4YNvmfPntDFqLWN23f1bYDmZme0e9umACUaX1nfpS511ttgSO0gt/cS+6DvKw3/zuMECmnLFKt+5e/HJN26/eJyClVj/erbJLna22ZswWnVt+86q8txHZMxs73uvqHfY/RAY4U6XQIt67vUpc7SDvTbunmdtr73puPSOKanhi/nPk5PZ+jZQybV2xO7qoRZKGJUVi9rd323FpeOBs9SnD2IVd++66wux3UUhwAaK1TxEuggZX2XutRZ2gaj07CnmYVj0sCpDo1Y94nDoB7HUNPwlRHYln0pvFPf/XoQYwtO67B911VdjusoDrNwYIWiRuWHUNZ3qUudZZmpY8v6Oe27/Bn60vaL9aXtF2vhd5/RN3i+7Nqb1VpckutY4JRl1om6zRazZf1cobNQZJHH75NGqJkx0gSn8wstbdy+K9iMKHXbvuukLsd1FIceaKxQtXl2hynru1Slzkb1Nsa4yt04ZYp9UFYsC2qUlT4Qqpd1VA9i1p7xIrarKi4M1BRVOa4jHAJoHCeWBj4PZX2X2OssTbAQ4yp3WcvEyPn0ygpsQ1wKn19o6d7vHTru/u7gNMsJRFHbVZlBWuwnljGK/biOsAiggQZIGyzk1WDML7RyGzCXpUwMykqvrMC27F7WQTOfzM5M64pnHcvTz3ICUeR2VUaQxoklkD9yoIEGKPMyeqex7hc8F315OrZBWXnk2BaVp1tWjmfZed/9gl1JOnn1CSs+M0v+cWzbVVas0Ajkjx5ooAHKvIw+KICZMit8wFxMI+fz6PUrsuewzPSBMi+Fpw12s/SMx7RdjaPqJwBAjOiBBhqgzBHlgxrlI+6FB1ExjZzPo9ev6J7DLevntHvbJt26/WLt3rapFpfz0/YsZ+kZj2m7GgezfQD5C9IDbWY/JekKSY+Q9AR3Z3lBoEBl9jaG7K2LaeR8Hr1+9Bwek3YQXJae5bQ94zFtV+Ngtg8gf6FSOP5d0qWS3hzo84HGKesyeujGOpaR83mcSFQ9dSAvWVJZigp2Y9muxlH1EwAgRkECaHf/giSZWYiPB1Cg0I11LNN15XEiEfpkpFeous06C0aVg92iUCdAvqIfRGhmL5b0Ykk655xzApcGQBqhGuuYpuvK40Qi9MlIt5B1SyoLgNgUFkCb2cclPajPQ7/j7h9I+z7ufrWkqyVpw4YNx8+LBWCkWHplixbbPNB5nEjE0nMYsm5JZQEQm8ICaHd/elHvDSC9mHpli0ZPZX+TnEB1XtsvgJXKqdvYUlkAgGnsgJpr0iIKTNd1vM4JVGtxSa5jJ1BpFmTpfu0gZc2uUuZiLAAwSqhp7J4j6c8lrZF0vZntc/fNIcqC/ppyyb8MoeuySb2y9FQeb5LUi0GL4nQ0cXYV5Cf0sRGYRKhZON4v6f0hPhujNemSf9FiqMsm5Y/GNOguFpOcQA17zhx12wiTBrmDXh/DsRGYRPSzcKB8sQ3EqrIY6rJpvbJV76nMu1dukhOoQa+dMiN4boBJg9xhr4/h2AhMghzoGptfaGnj9l1au+16bdy+K1XOo9SsS/5Fi6EuyR+tjknylQeZZBnqfq+VpMPuE5cL8Zt0/MSw18dwbAQmQQ90TU3Sc9CkS/5Fi6Uuq94r2xRF9MpNktbSec4r3nOTDvvKWUTz6i0kDzZekwa5w14fy7ERGBc90DU1Sc/BJD1WWGnr5nWaXrVyxc3pVUZdoq+ieuW2rJ/T7m2bdOv2i7V726bMi7kc8f5T8E9ariJ63JGfSWe1GfZ62hlUHQF0TU3SEHPJP2e9K9azgj0GiHUavqLK1aQpFqto0iB32OtpZ1B1pHDU1KSXx7jkn48dOw9o+fDK3rvlw85AGfQV64DPccqVJjWDPNi4TTqrzajX0840U13StgigayrWhrhpCBCQRazT8GUtV9oxGOTBxm/SIJcgGd3qNH0hAXRNxdoQNw0BArKKNeDIUq60gyE50QeapU7TFxJA11isDXGTxBQg1OWyGcJJuw2lvfLCiT7QLHW6KksADRQolgChTpfNytTEk448Vo7LcuWFE32gOep0VZYAGihYDAFCnS6blaWJJx15rRwX05UXAPGo07GBABpogDpdNitLE0868lo5LpYrL5No4tUHoGh1ODZ0EEADDVCny2ZlaeJJR54rx8Vw5WVcIa4+ELCjKap8bOjGQipAA7DqV3axLmpSJFaOayt7gRdWZASqhwAaaIAsq37NL7S0cfsurd12vTZu39XYRrxJAWMHK8e1lX31gRUZgeohhQNoiDSXzZo4cG6QOuXqpcXKcW1lpzw1MV0IqDoCaABHNXHg3DCxBIxl5sfG8p1DKnumAMYoANVDCgeAo+gJiw/5seUrO12lielCQNXRAw3gKHrC4sNVgTDK7IlvYroQUHUE0ACOqtMk93XBVYFmIHUGqBYCaKAiysiDpScsPlwVAID4EEADFVDm7Bj0hMWFqwIAEB8GEQIVwDyxzdWk+ZcBoCrogQYqgDzYZuOqQPnGSZliOW6gOQiggQqIKQ+WIKEYVajXKpQxD+OkTLEIEdAspHAAFRDLPLHMSVyMKtRrFcqYl3FSpkizApqFABqogFjyYKscJMwvtLRx+y6t3Xa9Nm7fFVXgV4V6rUIZ8zJOyhRpVkCzkMIBVEQMebBVDRJiv7xehXqtQhnzMk7K1KDXrDLT2m3X1zrlBWgieqABpDYogIh9TuIrrtsfde9pFeq1CmXMyzgpU/1eI0mH3Wuf8gI0EQE0gJE66Q+txSVZz2Oxz0k8v9DS4tJy38di6T2NJcd9mCqUMS/jpEz1vmbKeveUuE7aAEyGFA4AQ/WmP7gkS/6dq8Bl6WEBSyy9p1VYAbIKZczTOClT3a9Zu+36vs+J5aQNwGQIoAEM1W/wWCd43r1tU5hCZTAsYImp9zSGHPdRqlDGWMQ09SSA/JHCAWCoqg8eGxSwnH7SNMEgCtOklBegiQigAQxV9cFjgwKZyy85P1CJ0ASxTD0JoBikcAAYaH6hpe/cd+i4+6vUk9a03F3Eg5QXoL4IoAH01Tt4sOP0k6Z1+SXnVyowIJABVmrKsuxAUQiggQops9HrN3hQkk663wk0tECFxb6wEFAFBNBARZTd6FV98CDKR69mNQxblp3fC0iHQYRARQxr9IpQ9cGDKFfnBK+1uMTKe5Hj5BiYHAE0UBFlN3pMw4Usyj7Bw/g4OQYmRwANVETZjR7TcCELejWrg5NjYHLkQAMVsXXzuuNmxSi60WP2CqTFynvVwdSOwOQIoIGKoNHLH4Pe8hPiBA/j4+QYmAwBNFAhNHr5YSqvfHGCB6BJCKABNBJTeeWPEzwATcEgQgCNxKA3A7hZygAADBdJREFUAMC4CKABNBJTeQEAxkUADaCRmMoLADAucqABNBKD3gAA4woSQJvZDkmXSPqepP+W9EJ3XwxRFgDNxaA3AMA4QqVwfEzSo9z9MZL+U9JlgcoBAIWZX2hp4/ZdWrvtem3cvkvzC63QRQIA5CBIAO3uH3X3Q8mfN0p6cIhyAEBROvNMtxaX5Do2zzRBNABUXwyDCF8k6SODHjSzF5vZHjPbc/DgwRKLBQDjGzbPNACg2grLgTazj0t6UJ+HfsfdP5A853ckHZL0zkHv4+5XS7pakjZs2OAFFBUAcsc80wBQX4UF0O7+9GGPm9kvSHqmpB91dwJjALVy1uyMWn2CZeaZBoDqC5LCYWYXSfotSc9y93tDlAEAisQ80wBQX6Hmgb5K0mpJHzMzSbrR3V8SqCwAkDvmmQaA+goSQLv7w0N8LgCUiXmmAaCeYpiFAwAAAKgMAmgAAAAgg1A50AAAVN78Qos8d6CBCKABABhDZ7XJzoI5ndUmJRFEAzVHCgcAAGNgtUmguQigAQAYA6tNAs1FAA0AwBgGrSrJapNA/RFAAwAwBlabBJqLQYQAAIyB1SaB5iKABgBgTKw2CTQTKRwAAABABgTQAAAAQAYE0AAAAEAGBNAAAABABgwiBAAAuZtfaDFDCWqLABoAxkSAAPQ3v9DSZdfefHSp89biki679mZJYh9BLZDCAQBj6AQIrcUluY4FCPMLrdBFA4LbsfPA0eC5Y2n5sHbsPBCoREC+CKABYAwECMBgdy4uZbofqBpSOIAxcOkeBAjAYGfNzqjVZ184a3YmQGmA/NEDDWTEpXtIgwMBAgRA2rp5nWamp1bcNzM9pa2b1wUqEZAvAmggIy7dQyJAAIbZsn5OV176aM3Nzsgkzc3O6MpLH82VOtQGKRxARly6h3RsJgFSeYD+tqyfY39AbRFAAxmR24cOAgQAaCZSOICMuHQPAECz0QMNZMSlewAAmo0AGhgDl+4BAGguUjgAAACADAigAQAAgAwIoAEAAIAMCKABAACADAigAQAAgAwIoAEAAIAMCKABAACADAigAQAAgAwIoAEAAIAMCKABAACADAigAQAAgAwIoAEAAIAMCKABAACADAigAQAAgAwIoAEAAIAMzN1DlyE1Mzso6cuhy9HlTElfD12ICqLexkfdjYd6Gw/1Nh7qbXzU3Xiot/GMqreHuPuafg9UKoCOjZntcfcNoctRNdTb+Ki78VBv46HexkO9jY+6Gw/1Np5J6o0UDgAAACADAmgAAAAgAwLoyVwdugAVRb2Nj7obD/U2HuptPNTb+Ki78VBv4xm73siBBgAAADKgBxoAAADIgAA6BTO7yMwOmNl/mdm2Po+fZ2b/Ymb3mdkrQ5QxRinq7QVm9vnk9s9m9tgQ5YxNinp7dlJn+8xsj5n9rxDljM2oeut63uPN7LCZPbfM8sUsxTb3VDP7ZrLN7TOz3w1Rztik2eaSuttnZvvN7JNllzFGKba3rV3b2r8n++sZIcoakxT1dpqZfdDMbkq2txeGKGeMUtTd6Wb2/qRt/Tcze9TIN3V3bkNukqYk/bekh0q6n6SbJD2y5zkPkPR4Sa+V9MrQZY7hlrLefkjS6cn/f1zSv4Yud+hbyno7RcfSrx4j6ZbQ5Q59S1NvXc/bJenDkp4butwx3FJuc0+V9KHQZY3plrLeZiX9h6Rzkr8fELrcoW9p99Wu518iaVfocoe+pdzeflvS65L/r5F0l6T7hS576FvKutsh6fLk/+dJ+qdR70sP9GhPkPRf7v5Fd/+epHdLenb3E9z9a+7+WUnLIQoYqTT19s/ufnfy542SHlxyGWOUpt7u8WQvl3SyJAYypKi3xK9Jep+kr5VZuMilrTuslKbeflbSte5+m9RuK0ouY4yybm8/I+ldpZQsbmnqzSWdamamdkfLXZIOlVvMKKWpu0dK+idJcvdbJJ1rZg8c9qYE0KPNSbq96+87kvswXNZ6+yVJHym0RNWQqt7M7Dlmdouk6yW9qKSyxWxkvZnZnKTnSHpTieWqgrT76pOTS8MfMbPzyyla1NLU2w9KOt3MbjCzvWb286WVLl6p2wYzO0nSRWqf9DZdmnq7StIjJN0p6WZJL3X3I+UUL2pp6u4mSZdKkpk9QdJDNKJTjwB6NOtzHz1+o6WuNzN7mtoB9G8VWqJqSFVv7v5+dz9P0hZJv194qeKXpt7+RNJvufvhEspTJWnq7nNqL2n7WEl/Lmm+8FLFL029nSDpQkkXS9os6dVm9oNFFyxyWdrUSyTtdve7CixPVaSpt82S9kk6S9IFkq4ys/sXXbAKSFN329U+2d2n9pXKBY3ovT8hn7LV2h2Szu76+8Fqn91huFT1ZmaPkfQWST/u7