{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simple logistic regression\n",
    "\n",
    "This notebook follows John H McDonald's [Handbook of Biological Statistics](http://www.biostathandbook.com/simplelogistic.html) chapter on simple logistic regression.\n",
    "\n",
    "This notebook is provided with a CC-BY-SA license."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import io\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import scipy.stats\n",
    "import scipy.special\n",
    "import seaborn as sns\n",
    "sns.set_style('white')\n",
    "sns.set_context('notebook')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Spider data from *Suzuki et al. (2006)*:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Grain size (mm)</th>\n",
       "      <th>Spiders</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.245</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.247</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.285</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.299</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.327</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Grain size (mm) Spiders\n",
       "0            0.245   False\n",
       "1            0.247   False\n",
       "2            0.285    True\n",
       "3            0.299    True\n",
       "4            0.327    True"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = \"\"\"Grain size (mm)\tSpiders\n",
    "0.245\tabsent\n",
    "0.247\tabsent\n",
    "0.285\tpresent\n",
    "0.299\tpresent\n",
    "0.327\tpresent\n",
    "0.347\tpresent\n",
    "0.356\tabsent\n",
    "0.36\tpresent\n",
    "0.363\tabsent\n",
    "0.364\tpresent\n",
    "0.398\tabsent\n",
    "0.4\tpresent\n",
    "0.409\tabsent\n",
    "0.421\tpresent\n",
    "0.432\tabsent\n",
    "0.473\tpresent\n",
    "0.509\tpresent\n",
    "0.529\tpresent\n",
    "0.561\tabsent\n",
    "0.569\tabsent\n",
    "0.594\tpresent\n",
    "0.638\tpresent\n",
    "0.656\tpresent\n",
    "0.816\tpresent\n",
    "0.853\tpresent\n",
    "0.938\tpresent\n",
    "1.036\tpresent\n",
    "1.045\tpresent\n",
    "\"\"\"\n",
    "df = pd.read_table(io.StringIO(data))\n",
    "df.Spiders = df.Spiders == 'present'\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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LzPnhhx9q9NVcAAAAGEulim5UVJTefvttXVjlcPToUdWuXdux3WQyqU6dOpoxY4Z7UgIA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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10491cda0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.plot.scatter('Grain size (mm)', 'Spiders')\n",
    "plt.ylabel('Spiders present?')\n",
    "sns.despine()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I will analyse this with the *scikit-learn* package."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import sklearn.linear_model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "scikit-learn has a logisitic regression classifier which uses regularization. To eliminate regularization, we set the regularization parameter `C` to $10^{12}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-1.64748882] [[ 5.12118846]]\n"
     ]
    }
   ],
   "source": [
    "# C=1e12 is effectively no regularization - see https://github.com/scikit-learn/scikit-learn/issues/6738\n",
    "clf = sklearn.linear_model.LogisticRegression(C=1e12, random_state=0)\n",
    "clf.fit(df['Grain size (mm)'].reshape(-1, 1), df['Spiders'])\n",
    "print(clf.intercept_, clf.coef_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is in agreement with the equation John reports:\n",
