{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Generalized Linear Models (Formula)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook illustrates how you can use R-style formulas to fit Generalized Linear Models.\n",
    "\n",
    "To begin, we load the ``Star98`` dataset and we construct a formula and pre-process the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from __future__ import print_function\n",
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf\n",
    "star98 = sm.datasets.star98.load_pandas().data\n",
    "formula = 'SUCCESS ~ LOWINC + PERASIAN + PERBLACK + PERHISP + PCTCHRT + \\\n",
    "           PCTYRRND + PERMINTE*AVYRSEXP*AVSALK + PERSPENK*PTRATIO*PCTAF'\n",
    "dta = star98[['NABOVE', 'NBELOW', 'LOWINC', 'PERASIAN', 'PERBLACK', 'PERHISP',\n",
    "              'PCTCHRT', 'PCTYRRND', 'PERMINTE', 'AVYRSEXP', 'AVSALK',\n",
    "              'PERSPENK', 'PTRATIO', 'PCTAF']].copy()\n",
    "endog = dta['NABOVE'] / (dta['NABOVE'] + dta.pop('NBELOW'))\n",
    "del dta['NABOVE']\n",
    "dta['SUCCESS'] = endog"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then, we fit the GLM model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "mod1 = smf.glm(formula=formula, data=dta, family=sm.families.Binomial()).fit()\n",
    "mod1.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we define a function to operate customized data transformation using the formula framework:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def double_it(x):\n",
    "    return 2 * x\n",
    "formula = 'SUCCESS ~ double_it(LOWINC) + PERASIAN + PERBLACK + PERHISP + PCTCHRT + \\\n",
    "           PCTYRRND + PERMINTE*AVYRSEXP*AVSALK + PERSPENK*PTRATIO*PCTAF'\n",
    "mod2 = smf.glm(formula=formula, data=dta, family=sm.families.Binomial()).fit()\n",
    "mod2.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As expected, the coefficient for ``double_it(LOWINC)`` in the second model is half the size of the ``LOWINC`` coefficient from the first model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "print(mod1.params[1])\n",
    "print(mod2.params[1] * 2)"
   ]
  }
 ],
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