{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Gaussian GLM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-10-14T01:23:49.094651Z",
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     "iopub.status.idle": "2023-10-14T01:23:50.283296Z",
     "shell.execute_reply": "2023-10-14T01:23:50.282506Z",
     "shell.execute_reply.started": "2023-10-14T01:23:49.094628Z"
    }
   },
   "outputs": [],
   "source": [
    "from spglm.glm import GLM\n",
    "import libpysal\n",
    "import numpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-10-14T01:23:50.947534Z",
     "iopub.status.busy": "2023-10-14T01:23:50.946850Z",
     "iopub.status.idle": "2023-10-14T01:23:50.956114Z",
     "shell.execute_reply": "2023-10-14T01:23:50.954841Z",
     "shell.execute_reply.started": "2023-10-14T01:23:50.947502Z"
    }
   },
   "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",
    "\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": "2023-10-14T01:23:52.355767Z",
     "iopub.status.busy": "2023-10-14T01:23:52.355010Z",
     "iopub.status.idle": "2023-10-14T01:23:52.367917Z",
     "shell.execute_reply": "2023-10-14T01:23:52.366305Z",
     "shell.execute_reply.started": "2023-10-14T01:23:52.355719Z"
    }
   },
   "outputs": [],
   "source": [
    "# Estimate Gaussian GLM\n",
    "\n",
    "# First instantiate a GLM model object\n",
    "# -- Gaussian is the default family parameter so it doesn't need to be set\n",
    "model = GLM(y, X)  \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": "2023-10-14T01:23:53.261041Z",
     "iopub.status.busy": "2023-10-14T01:23:53.260511Z",
     "iopub.status.idle": "2023-10-14T01:23:53.267351Z",
     "shell.execute_reply": "2023-10-14T01:23:53.266163Z",
     "shell.execute_reply.started": "2023-10-14T01:23:53.261004Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[46.42818268  0.62898397 -0.48488854]\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": "2023-10-14T01:23:54.091698Z",
     "iopub.status.busy": "2023-10-14T01:23:54.091257Z",
     "iopub.status.idle": "2023-10-14T01:23:54.097334Z",
     "shell.execute_reply": "2023-10-14T01:23:54.096406Z",
     "shell.execute_reply.started": "2023-10-14T01:23:54.091672Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[13.19175703  0.53591045  0.18267291]\n"
     ]
    }
   ],
   "source": [
    "# Parameter standard errors\n",
    "print(results.bse)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-10-14T01:23:55.947271Z",
     "iopub.status.busy": "2023-10-14T01:23:55.946980Z",
     "iopub.status.idle": "2023-10-14T01:23:55.952002Z",
     "shell.execute_reply": "2023-10-14T01:23:55.950887Z",
     "shell.execute_reply.started": "2023-10-14T01:23:55.947249Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 3.51948437  1.17367365 -2.65440864]\n"
     ]
    }
   ],
   "source": [
    "# Parameter t-values\n",
    "print(results.tvalues)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-10-14T01:23:57.273553Z",
     "iopub.status.busy": "2023-10-14T01:23:57.273234Z",
     "iopub.status.idle": "2023-10-14T01:23:57.278805Z",
     "shell.execute_reply": "2023-10-14T01:23:57.277856Z",
     "shell.execute_reply.started": "2023-10-14T01:23:57.273534Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "408.73548964604873\n"
     ]
    }
   ],
   "source": [
    "# Model AIC\n",
    "print(results.aic)"
   ]
  }
 ],
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