{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Poisson GLM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-10-14T01:25:20.621872Z",
     "iopub.status.busy": "2023-10-14T01:25:20.621661Z",
     "iopub.status.idle": "2023-10-14T01:25:22.812768Z",
     "shell.execute_reply": "2023-10-14T01:25:22.811710Z",
     "shell.execute_reply.started": "2023-10-14T01:25:20.621847Z"
    }
   },
   "outputs": [],
   "source": [
    "from spglm.glm import GLM\n",
    "from spglm.family import Poisson\n",
    "import libpysal\n",
    "import numpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-10-14T01:25:22.816050Z",
     "iopub.status.busy": "2023-10-14T01:25:22.815535Z",
     "iopub.status.idle": "2023-10-14T01:25:22.827971Z",
     "shell.execute_reply": "2023-10-14T01:25:22.827075Z",
     "shell.execute_reply.started": "2023-10-14T01:25:22.816027Z"
    }
   },
   "outputs": [],
   "source": [
    "# Load sample dataset - columbus dataset\n",
    "db = libpysal.io.open(libpysal.examples.get_path(\"columbus.dbf\"))\n",
    "\n",
    "# Set dependent variable\n",
    "y = numpy.array(db.by_col(\"HOVAL\"))\n",
    "y = numpy.reshape(y, (49, 1))\n",
    "# Round dependent variable and convert to integer\n",
    "# for the example since Poisson is for discrete data\n",
    "y = numpy.round(y).astype(int)\n",
    "\n",
    "# Set indepdent varibLES\n",
    "X = []\n",
    "X.append(db.by_col(\"INC\"))\n",
    "X.append(db.by_col(\"CRIME\"))\n",
    "X = numpy.array(X).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-10-14T01:25:22.830327Z",
     "iopub.status.busy": "2023-10-14T01:25:22.829264Z",
     "iopub.status.idle": "2023-10-14T01:25:22.838574Z",
     "shell.execute_reply": "2023-10-14T01:25:22.837728Z",
     "shell.execute_reply.started": "2023-10-14T01:25:22.830299Z"
    }
   },
   "outputs": [],
   "source": [
    "# Estimate Poisson GLM\n",
    "\n",
    "# First instantiate a GLM model object\n",
    "# -- Set family to Poisson family object for Poisson GLM\n",
    "model = GLM(y, X, family=Poisson())  \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": "2023-10-14T01:25:22.840741Z",
     "iopub.status.busy": "2023-10-14T01:25:22.840162Z",
     "iopub.status.idle": "2023-10-14T01:25:22.847860Z",
     "shell.execute_reply": "2023-10-14T01:25:22.846183Z",
     "shell.execute_reply.started": "2023-10-14T01:25:22.840709Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 3.92159085  0.01183491 -0.01371397]\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": "2023-10-14T01:25:22.849667Z",
     "iopub.status.busy": "2023-10-14T01:25:22.849168Z",
     "iopub.status.idle": "2023-10-14T01:25:22.856454Z",
     "shell.execute_reply": "2023-10-14T01:25:22.855375Z",
     "shell.execute_reply.started": "2023-10-14T01:25:22.849638Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.13049161 0.00511599 0.00193769]\n"
     ]
    }
   ],
   "source": [
    "# Parameter standard errors\n",
    "print(results.bse)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-10-14T01:25:22.858131Z",
     "iopub.status.busy": "2023-10-14T01:25:22.857667Z",
     "iopub.status.idle": "2023-10-14T01:25:22.862737Z",
     "shell.execute_reply": "2023-10-14T01:25:22.861829Z",
     "shell.execute_reply.started": "2023-10-14T01:25:22.858109Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[30.0524361   2.31331634 -7.07748998]\n"
     ]
    }
   ],
   "source": [
    "# Parameter t-values\n",
    "print(results.tvalues)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-10-14T01:25:22.867196Z",
     "iopub.status.busy": "2023-10-14T01:25:22.866846Z",
     "iopub.status.idle": "2023-10-14T01:25:22.873009Z",
     "shell.execute_reply": "2023-10-14T01:25:22.870993Z",
     "shell.execute_reply.started": "2023-10-14T01:25:22.867174Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "500.8518417993878\n"
     ]
    }
   ],
   "source": [
    "# Model AIC\n",
    "print(results.aic)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda env:py311_spglm]",
   "language": "python",
   "name": "conda-env-py311_spglm-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}