{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This code is taken from the beautiful lecture https://lectures.quantecon.org/py/mle.html "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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I2dKTNX1SF9MIQxEREZFypiDuk3gsTE8ihXPvGfYiIiIiImVAQdwntdEII+kc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\njDHGmBqwRNwYY4wxxpga+P/uzN9XTgfdMwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8c83aef2e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from numpy import exp\n",
    "from scipy.special import factorial\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "poisson_pmf = lambda y, μ: μ**y / factorial(y) * exp(-μ)\n",
    "y_values = range(0, 50)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(12, 8))\n",
    "\n",
    "for μ in [1, 5, 10]:\n",
    "    distribution = []\n",
    "    for y_i in y_values:\n",
    "        distribution.append(poisson_pmf(0.5*y_i, μ))\n",
    "    ax.plot(y_values,\n",
    "            distribution,\n",
    "            label=f'$\\mu$={μ}',\n",
    "            alpha=0.5,\n",
    "            marker='o',\n",
    "            markersize=8)\n",
    "\n",
    "ax.grid()\n",
    "ax.set_xlabel('$y$', fontsize=14)\n",
    "ax.set_ylabel('$f(y \\mid \\mu)$', fontsize=14)\n",
    "ax.axis(xmin=0, ymin=0)\n",
    "ax.legend(fontsize=14)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>country</th>\n",
       "      <th>ccode</th>\n",
       "      <th>year</th>\n",
       "      <th>cyear</th>\n",
       "      <th>numbil</th>\n",
       "      <th>...</th>\n",
       "      <th>topint08</th>\n",
       "      <th>rintr</th>\n",
       "      <th>noyrs</th>\n",
       "      <th>roflaw</th>\n",
       "      <th>nrrents</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>United States</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1990.0</td>\n",
       "      <td>21990.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>39.799999</td>\n",
       "      <td>4.988405</td>\n",
       "      <td>20.0</td>\n",
       "      <td>1.61</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>United States</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1991.0</td>\n",
       "      <td>21991.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>39.799999</td>\n",
       "      <td>4.988405</td>\n",
       "      <td>20.0</td>\n",
       "      <td>1.61</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>United States</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1992.0</td>\n",
       "      <td>21992.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>39.799999</td>\n",
       "      <td>4.988405</td>\n",
       "      <td>20.0</td>\n",
       "      <td>1.61</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>United States</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1993.0</td>\n",
       "      <td>21993.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>39.799999</td>\n",
       "      <td>4.988405</td>\n",
       "      <td>20.0</td>\n",
       "      <td>1.61</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>United States</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1994.0</td>\n",
       "      <td>21994.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>39.799999</td>\n",
       "      <td>4.988405</td>\n",
       "      <td>20.0</td>\n",
       "      <td>1.61</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 36 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "         country  ccode    year    cyear  numbil   ...      topint08  \\\n",
       "0  United States    2.0  1990.0  21990.0     NaN   ...     39.799999   \n",
       "1  United States    2.0  1991.0  21991.0     NaN   ...     39.799999   \n",
       "2  United States    2.0  1992.0  21992.0     NaN   ...     39.799999   \n",
       "3  United States    2.0  1993.0  21993.0     NaN   ...     39.799999   \n",
       "4  United States    2.0  1994.0  21994.0     NaN   ...     39.799999   \n",
       "\n",
       "      rintr  noyrs  roflaw  nrrents  \n",
       "0  4.988405   20.0    1.61      NaN  \n",
       "1  4.988405   20.0    1.61      NaN  \n",
       "2  4.988405   20.0    1.61      NaN  \n",
       "3  4.988405   20.0    1.61      NaN  \n",
       "4  4.988405   20.0    1.61      NaN  \n",
       "\n",
       "[5 rows x 36 columns]"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "pd.options.display.max_columns = 10\n",
    "\n",
    "# Load in data and view\n",
    "df = pd.read_stata('https://github.com/QuantEcon/QuantEcon.lectures.code/raw/master/mle/fp.dta')\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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XkuM2e3xV7UiyI0m2bz86l5y+Z7NuB219fX3o8VgNu3fv9t5zyIwjRjGWGMVYWryFh+uq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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8c83b25198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "numbil0_2008 = df[(df['year'] == 2008) & (\n",