t8oqWwxy7S9ufunzOxhZnamu3+98NLFK029bZD07vbVTZ0p6SfM7JC7Nz0YHFl37v6trv9/2MzeyDaXapu7Q9LX3f07kr5jZp+S9FhJ/1lOEaOU5Rj3fJG+0ZGm3l4oaXuS4vdfZnar2vm8/1ZOEaOV9hj3QklKUmBuTW4D0QM92mcl/YCZrTWz+6m9Q18XuExVMLLezOwcSddK+jl3b3KD0i1NvT082cFlZo9Te1BE008+Rtabu69193Pd/VxJ/yDp/xI8S0q3zT2oa5t7gtptB9vc6LbhA5J+2MxOSNIRnijpCyWXMzap2lQzO03SU9SuQ6Srt9sk/agkJfm76yR9sdRSxinNMW42eUySflnSp7o7DvqhB3oEdz9kZr8qaafaIznf6u77zewlyeNvMrMHSdoj6f6SjpjZy9Qe4Tm08ussTb1J+l1J3yfpjUnbfMjdN4QqcwxS1ttPSvp5M1uWtCTpeV2DChspZb2hj5R191xJ/6+ZHVJ7m3s+29zoenP3L5jZP0r6vKQjkt7i7v8ertThZdhXnyPpo0nvfeOlrLffl/Q3Znaz2mkLv9Xwq0SSUtfdIyS93cwOqz1zzi+Nel9WIgQAAAAyIIUDAAAAyIAAGgAAAMiAABoAAADIgAAaAAAAyIAAGgAAAMiAABoACmZmh81sX9ftXDPbYGZ/ljz+VDP7oa7nbzGzR47xOff0ue8GM9vcc9/LzOyNWd8LANDGPNAAULwld7+g574vqT1/vCQ9VdI9kv45+XuLpA+pPR/ppN6l9sIBO7vue76krTm8NwA0Ej3QABBA0uv8ITM7V9JLJL086Z1+iqRnSdqR/P2w5PaPZrbXzD5tZucl77HWzP7FzD5rZr8/4KP+QdIzzWx18ppzJZ0l6TNmdoqZ/ZOZfc7MbjazZw8qZ9ffV5nZLyb/v9DMPpmUa6eZfX9y/6+b2X+Y2efN7N25VBgARIQeaAAo3oyZ7Uv+f6u7P6fzgLt/yczeJOked/8jSTKz6yR9yN3/Ifn7nyS9xN3/PzN7oqQ3Stok6U8l/aW7v93MfqXfB7v7N8zs3yRdpPayyM+XdI27u5l9V9Jz3P1bZnampBvN7Lo0qwya2bSkP5f0bHc/aGbPk/RaSS+StE3SWne/z8xms1YWAMSOABoAitcvhSMVMztF0g9Jem+y5L0krU7+3aj20u6S9HeSXjfgbTppHJ0A+kWdt5f0h2b2I2ovNT0n6YGSvpqiaOskPUrSx5JyTUn6SvLY5yW908zmJc2neC8AqBQCaACI2ypJi0MC8JG9xWoHsa83s8dJmnH3zyX3v0DSGkkXuvuymX1J0ok9rz2klel+ncdN0n53f3Kfz7tY0o+onYryajM7390PpSgnAFQCOdAAEN63JZ3a7293/5akW83spyTJ2h6bPG+32j3KUjsY7svd75F0g6S3qt0b3XGapK8lwfPTJD2kz8u/LOmRZrbazE6T9KPJ/QckrTGzJyflmjaz881slaSz3f0Tkn5T0qykU1LUAQBUBgE0AIT3QUnPSQYN/rCkd0vaamYLZvYwtYPjXzKzmyTtl9QZ7PdSSb9iZp9VOxge5l2SHpu8d8c7JW0wsz3JZ9zS+yJ3v13Se5SkZUhaSO7/nqTnSnpdUq59aqeaTEl6h5ndnDz3De6+mKk2ACBylmKsCAAAAIAEPdAAAABABgTQAAAAQAYE0AAAAEAGBNAAAABABgTQAAAAQAYE0AAAAEAGBNAAAABABgTQAAAAQAb/P7ylYIvnTNoyAAAAAElFTkSuQmCC\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": "3.8.2rc2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