    "$$\n",
    "probability of spider presence = \\frac{e^{-1.6476+5.1215(grain \\; size)}}{(1+e^{-1.6476+5.1215(grain \\; size)}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_log_reg(x, y, data, clf, xmin=None, xmax=None, alpha=1, ax=None):\n",
    "    if ax is None:\n",
    "        fig, ax = plt.subplots()\n",
    "    else:\n",
    "        fig = ax.figure\n",
    "    ax.scatter(data[x], data[y], color='black', zorder=20, alpha=alpha)\n",
    "    if xmin is None:\n",
    "        xmin = x.min()\n",
    "    if xmax is None:\n",
    "        xmax = x.max()\n",
    "    X_test = np.linspace(xmin, xmax, 300)\n",
    "\n",
    "    loss = scipy.special.expit(X_test * clf.coef_ + clf.intercept_).ravel()\n",
    "    ax.plot(X_test, loss, linewidth=3)\n",
    "\n",
    "    ax.set_xlabel(x)\n",
    "    ax.set_ylabel(y)\n",
    "    fig.tight_layout()\n",
    "    sns.despine()\n",
    "    return fig, ax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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GqmWjWLVsGEtZAGAaCgQAAJUkv6hUG3dla+PObG1Kz9Gh7PwKvU6jpCilNI1XcpM4JTeN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\nBAgAAAAAphEgAAAAAJj2f7Nv8cLOjrlOAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1127732b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_log_reg(x='Grain size (mm)', y='Spiders', data=df, clf=clf, xmin=0, xmax=1.5);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hypothesis testing\n",
    "\n",
    "To test if *Grain size* is a significant factor, we use the [**likelihood ratio test**](https://en.wikipedia.org/wiki/Logistic_regression#Evaluating_goodness_of_fit).\n",
    "\n",
    "We calculate the likelihood of the model with the grain size (the alternative model):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def log_reg_null_model(X, y):\n",
    "    X_ = np.zeros_like(X)\n",
    "    if X_.ndim == 1:\n",
    "        X_ = X_.reshape(-1, 1)\n",
    "    clf = sklearn.linear_model.LogisticRegression(C=1e12)\n",
    "    clf.fit(X_, y)\n",
    "    return clf\n",
    "\n",
    "clf0 = log_reg_null_model(df['Grain size (mm)'], df['Spiders'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The likelihood ratio test operates by calculating the test statistic $D$ from the likelihoods of the null and alternative models:\n",
    "$$\n",
    "D = -2 \\log{ \\frac{L(H_0)}{L(H_1)} }\n",
    "$$\n",
    "The test statistic is then approximately chisquare distributed.\n",
    "\n",
    "*scikit-learn* has a log-loss function that can help us do that. \n",
    "The log-loss is defined as the negative log-likelihood, so we can rewrite:\n",
    "$$\n",
    "D = 2 (-\\log{L(H_0)} + \\log{L(H_1)}) \\Rightarrow \\\\\n",
    "D = 2 (logloss(H_0) - logloss(H_1))\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import sklearn.metrics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def log_reg_lik_ratio_test(X, Y, clf0, clf1, df=1):\n",
    "    if X.ndim == 1:\n",
    "        X = X.reshape(-1, 1)\n",
    "    y_prob0 = clf0.predict_proba(X)\n",
    "    loss0 = sklearn.metrics.log_loss(Y, y_prob0, normalize=False)\n",
    "    y_prob1 = clf1.predict_proba(X)\n",
    "    loss1 = sklearn.metrics.log_loss(Y, y_prob1, normalize=False)\n",
    "    D = 2 * (loss0 - loss1)\n",
    "    return scipy.stats.distributions.chi2.sf(D, df=df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.033243767135570736"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_reg_lik_ratio_test(df['Grain size (mm)'], df['Spiders'].astype(np.float64), clf0, clf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "John indeed reports 0.033.\n",