    "    df['country'] != 'United States')].loc[:, 'numbil0']\n",
    "\n",
    "plt.subplots(figsize=(12, 8))\n",
    "plt.hist(numbil0_2008, bins=30)\n",
    "plt.xlim(xmin=0)\n",
    "plt.grid()\n",
    "plt.xlabel('Number of billionaires in 2008')\n",
    "plt.ylabel('Count')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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dQE5nk45klyEiIiIiSaDgnUCF/gwaW8PE1NlEREREZMRR8E6ggN9HNGY53RZO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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8c6f4f26a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "y_values = range(0, 20)\n",
    "\n",
    "# Define a parameter vector with estimates\n",
    "β = np.array([0.26, 0.18, 0.25, -0.1, -0.22]).T\n",
    "\n",
    "# Create some observations X\n",
    "datasets = [np.array([0, 1, 1, 1, 2]),\n",
    "            np.array([2, 3, 2, 4, 0]),\n",
    "            np.array([3, 4, 5, 3, 2]),\n",
    "            np.array([6, 5, 4, 4, 7])]\n",
    "\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(12, 8))\n",
    "\n",
    "for X in datasets:\n",
    "    μ = exp(X @ β)\n",
    "    distribution = []\n",
    "    for y_i in y_values:\n",
    "        distribution.append(poisson_pmf(y_i, μ))\n",
    "    ax.plot(y_values,\n",
    "            distribution,\n",
    "            label=f'$\\mu_i$={μ:.1}',\n",
    "            marker='o',\n",
    "            markersize=8,\n",
    "            alpha=0.5)\n",
    "\n",
    "ax.grid()\n",
    "ax.legend()\n",
    "ax.set_xlabel('$y \\mid x_i$')\n",
    "ax.set_ylabel(r'$f(y \\mid x_i; \\beta )$')\n",
    "ax.axis(xmin=0, ymin=0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class PoissonRegression:\n",
    "\n",
    "    def __init__(self, y, X, β):\n",
    "        self.X, self.y, self.β = X, y, β\n",
    "        self.n, self.k = X.shape\n",
    "\n",
    "    def μ(self):\n",
    "        return np.exp(self.X @ self.β.T)\n",
    "\n",
    "    def logL(self):\n",
    "        y = self.y\n",
    "        μ = self.μ()\n",
    "        return np.sum(y * np.log(μ) - μ - np.log(factorial(y)))\n",
    "\n",
    "    def G(self):\n",
    "        μ = self.μ()\n",
    "        return ((self.y - μ) @ self.X).reshape(self.k, 1)\n",
    "\n",
    "    def H(self):\n",
    "        X = self.X\n",
    "        μ = self.μ()\n",
    "        return -(μ * X.T @ X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def newton_raphson(model, tol=1e-3, max_iter=1000, display=True):\n",
    "\n",
    "    i = 0\n",
    "    error = 100  # Initial error value\n",
    "\n",
    "    # Print header of output\n",
    "    if display:\n",
    "        header = f'{\"Iteration_k\":<13}{\"Log-likelihood\":<16}{\"θ\":<60}'\n",
    "        print(header)\n",
    "        print(\"-\" * len(header))\n",
    "\n",
    "    # While loop runs while any value in error is greater\n",
    "    # than the tolerance until max iterations are reached\n",
    "    while np.any(error > tol) and i < max_iter:\n",
    "        H, G = model.H(), model.G()\n",
    "        β_new = model.β - (np.linalg.inv(H) @ G).T\n",
    "        error = β_new - model.β\n",
    "        model.β = β_new.flatten()\n",
    "\n",
    "        # Print iterations\n",
    "        if display:\n",
    "            β_list = [f'{t:.3}' for t in list(model.β)]\n",
    "            update = f'{i:<13}{model.logL():<16.8}{β_list}'\n",
    "            print(update)\n",
    "\n",
    "        i += 1\n",
    "\n",
    "    print(f'Number of iterations: {i}')\n",
    "    print(f'β_hat = {model.β}')\n",
    "\n",
    "    return model.β"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration_k  Log-likelihood  θ                                                           \n",
      "-----------------------------------------------------------------------------------------\n",
      "0            -4.3447622      ['-1.49', '0.265', '0.244']\n",
      "1            -3.5742413      ['-3.38', '0.528', '0.474']\n",
      "2            -3.3999526      ['-5.06', '0.782', '0.702']\n",
      "3            -3.3788646      ['-5.92', '0.909', '0.82']\n",
      "4            -3.3783559      ['-6.07', '0.933', '0.843']\n",
      "5            -3.3783555      ['-6.08', '0.933', '0.843']\n",
      "Number of iterations: 6\n",
      "β_hat = [-6.07848205  0.93340226  0.84329625]\n"
     ]
    }
   ],
   "source": [
    "X = np.array([[1, 2, 5],\n",
    "              [1, 1, 3],\n",
    "              [1, 4, 2],\n",
    "              [1, 5, 2],\n",
    "              [1, 3, 1]])\n",
    "\n",
    "y = np.array([1, 0, 1, 1, 0])\n",
    "\n",
    "# Take a guess at initial βs\n",
    "init_β = np.array([0.1, 0.1, 0.1])\n",
