{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Discrete Choice Models Overview"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from __future__ import print_function\n",
    "import numpy as np\n",
    "import statsmodels.api as sm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data\n",
    "\n",
    "Load data from Spector and Mazzeo (1980). Examples follow Greene's Econometric Analysis Ch. 21 (5th Edition)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "spector_data = sm.datasets.spector.load()\n",
    "spector_data.exog = sm.add_constant(spector_data.exog, prepend=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Inspect the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "print(spector_data.exog[:5,:])\n",
    "print(spector_data.endog[:5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear Probability Model (OLS)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "lpm_mod = sm.OLS(spector_data.endog, spector_data.exog)\n",
    "lpm_res = lpm_mod.fit()\n",
    "print('Parameters: ', lpm_res.params[:-1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Logit Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "logit_mod = sm.Logit(spector_data.endog, spector_data.exog)\n",
    "logit_res = logit_mod.fit(disp=0)\n",
    "print('Parameters: ', logit_res.params)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Marginal Effects"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "margeff = logit_res.get_margeff()\n",
    "print(margeff.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As in all the discrete data models presented below, we can print a nice summary of results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "print(logit_res.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Probit Model "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "probit_mod = sm.Probit(spector_data.endog, spector_data.exog)\n",
    "probit_res = probit_mod.fit()\n",
    "probit_margeff = probit_res.get_margeff()\n",
    "print('Parameters: ', probit_res.params)\n",
    "print('Marginal effects: ')\n",
    "print(probit_margeff.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multinomial Logit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load data from the American National Election Studies:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "anes_data = sm.datasets.anes96.load()\n",
    "anes_exog = anes_data.exog\n",
    "anes_exog = sm.add_constant(anes_exog, prepend=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Inspect the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "print(anes_data.exog[:5,:])\n",
    "print(anes_data.endog[:5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit MNL model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "mlogit_mod = sm.MNLogit(anes_data.endog, anes_exog)\n",
    "mlogit_res = mlogit_mod.fit()\n",
    "print(mlogit_res.params)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Poisson\n",
    "\n",
    "Load the Rand data. Note that this example is similar to Cameron and Trivedi's `Microeconometrics` Table 20.5, but it is slightly different because of minor changes in the data. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "rand_data = sm.datasets.randhie.load()\n",
    "rand_exog = rand_data.exog.view(float).reshape(len(rand_data.exog), -1)\n",
    "rand_exog = sm.add_constant(rand_exog, prepend=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit Poisson model: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "poisson_mod = sm.Poisson(rand_data.endog, rand_exog)\n",
    "poisson_res = poisson_mod.fit(method=\"newton\")\n",
    "print(poisson_res.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Negative Binomial\n",
    "\n",
    "The negative binomial model gives slightly different results. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "mod_nbin = sm.NegativeBinomial(rand_data.endog, rand_exog)\n",
    "res_nbin = mod_nbin.fit(disp=False)\n",
    "print(res_nbin.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Alternative solvers\n",
    "\n",
    "The default method for fitting discrete data MLE models is Newton-Raphson. You can use other solvers by using the ``method`` argument: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "mlogit_res = mlogit_mod.fit(method='bfgs', maxiter=100)\n",
    "print(mlogit_res.summary())"
   ]
  }
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