    "\n",
    "Note that the log-loss calculation in equivalent to:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "15.3157739197 15.3157739197\n"
     ]
    }
   ],
   "source": [
    "_ = clf.predict_proba(df['Grain size (mm)'].reshape(-1, 1))\n",
    "df['prob_absent'], df['prob_present'] = _[:,0], _[:,1]\n",
    "lik = df.loc[df['Spiders'], 'prob_present'].prod() * df.loc[~df['Spiders'], 'prob_absent'].prod()\n",
    "print(\n",
    "    -np.log(lik), \n",
    "    sklearn.metrics.log_loss(\n",
    "        df['Spiders'], \n",
    "        clf.predict_proba(df['Grain size (mm)'].reshape(-1, 1)), \n",
    "        normalize=False\n",
    "    )\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Second example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Location</th>\n",
       "      <th>Latitude</th>\n",
       "      <th>Mpi90</th>\n",
       "      <th>Mpi100</th>\n",
       "      <th>p, Mpi100</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Port Townsend, WA</td>\n",
       "      <td>48.1</td>\n",
       "      <td>47</td>\n",
       "      <td>139</td>\n",
       "      <td>0.748</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Neskowin, OR</td>\n",
       "      <td>45.2</td>\n",
       "      <td>177</td>\n",
       "      <td>241</td>\n",
       "      <td>0.577</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Siuslaw R., OR</td>\n",
       "      <td>44.0</td>\n",
       "      <td>1087</td>\n",
       "      <td>1183</td>\n",
       "      <td>0.521</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Umpqua R., OR</td>\n",
       "      <td>43.7</td>\n",
       "      <td>187</td>\n",
       "      <td>175</td>\n",
       "      <td>0.483</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Coos Bay, OR</td>\n",
       "      <td>43.5</td>\n",
       "      <td>397</td>\n",
       "      <td>671</td>\n",
       "      <td>0.628</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Location  Latitude  Mpi90  Mpi100  p, Mpi100\n",
       "0  Port Townsend, WA      48.1     47     139      0.748\n",
       "1       Neskowin, OR      45.2    177     241      0.577\n",
       "2     Siuslaw R., OR      44.0   1087    1183      0.521\n",
       "3      Umpqua R., OR      43.7    187     175      0.483\n",
       "4       Coos Bay, OR      43.5    397     671      0.628"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = \"\"\"Location\tLatitude\tMpi90\tMpi100\tp, Mpi100\n",
    "Port Townsend, WA\t48.1\t47\t139\t0.748\n",
    "Neskowin, OR\t45.2\t177\t241\t0.577\n",
    "Siuslaw R., OR\t44\t1087\t1183\t0.521\n",
    "Umpqua R., OR\t43.7\t187\t175\t0.483\n",
    "Coos Bay, OR\t43.5\t397\t671\t0.628\n",
    "San Francisco, CA\t37.8\t40\t14\t0.259\n",
    "Carmel, CA\t36.6\t39\t17\t0.304\n",
    "Santa Barbara, CA\t34.3\t30\t0\t0\n",
    "\"\"\"\n",
    "df = pd.read_table(io.StringIO(data))\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ff60XXnhBd9xxh1544QVt3rxZU6ZM0datW9WtWzev3xsAAABm8ngLsZSUFEnSrFmzlJiY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\nYJz/Bw4QhS8UCMlvAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112806ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.sort_values('Latitude').plot('Latitude', 'p, Mpi100', ls='', marker='o')\n",
    "plt.ylabel('Mpi100 proportion')\n",
    "plt.legend().set_visible(False)\n",
    "plt.xlim(30, 50)\n",