    "\n",
    "# Create an object with Poisson model values\n",
    "poi = PoissonRegression(y, X, β=init_β)\n",
    "\n",
    "# Use newton_raphson to find the MLE\n",
    "β_hat = newton_raphson(poi, display=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ -3.95169228e-07],\n",
       "       [ -1.00114805e-06],\n",
       "       [ -7.73114562e-07]])"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poi.G()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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v3mZ8fLzVYdRbmZmZBAZqNRCrqP+rX9I3SUTPjKbL77ow9JGhl9XW448/TlBQEFOmTPnF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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8c83af0e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "logL = lambda x: -(x - 10) ** 2 - 10\n",
    "\n",
    "def find_tangent(β, a=0.01):\n",
    "    y1 = logL(β)\n",
    "    y2 = logL(β+a)\n",
    "    x = np.array([[β, 1], [β+a, 1]])\n",
    "    m, c = np.linalg.lstsq(x, np.array([y1, y2]))[0]\n",
    "    return m, c\n",
    "\n",
    "β = np.linspace(2, 18)\n",
    "fig, ax = plt.subplots(figsize=(12, 8))\n",
    "ax.plot(β, logL(β), lw=2, c='black')\n",
    "\n",
    "for β in [7, 8.5, 9.5, 10]:\n",
    "    β_line = np.linspace(β-2, β+2)\n",
    "    m, c = find_tangent(β)\n",
    "    y = m * β_line + c\n",
    "    ax.plot(β_line, y, '-', c='purple', alpha=0.8)\n",
    "    ax.text(β+2.05, y[-1], f'$G({β}) = {abs(m):.0f}$', fontsize=12)\n",
    "    ax.vlines(β, -24, logL(β), linestyles='--', alpha=0.5)\n",
    "    ax.hlines(logL(β), 6, β, linestyles='--', alpha=0.5)\n",
    "\n",
    "ax.set(ylim=(-24, -4), xlim=(6, 13))\n",
    "ax.set_xlabel(r'$\\beta$', fontsize=15)\n",
    "ax.set_ylabel(r'$log \\mathcal{L(\\beta)}$',\n",
    "               rotation=0,\n",
    "               labelpad=25,\n",
    "               fontsize=15)\n",
    "ax.grid(alpha=0.3)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.675671\n",
      "         Iterations 7\n",
      "                          Poisson Regression Results                          \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   No. Observations:                    5\n",
      "Model:                        Poisson   Df Residuals:                        2\n",
      "Method:                           MLE   Df Model:                            2\n",
      "Date:                Fri, 04 May 2018   Pseudo R-squ.:                  0.2546\n",
      "Time:                        07:40:47   Log-Likelihood:                -3.3784\n",
      "converged:                       True   LL-Null:                       -4.5325\n",
      "                                        LLR p-value:                    0.3153\n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         -6.0785      5.279     -1.151      0.250     -16.425       4.268\n",
      "x1             0.9334      0.829      1.126      0.260      -0.691       2.558\n",
      "x2             0.8433      0.798      1.057      0.291      -0.720       2.407\n",
      "==============================================================================\n"
     ]
    }
   ],
   "source": [
    "from statsmodels.api import Poisson\n",
    "from scipy import stats\n",
    "stats.chisqprob = lambda chisq, df: stats.chi2.sf(chisq, df)\n",
    "\n",
    "X = np.array([[1, 2, 5],\n",
    "              [1, 1, 3],\n",
    "              [1, 4, 2],\n",
    "              [1, 5, 2],\n",
    "              [1, 3, 1]])\n",
    "\n",
    "y = np.array([1, 0, 1, 1, 0])\n",
    "\n",
    "stats_poisson = Poisson(y, X).fit()\n",
    "print(stats_poisson.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Keep only year 2008\n",
    "df = df[df['year'] == 2008]\n",
    "\n",
    "# Add a constant\n",
    "df['const'] = 1\n",
    "\n",
    "# Variable sets\n",
    "reg1 = ['const', 'lngdppc', 'lnpop', 'gattwto08']\n",
    "reg2 = ['const', 'lngdppc', 'lnpop',\n",
    "        'gattwto08', 'lnmcap08', 'rintr', 'topint08']\n",
    "reg3 = ['const', 'lngdppc', 'lnpop', 'gattwto08', 'lnmcap08',\n",
    "        'rintr', 'topint08', 'nrrents', 'roflaw']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Warning: Maximum number of iterations has been exceeded.\n",
      "         Current function value: 2.226090\n",
      "         Iterations: 35\n",
      "                          Poisson Regression Results                          \n",
      "==============================================================================\n",
      "Dep. Variable:                numbil0   No. Observations:                  197\n",
      "Model:                        Poisson   Df Residuals:                      193\n",
      "Method:                           MLE   Df Model:                            3\n",
      "Date:                Fri, 04 May 2018   Pseudo R-squ.:                  0.8574\n",
