{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Binomial GLM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-10-14T01:22:52.996793Z",
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     "iopub.status.idle": "2023-10-14T01:22:54.292332Z",
     "shell.execute_reply": "2023-10-14T01:22:54.291240Z",
     "shell.execute_reply.started": "2023-10-14T01:22:52.996686Z"
    }
   },
   "outputs": [],
   "source": [
    "from spglm.glm import GLM\n",
    "from spglm.family import Binomial\n",
    "import numpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-10-14T01:22:54.296350Z",
     "iopub.status.busy": "2023-10-14T01:22:54.295680Z",
     "iopub.status.idle": "2023-10-14T01:22:54.316200Z",
     "shell.execute_reply": "2023-10-14T01:22:54.314911Z",
     "shell.execute_reply.started": "2023-10-14T01:22:54.296296Z"
    }
   },
   "outputs": [],
   "source": [
    "# Load sample dataset - Subset of london house price dataset\n",
    "#db = ps.open(ps.get_path(\"columbus.dbf\"), \"r\")\n",
    "\n",
    "#Set dependent variable\n",
    "y = numpy.array([0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,\n",
    "    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0,\n",
    "    0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,\n",
    "    0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
    "    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,\n",
    "    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
    "    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
    "    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,\n",
    "    0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1,\n",
    "    0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,\n",
    "    0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,\n",
    "    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,\n",
    "    0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0,\n",
    "    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])\n",
    "y = y.reshape((316,1))\n",
    "\n",
    "#Set independent variable (FLOORSZ)\n",
    "X = numpy.array([ 77,  75,  64,  95, 107, 100,  81, 151,  98, 260, 171, 161,  91,\n",
    "    80,  50,  85,  52,  69,  60,  84, 155,  97,  69, 126,  90,  43,\n",
    "    51,  41, 140,  80,  52,  86,  66,  60,  40, 155, 138,  97, 115,\n",
    "    148, 206,  60,  53,  96,  88, 160,  31,  43, 154,  60, 131,  60,\n",
    "    46,  61, 125, 150,  76,  92,  96, 100, 105,  72,  48,  41,  72,\n",
    "    65,  60,  65,  98,  33, 144, 111,  91, 108,  38,  48,  95,  63,\n",
    "    98, 129, 108,  51, 131,  66,  48, 127,  76,  68,  52,  64,  57,\n",
    "    121,  67,  76, 112,  96,  90,  53,  93,  64,  97,  58,  44, 157,\n",
    "    53,  70,  71, 167,  47,  70,  96,  77,  75,  71,  67,  47,  71,\n",
    "    90,  69,  64,  65,  95,  60,  60,  65,  54, 121, 105,  50,  85,\n",
    "    69,  69,  62,  65,  93,  93,  70,  62, 155,  68, 117,  80,  80,\n",
    "    75,  98, 114,  86,  70,  50,  51, 163, 124,  59,  95,  51,  63,\n",
    "    85,  53,  46, 102, 114,  83,  47,  40,  63, 123, 100,  63, 110,\n",
    "    79,  98,  99, 120,  52,  48,  37,  81,  30,  88,  50,  35, 116,\n",
    "    67,  45,  80,  86, 109,  59,  75,  60,  71, 141, 121,  50, 168,\n",
    "    90,  51, 133,  75, 133, 127,  37,  68, 105,  61, 123, 151, 110,\n",
    "    77, 220,  94,  77,  70, 100,  98, 126,  55, 105,  60, 176, 104,\n",
    "    68,  62,  70,  48, 102,  80,  97,  66,  80, 102, 160,  55,  60,\n",
    "    71, 125,  85,  85, 190, 137,  48,  41,  42,  51,  57,  60, 114,\n",
    "    88,  84, 108,  66,  85,  42,  98,  90, 127, 100,  55,  76,  82,\n",
    "    63,  80,  71,  76, 121, 109,  92, 160, 109, 185, 100,  90,  90,\n",
    "    86,  88,  95, 116, 135,  61,  74,  60, 235,  76,  66, 100,  49,\n",
    "    50,  37, 100,  88,  90,  52,  95,  81,  79,  96,  75,  91,  86,\n",
    "    83, 180, 108,  80,  96,  49, 117, 117,  86,  46,  66,  95,  57,\n",
    "    120, 137,  68, 240])\n",
    "X = X.reshape((316,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-10-14T01:22:54.317859Z",
     "iopub.status.busy": "2023-10-14T01:22:54.317442Z",
     "iopub.status.idle": "2023-10-14T01:22:54.328544Z",
     "shell.execute_reply": "2023-10-14T01:22:54.327834Z",
     "shell.execute_reply.started": "2023-10-14T01:22:54.317826Z"
    }
   },
   "outputs": [],
   "source": [
    "# Estimate Binomial GLM\n",
    "\n",
    "# First instantiate a GLM model object\n",
    "# -- Set family to Binomial family object for Binomial GLM\n",
    "model = GLM(y, X, family=Binomial())  \n",
    "\n",
    "# Then use the fit method to estimate coefficients and compute diagnostics\n",
    "results = model.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-10-14T01:22:54.330385Z",
     "iopub.status.busy": "2023-10-14T01:22:54.329865Z",
     "iopub.status.idle": "2023-10-14T01:22:54.335674Z",
     "shell.execute_reply": "2023-10-14T01:22:54.334451Z",
     "shell.execute_reply.started": "2023-10-14T01:22:54.330362Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-5.33638276  0.0287754 ]\n"
     ]
    }
   ],
   "source": [
    "# Estimated prameters, intercept is always the first column on the left\n",
    "print(results.params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-10-14T01:22:54.337573Z",
     "iopub.status.busy": "2023-10-14T01:22:54.337242Z",
     "iopub.status.idle": "2023-10-14T01:22:54.342482Z",
     "shell.execute_reply": "2023-10-14T01:22:54.341622Z",
     "shell.execute_reply.started": "2023-10-14T01:22:54.337545Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.64499904 0.00518312]\n"
     ]
    }
   ],
   "source": [
    "# Parameter standard errors\n",
    "print(results.bse)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-10-14T01:22:54.344204Z",
     "iopub.status.busy": "2023-10-14T01:22:54.343721Z",
     "iopub.status.idle": "2023-10-14T01:22:54.349208Z",
     "shell.execute_reply": "2023-10-14T01:22:54.348295Z",
     "shell.execute_reply.started": "2023-10-14T01:22:54.344177Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-8.27347396  5.55175826]\n"
     ]
    }
   ],
   "source": [
    "# Parameter t-values\n",
    "print(results.tvalues)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-10-14T01:22:54.354033Z",
     "iopub.status.busy": "2023-10-14T01:22:54.353469Z",
     "iopub.status.idle": "2023-10-14T01:22:54.358243Z",
     "shell.execute_reply": "2023-10-14T01:22:54.356998Z",
     "shell.execute_reply.started": "2023-10-14T01:22:54.354007Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "155.1934753034247\n"
     ]
    }
   ],
   "source": [
    "# Model AIC\n",
    "print(results.aic)"
   ]
  }
 ],
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