    "plt.ylim(-0.1, 1.1)\n",
    "sns.despine()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Allele</th>\n",
       "      <th>Latitude</th>\n",
       "      <th>Location</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>48.1</td>\n",
       "      <td>Port Townsend, WA</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>48.1</td>\n",
       "      <td>Port Townsend, WA</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>48.1</td>\n",
       "      <td>Port Townsend, WA</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>48.1</td>\n",
       "      <td>Port Townsend, WA</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>48.1</td>\n",
       "      <td>Port Townsend, WA</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Allele  Latitude           Location\n",
       "0       0      48.1  Port Townsend, WA\n",
       "1       0      48.1  Port Townsend, WA\n",
       "2       0      48.1  Port Townsend, WA\n",
       "3       0      48.1  Port Townsend, WA\n",
       "4       0      48.1  Port Townsend, WA"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rows = []\n",
    "for i, row in df.iterrows():\n",
    "    for _ in range(row['Mpi90']):\n",
    "        rows.append({'Location':row['Location'], 'Latitude': row['Latitude'], 'Allele': 0})\n",
    "    for _ in range(row['Mpi100']):\n",
    "        rows.append({'Location':row['Location'], 'Latitude': row['Latitude'], 'Allele': 1})\n",
    "raw_df = pd.DataFrame(rows)\n",
    "raw_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-7.59881547] [[ 0.17754715]]\n"
     ]
    }
   ],
   "source": [
    "clf = sklearn.linear_model.LogisticRegression(C=1e12, random_state=0)\n",
    "clf.fit(raw_df['Latitude'].reshape(-1, 1), raw_df['Allele'])\n",
    "print(clf.intercept_, clf.coef_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "which is very close to McDonald's intercept of -7.6469 and slope of 0.1786."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1127e4240>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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VOCCnCBCvvPKKioqKtG7dOlVWVurJJ59UdHS0Fi9e3KuutbVVP//5z5WVlaVX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\n5pbqTG7dLELd42KdL7r2eyn8lLeHa91MQpivunX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pMpvNev7553X77bdr9OjRDU5xAhzp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\nAABg2P8HGXELsQbiTR4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112089c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plot_log_reg(x='Latitude', y='Allele', data=raw_df, clf=clf, xmin=30, xmax=50, alpha=0.02)\n",
    "df.sort_values('Latitude').plot('Latitude', 'p, Mpi100', ls='', marker='o', ax=ax)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.19685284] [[ 0.]]\n"
     ]
    }
   ],
   "source": [
    "clf0 = log_reg_null_model(raw_df['Latitude'], raw_df['Allele'])\n",
    "print(clf0.intercept_, clf0.coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.0572187317602719e-20"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_reg_lik_ratio_test(raw_df['Latitude'], raw_df['Allele'], clf0, clf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multiple logistic regression\n",
    "\n",
    "Now following the [chapter of the same name](http://www.biostathandbook.com/multiplelogistic.html) in the same book.\n",
    "\n",
    "Here is an example using the data on bird introductions to New Zealand."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>species</th>\n",
       "      <th>status</th>\n",