      "Time:                        09:54:24   Log-Likelihood:                -438.54\n",
      "converged:                      False   LL-Null:                       -3074.7\n",
      "                                        LLR p-value:                     0.000\n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const        -29.0495      2.578    -11.268      0.000     -34.103     -23.997\n",
      "lngdppc        1.0839      0.138      7.834      0.000       0.813       1.355\n",
      "lnpop          1.1714      0.097     12.024      0.000       0.980       1.362\n",
      "gattwto08      0.0060      0.007      0.868      0.386      -0.008       0.019\n",
      "==============================================================================\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/scratch/users/jteichma/.local/lib/python3.6/site-packages/statsmodels/base/model.py:496: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals\n",
      "  \"Check mle_retvals\", ConvergenceWarning)\n"
     ]
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "\n",
    "# Specify model\n",
    "poisson_reg = sm.Poisson(df[['numbil0']], df[reg1],\n",
    "                         missing='drop').fit(cov_type='HC0')\n",
    "print(poisson_reg.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 2.226090\n",
      "         Iterations 36\n",
      "                          Poisson Regression Results                          \n",
      "==============================================================================\n",
      "Dep. Variable:                numbil0   No. Observations:                  197\n",
      "Model:                        Poisson   Df Residuals:                      193\n",
      "Method:                           MLE   Df Model:                            3\n",
      "Date:                Fri, 04 May 2018   Pseudo R-squ.:                  0.8574\n",
      "Time:                        09:54:54   Log-Likelihood:                -438.54\n",
      "converged:                       True   LL-Null:                       -3074.7\n",
      "                                        LLR p-value:                     0.000\n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const        -29.0495      2.578    -11.268      0.000     -34.103     -23.997\n",
      "lngdppc        1.0839      0.138      7.834      0.000       0.813       1.355\n",
      "lnpop          1.1714      0.097     12.024      0.000       0.980       1.362\n",
      "gattwto08      0.0060      0.007      0.868      0.386      -0.008       0.019\n",
      "==============================================================================\n"
     ]
    }
   ],
   "source": [
    "poisson_reg = sm.Poisson(df[['numbil0']], df[reg1],\n",
    "                         missing='drop').fit(cov_type='HC0', maxiter=100)\n",
    "print(poisson_reg.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Table 1 - Explaining the Number of Billionaires in 2008\n",
      "=================================================\n",
      "                  Model 1    Model 2    Model 3  \n",
      "-------------------------------------------------\n",
      "const            -29.050*** -19.444*** -20.858***\n",
      "                 (2.578)    (4.820)    (4.255)   \n",
      "lngdppc          1.084***   0.717***   0.737***  \n",
      "                 (0.138)    (0.244)    (0.233)   \n",
      "lnpop            1.171***   0.806***   0.929***  \n",
      "                 (0.097)    (0.213)    (0.195)   \n",
      "gattwto08        0.006      0.007      0.004     \n",
      "                 (0.007)    (0.006)    (0.006)   \n",
      "lnmcap08                    0.399**    0.286*    \n",
      "                            (0.172)    (0.167)   \n",
      "rintr                       -0.010     -0.009    \n",
      "                            (0.010)    (0.010)   \n",
      "topint08                    -0.051***  -0.058*** \n",
      "                            (0.011)    (0.012)   \n",
      "nrrents                                -0.005    \n",
      "                                       (0.010)   \n",
      "roflaw                                 0.203     \n",
      "                                       (0.372)   \n",
      "Pseudo R-squared 0.86       0.90       0.90      \n",
      "No. observations 197        131        131       \n",
      "=================================================\n",
      "Standard errors in parentheses.\n",
      "* p<.1, ** p<.05, ***p<.01\n"
     ]
    }
   ],
   "source": [
    "from statsmodels.iolib.summary2 import summary_col\n",
    "\n",
    "regs = [reg1, reg2, reg3]\n",
    "reg_names = ['Model 1', 'Model 2', 'Model 3']\n",
    "info_dict = {'Pseudo R-squared': lambda x: f\"{x.prsquared:.2f}\",\n",