       "      <th>length</th>\n",
       "      <th>mass</th>\n",
       "      <th>range</th>\n",
       "      <th>migr</th>\n",
       "      <th>insect</th>\n",
       "      <th>diet</th>\n",
       "      <th>clutch</th>\n",
       "      <th>broods</th>\n",
       "      <th>wood</th>\n",
       "      <th>upland</th>\n",
       "      <th>water</th>\n",
       "      <th>release</th>\n",
       "      <th>indiv</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Cyg_olor</td>\n",
       "      <td>1</td>\n",
       "      <td>1520</td>\n",
       "      <td>9600.0</td>\n",
       "      <td>1.21</td>\n",
       "      <td>1</td>\n",
       "      <td>12.0</td>\n",
       "      <td>2</td>\n",
       "      <td>6.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "      <td>29.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Cyg_atra</td>\n",
       "      <td>1</td>\n",
       "      <td>1250</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>0.56</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1</td>\n",
       "      <td>6.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>10</td>\n",
       "      <td>85.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Cer_nova</td>\n",
       "      <td>1</td>\n",
       "      <td>870</td>\n",
       "      <td>3360.0</td>\n",
       "      <td>0.07</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>8.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Ans_caer</td>\n",
       "      <td>0</td>\n",
       "      <td>720</td>\n",
       "      <td>2517.0</td>\n",
       "      <td>1.10</td>\n",
       "      <td>3</td>\n",
       "      <td>12.0</td>\n",
       "      <td>2</td>\n",
       "      <td>3.8</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>10.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Ans_anse</td>\n",
       "      <td>0</td>\n",
       "      <td>820</td>\n",
       "      <td>3170.0</td>\n",
       "      <td>3.45</td>\n",
       "      <td>3</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1</td>\n",
       "      <td>5.9</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>7.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    species  status  length    mass  range  migr  insect  diet  clutch  \\\n",
       "0  Cyg_olor       1    1520  9600.0   1.21     1    12.0     2     6.0   \n",
       "1  Cyg_atra       1    1250  5000.0   0.56     1     0.0     1     6.0   \n",
       "2  Cer_nova       1     870  3360.0   0.07     1     0.0     1     4.0   \n",
       "3  Ans_caer       0     720  2517.0   1.10     3    12.0     2     3.8   \n",
       "4  Ans_anse       0     820  3170.0   3.45     3     0.0     1     5.9   \n",
       "\n",
       "   broods  wood  upland  water  release  indiv  \n",
       "0     1.0     0       0      1        6   29.0  \n",
       "1     1.0     0       0      1       10   85.0  \n",
       "2     1.0     0       0      1        3    8.0  \n",
       "3     1.0     0       0      1        1   10.0  \n",
       "4     1.0     0       0      1        2    7.0  "
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data=\"\"\"\n",
    "Cyg_olor 1 1520  9600 1.21 1 12 2  6   1 0 0 1  6 29\n",
    "Cyg_atra 1 1250  5000 0.56 1  0 1  6   1 0 0 1 10 85\n",
    "Cer_nova 1  870  3360 0.07 1  0 1  4   1 0 0 1  3 8\n",
    "Ans_caer 0  720  2517 1.1  3 12 2  3.8 1 0 0 1  1 10\n",
    "Ans_anse 0  820  3170 3.45 3  0 1  5.9 1 0 0 1  2 7\n",
    "Bra_cana 1  770  4390 2.96 2  0 1  5.9 1 0 0 1 10 60\n",
    "Bra_sand 0   50  1930 0.01 1  0 1  4   2 0 0 0  1 2\n",
    "Alo_aegy 0  680  2040 2.71 1  . 2  8.5 1 0 0 1  1 8\n",
    "Ana_plat 1  570  1020 9.01 2  6 2 12.6 1 0 0 1 17 1539\n",
    "Ana_acut 0  580   910 7.9  3  6 2  8.3 1 0 0 1  3 102\n",
    "Ana_pene 0  480   590 4.33 3  0 1  8.7 1 0 0 1  5 32\n",
    "Aix_spon 0  470   539 1.04 3 12 2 13.5 2 1 0 1  5 10\n",
    "Ayt_feri 0  450   940 2.17 3 12 2  9.5 1 0 0 1  3 9\n",
    "Ayt_fuli 0  435   684 4.81 3 12 2 10.1 1 0 0 1  2 5\n",
    "Ore_pict 0  275   230 0.31 1  3 1  9.5 1 1 1 0  9 398\n",
    "Lop_cali 1  256   162 0.24 1  3 1 14.2 2 0 0 0 15 1420\n",
    "Col_virg 1  230   170 0.77 1  3 1 13.7 1 0 0 0 17 1156\n",
    "Ale_grae 1  330   501 2.23 1  3 1 15.5 1 0 1 0 15 362\n",
    "Ale_rufa 0  330   439 0.22 1  3 2 11.2 2 0 0 0  2 20\n",
    "Per_perd 0  300   386 2.4  1  3 1 14.6 1 0 1 0 24 676\n",
    "Cot_pect 0  182    95 0.33 3  . 2  7.5 1 0 0 0  3 .\n",
    "Cot_aust 1  180    95 0.69 2 12 2 11   1 0 0 1 11 601\n",
    "Lop_nyct 0  800  1150 0.28 1 12 2  5   1 1 1 0  4 6\n",
    "Pha_colc 1  710   850 1.25 1 12 2 11.8 1 1 0 0 27 244\n",
    "Syr_reev 0  750   949 0.2  1 12 2  9.5 1 1 1 0  2 9\n",
    "Tet_tetr 0  470   900 4.17 1  3 1  7.9 1 1 1 0  2 13\n",
    "Lag_lago 0  390   517 7.29 1  0 1  7.5 1 1 1 0  2 4\n",
    "Ped_phas 0  440   815 1.83 1  3 1 12.3 1 1 0 0  1 22\n",
    "Tym_cupi 0  435   770 0.26 1  4 1 12   1 0 0 0  3 57\n",
    "Van_vane 0  300   226 3.93 2 12 3  3.8 1 0 0 0  8 124\n",
    "Plu_squa 0  285   318 1.67 3 12 3  4   1 0 0 1  2 3\n",
    "Pte_alch 0  350   225 1.21 2  0 1  2.5 2 0 0 0  1 8\n",
    "Pha_chal 0  320   350 0.6  1 12 2  2   2 1 0 0  8 42\n",
    "Ocy_loph 0  330   205 0.76 1  0 1  2   7 1 0 1  4 23\n",
    "Leu_mela 0  372     . 0.07 1 12 2  2   1 1 0 0  6 34\n",
    "Ath_noct 1  220   176 4.84 1 12 3  3.6 1 1 0 0  7 221\n",
    "Tyt_alba 0  340   298 8.9  2  0 3  5.7 2 1 0 0  1 7\n",
    "Dac_nova 1  460   382 0.34 1 12 3  2   1 1 0 0  7 21\n",
    "Lul_arbo 0  150  32.1 1.78 2  4 2  3.9 2 1 0 0  1 5\n",
    "Ala_arve 1  185  38.9 5.19 2 12 2  3.7 3 0 0 0 11 391\n",
    "Pru_modu 1  145  20.5 1.95 2 12 2  3.4 2 1 0 0 14 245\n",
    "Eri_rebe 0  140  15.8 2.31 2 12 2  5   2 1 0 0 11 123\n",
    "Lus_mega 0  161  19.4 1.88 3 12 2  4.7 2 1 0 0  4 7\n",
    "Tur_meru 1  255  82.6 3.3  2 12 2  3.8 3 1 0 0 16 596\n",
    "Tur_phil 1  230  67.3 4.84 2 12 2  4.7 2 1 0 0 12 343\n",
    "Syl_comm 0  140  12.8 3.39 3 12 2  4.6 2 1 0 0  1 2\n",
    "Syl_atri 0  142  17.5 2.43 2  5 2  4.6 1 1 0 0  1 5\n",
    "Man_mela 0  180     . 0.04 1 12 3  1.9 5 1 0 0  1 2\n",
    "Man_mela 0  265    59 0.25 1 12 2  2.6 . 1 0 0  1 80\n",
    "Gra_cyan 0  275   128 0.83 1 12 3  3   2 1 0 1  1 .\n",
    "Gym_tibi 1  400   380 0.82 1 12 3  4   1 1 0 0 15 448\n",
    "Cor_mone 0  335   203 3.4  2 12 2  4.5 1 1 0 0  2 3\n",
    "Cor_frug 1  400   425 3.73 1 12 2  3.6 1 1 0 0 10 182\n",
    "Stu_vulg 1  222  79.8 3.33 2  6 2  4.8 2 1 0 0 14 653\n",
    "Acr_tris 1  230 111.3 0.56 1 12 2  3.7 1 1 0 0  5 88\n",
    "Pas_dome 1  149  28.8 6.5  1  6 2  3.9 3 1 0 0 12 416\n",
    "Pas_mont 0  133    22 6.8  1  6 2  4.7 3 1 0 0  3 14\n",
    "Aeg_temp 0  120     . 0.17 1  6 2  4.7 3 1 0 0  3 14\n",
    "Emb_gutt 0  120    19 0.15 1  4 1  5   3 0 0 0  4 112\n",
    "Poe_gutt 0  100  12.4 0.75 1  4 1  4.7 3 0 0 0  1 12\n",
    "Lon_punc 0  110  13.5 1.06 1  0 1  5   3 0 0 0  1 8\n",
    "Lon_cast 0  100     . 0.13 1  4 1  5   . 0 0 1  4 45\n",
    "Pad_oryz 0  160     . 0.09 1  0 1  5   . 0 0 0  2 6\n",
    "Fri_coel 1  160  23.5 2.61 2 12 2  4.9 2 1 0 0 17 449\n",