    "             'No. observations': lambda x: f\"{int(x.nobs):d}\"}\n",
    "regressor_order = ['const',\n",
    "                   'lngdppc',\n",
    "                   'lnpop',\n",
    "                   'gattwto08',\n",
    "                   'lnmcap08',\n",
    "                   'rintr',\n",
    "                   'topint08',\n",
    "                   'nrrents',\n",
    "                   'roflaw']\n",
    "results = []\n",
    "\n",
    "for reg in regs:\n",
    "    result = sm.Poisson(df[['numbil0']], df[reg],\n",
    "                        missing='drop').fit(cov_type='HC0', maxiter=100, disp=0)\n",
    "    results.append(result)\n",
    "\n",
    "results_table = summary_col(results=results,\n",
    "                            float_format='%0.3f',\n",
    "                            stars=True,\n",
    "                            model_names=reg_names,\n",
    "                            info_dict=info_dict,\n",
    "                            regressor_order=regressor_order)\n",
    "results_table.add_title('Table 1 - Explaining the Number of Billionaires in 2008')\n",
    "print(results_table)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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JjqApnvcADu01lSRJkjRik2wsfEs74u6B7aW9quqUXlNJkiRJI9blsJUAha0ckiRJWuYm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\nSZI0IotoSZIkaUQW0ZIkSdKI/h/2Q79Uk3GjQwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8c6f433d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = ['const', 'lngdppc', 'lnpop', 'gattwto08', 'lnmcap08', 'rintr',\n",
    "        'topint08', 'nrrents', 'roflaw', 'numbil0', 'country']\n",
    "results_df = df[data].dropna()\n",
    "\n",
    "# Use last model (model 3)\n",
    "results_df['prediction'] = results[-1].predict()\n",
    "\n",
    "# Calculate difference\n",
    "results_df['difference'] = results_df['numbil0'] - results_df['prediction']\n",
    "\n",
    "# Sort in descending order\n",
    "results_df.sort_values('difference', ascending=False, inplace=True)\n",
    "\n",
    "# Plot the first 15 data points\n",
    "results_df[:15].plot('country', 'difference', kind='bar', figsize=(12,8), legend=False)\n",
    "plt.ylabel('Number of billionaires above predicted level')\n",
    "plt.xlabel('Country')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```none\n",
    "Iteration_k  Log-likelihood  θ\n",
    "-----------------------------------------------------------\n",
    "0            -2.37968841     ['-1.3400', '0.7750', '-0.1570']\n",
    "1            -2.36875259     ['-1.5350', '0.7750', '-0.0980']\n",
    "2            -2.36872942     ['-1.5460', '0.7780', '-0.0970']\n",
    "3            -2.36872942     ['-1.5460', '0.7780', '-0.0970']\n",
    "Number of iterations: 4\n",
    "β_hat = [-1.54625858  0.77778952 -0.09709757]\n",
    "```\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```none\n",
    "array([-1.54625858,  0.77778952, -0.09709757])\n",
    "```\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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    "collapsed": true
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   "outputs": [],
   "source": []
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   "metadata": {},
   "source": [
    "```none\n",
    "Optimization terminated successfully.\n",
    "         Current function value: 0.473746\n",
    "         Iterations 6\n",
    "                          Probit Regression Results\n",
    "==============================================================================\n",
    "Dep. Variable:                      y   No. Observations:                    5\n",
    "Model:                         Probit   Df Residuals:                        2\n",
    "Method:                           MLE   Df Model:                            2\n",
    "Date:                Wed, 26 Jul 2017   Pseudo R-squ.:                  0.2961\n",
    "Time:                        15:41:39   Log-Likelihood:                -2.3687\n",
    "converged:                       True   LL-Null:                       -3.3651\n",
    "                                        LLR p-value:                    0.3692\n",
    "==============================================================================\n",
    "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
    "------------------------------------------------------------------------------\n",
    "const         -1.5463      1.866     -0.829      0.407      -5.204       2.111\n",
    "x1             0.7778      0.788      0.986      0.324      -0.768       2.323\n",
    "x2            -0.0971      0.590     -0.165      0.869      -1.254       1.060\n",
    "==============================================================================\n",
    "```\n"
   ]
  }
 ],
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