    "Fri_mont 0  146  21.4 3.09 3 10 2  6   . 1 0 0  7 121\n",
    "Car_chlo 1  147    29 2.09 2  7 2  4.8 2 1 0 0  6 65\n",
    "Car_spin 0  117    12 2.09 3  3 1  4   2 1 0 0  3 54\n",
    "Car_card 1  120  15.5 2.85 2  4 1  4.4 3 1 0 0 14 626\n",
    "Aca_flam 1  115  11.5 5.54 2  6 1  5   2 1 0 0 10 607\n",
    "Aca_flavi 0  133    17 1.67 2  0 1  5   3 0 1 0  3 61\n",
    "Aca_cann 0  136  18.5 2.52 2  6 1  4.7 2 1 0 0 12 209\n",
    "Pyr_pyrr 0  142  23.5 3.57 1  4 1  4   3 1 0 0  2 .\n",
    "Emb_citr 1  160  28.2 4.11 2  8 2  3.3 3 1 0 0 14 656\n",
    "Emb_hort 0  163  21.6 2.75 3 12 2  5   1 0 0 0  1 6\n",
    "Emb_cirl 1  160  23.6 0.62 1 12 2  3.5 2 1 0 0  3 29\n",
    "Emb_scho 0  150  20.7 5.42 1 12 2  5.1 2 0 0 1  2 9\n",
    "Pir_rubr 0  170    31 0.55 3 12 2  4   . 1 0 0  1 2\n",
    "Age_phoe 0  210  36.9 2    2  8 2  3.7 1 0 0 1  1 2\n",
    "Stu_negl 0  225 106.5 1.2  2 12 2  4.8 2 0 0 0  1 2\n",
    "\"\"\"\n",
    "cols = 'species status length mass range migr insect diet clutch broods wood upland water release indiv'.split()\n",
    "ind_vars = cols[2:]\n",
    "df = pd.read_table(io.StringIO(data), names=cols, header=None, delim_whitespace=True, na_values=['.'])\n",
    "df.dropna(inplace=True)\n",
    "y_true = df['status']\n",
    "X = df[ind_vars]\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def log_reg_fit(X, y):\n",
    "    clf = sklearn.linear_model.LogisticRegression(C=1e12)\n",
    "    if X.ndim == 1:\n",
    "        X = X.reshape(-1, 1)\n",
    "    clf.fit(X, y)\n",
    "    return clf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Adding release with p-value 4.9e-09\n",
      "Adding upland with p-value 0.0044\n",
      "Adding migr with p-value 0.011\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "['release', 'upland', 'migr']"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def forward_selection(X, y_true, pvals_threshold = 0.05):\n",
    "    ind_vars = X.columns\n",
    "    clf0 = log_reg_null_model(y_true, y_true)\n",
    "    included_vars = []\n",
    "    excluded_vars = list(ind_vars)\n",
    "\n",
    "    while excluded_vars:\n",
    "        selected_var, pval = None, 1\n",
    "        for var in excluded_vars:\n",
    "            X_ = X[included_vars + [var]]\n",
    "            clf = log_reg_fit(X_, y_true)\n",
    "            pval_ = log_reg_lik_ratio_test(X_, y_true, clf0, clf)\n",
    "            if pval_ < pval:\n",
    "                selected_var, pval = var, pval_\n",
    "        if pval < pvals_threshold:\n",
    "            print(\"Adding {} with p-value {:.2g}\".format(selected_var, pval))\n",
    "            included_vars.append(selected_var)\n",
    "            excluded_vars.remove(selected_var)\n",
    "            X_ = X[included_vars].copy()\n",
    "            X_['placeholder'] = 0\n",
    "            clf0 = log_reg_fit(X_, y_true)\n",
    "        else:\n",
    "            break\n",
    "    return included_vars\n",
    "\n",
    "forward_selection(X, y_true)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I get a similar result to the one presented by John, but I need a smaller P value threshold (I used 0.05 instead of 0.15). With 0.15 I get several more variables. Not sure why... Maybe the P value calculation in the book is using Wald test (used by SAS in the example given in the book), whereas I'm using the likelihood ratio test (which I believe is a better choice here)."
   ]
  }
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