Aprendizaje_supervisado/Cuadernos/su_0050_Regresion_Poisson.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <span style=\"color:#F72585\"><center>Modelo de Regresión Poisson</center></span>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "<figure>\n",
    "<center>\n",
    "<img src=\"../Imagenes/Bacterias.jpg\" width=\"600\" height=\"600\" align=\"center\" /> \n",
    "</center>   \n",
    "</figure>\n",
    "\n",
    "<a href=\"https://commons.wikimedia.org/wiki/File:Bacteria_collage.jpg\">148LENIN</a>, <a href=\"https://creativecommons.org/licenses/by-sa/4.0\">CC BY-SA 4.0</a>, via Wikimedia Commons"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <span style=\"color:#4361EE\">Referencias</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. [Dobson y Baernett, An introduction oto Generalizer Linear Modesl](http://library.lol/main/472B57FA461867F6CFB4334BFED60010)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <span style=\"color:#4361EE\">Introducción</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En esta lección introducimos iuno de los modelos GLM mas utlizados en la práctica."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <span style=\"color:#4361EE\">Modelo Poission</span> "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <span style=\"color:#4CC9F0\">Distribución de probabilidad Poisson</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Primero vamos a recordar la distribución de Poisson. Este es un modelo de probabilidad que se encuentra usualmente en problemas de conteos. Piense por ejemplo en el número de vehículos que pasan por un punto de la ciudad en una hora y día de la semana en condiciones y fechas normales. Entonces ese número puede ser digamos 15, 16, 17, 18, 19, 20.\n",
    "\n",
    "La función de probabilidad del modelo Poisson es dado por\n",
    "\n",
    "$$\n",
    "p(x|\\mu) = \\frac{e^{-\\mu} \\mu^x }{x!}, \\mu >0, \\hspace{1mm} x =0,1,2, \\ldots\n",
    "$$\n",
    "\n",
    "El único parámetro $\\lambda$ en este caso puede interpretarse como la rata de valores que pueden observarse por unidad de tiempo, área, etc. Por ejemplo, en el caso mencionamos arriba de los automóviles, quizás esa rata sea un valor entre 17 y 18. \n",
    "\n",
    "Antes de avanzar vamos a suponer $\\mu = 17.5 $ y hagamos un gráfico de la función de probabilidad. Pero inicialmente vamos a calcular la media y la varianza de la distribución.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Distribución Poisson(17.5); media = 17.5, varianza 17.5\n",
      "Distribución Poisson(17.5); probabilidades=[0.25 0.5  0.75]; cuantiles=[15. 17. 20.]\n"
     ]
    }
   ],
   "source": [
    "# media y varianza de la distribución Poisson(17.5)\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import poisson \n",
    "\n",
    "mu = 17.5\n",
    "pois = poisson(mu)\n",
    "media, var = pois.stats(moments=\"mv\")\n",
    "print('Distribución Poisson(17.5); media = {}, varianza {}'.format(media, var))\n",
    "\n",
    "# calcula algunos cuantiles de la distribución\n",
    "prob = np.array([0.25, 0.5, 0.75])\n",
    "cuantiles = pois.ppf(prob)\n",
    "print('Distribución Poisson(17.5); probabilidades={}; cuantiles={}'.format(prob, cuantiles))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# función de probabilidad Poisson(17.5)\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import poisson\n",
    "\n",
    "mu = 17.5\n",
    "pois = poisson(mu)\n",
    "\n",
    "#Calcula los valores de probabilidad para los valores 0, 1, 2, ...,40\n",
    "x = range(40)\n",
    "prob_p = pois.pmf(x)\n",
    "data = pd.DataFrame(zip(x,prob_p))\n",
    "data.columns=['x','p']\n",
    "ax = sns.barplot(data=data, x='x', y='p')\n",
    "ax.set(xlabel='x', ylabel='p(x|$\\mu$)', title='Función de probabilidad de la distribución Poisson({})'.format(mu))\n",
    "ax.set_xticklabels(x, rotation=90, size=5)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <span style=\"color:#4361EE\">Estimación puntual del parámetro $\\mu$</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Supongamos que se hacen $n$ observaciones independientes de una distribución Pois$(\\mu)$. La distribución conjunta es data por\n",
    "\n",
    "$$\n",
    "p(x_1, x_2, \\ldots, x_n|\\mu) = \\prod_{i=1}^n  Pois(x_i|\\mu) = \\prod_{i=1}^n \\frac{e^{-\\mu} \\mu^{x_i}}{x_i!}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La función de log-verosimilitud es dada por\n",
    "\n",
    "\n",
    "$$\n",
    "\\mathcal{L}(\\mu) = \\sum_{i=1}^n - \\mu + x_i\\log \\mu - \\log x!.\n",
    "$$\n",
    "\n",
    "Derivando con respecto a $\\mu$ e igualando a cero se obtiene la solución\n",
    "\n",
    "$$\n",
    "\\hat{\\mu} = \\frac{1}{n}\\sum_{i=1}^n x_i.\n",
    "$$\n",
    "\n",
    "En el ejemplo de los vehículos, se tiene que $n=6$, $\\sum_{i=1}^n = 105$,  en consecuencia se tiene que\n",
    "\n",
    "$$\n",
    "\\hat{\\mu} = \\frac{105}{6} = 17.5.\n",
    "$$\n",
    "\n",
    "La siguiente imagen muestra la función de pérdida $\\mathcal{L}(\\mu)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "x = np.array(np.arange(15,21))\n",
    "mu = np.arange(12, 24.5,0.1)\n",
    "def loss(mu,x):\n",
    "    return np.sum(-mu + np.log(mu)*x - np.sum(np.arange(15,21)))\n",
    "y = np.array([loss(m,x) for m in mu])\n",
    "\n",
    "z = [17.5, 17.5]\n",
    "w = [-441., -434.5]\n",
    "plt.plot(mu,y,color='blue')\n",
    "plt.plot(z,w, color='red')\n",
    "plt\n",
    "plt.title('función de log-verosimilitud $\\mathcal{L}(\\mu)$')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <span style=\"color:#4CC9F0\">Regresión Poisson</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ejemplo tomado de [Regresión de Poisson](https://estadistica-dma.ulpgc.es/MEAV/Ejemplo_Regresi%C3%B3n_Poisson.html). En un estudio sobre la población de un parásito se hizo un recuento de parásitos en 15 localizaciones con diversas condiciones ambientales. Los datos obtenidos son los siguientes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Temperatura</th>\n",
       "      <th>Humedad</th>\n",
       "      <th>Conteo</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>15</td>\n",
       "      <td>70</td>\n",
       "      <td>156</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>16</td>\n",
       "      <td>65</td>\n",
       "      <td>157</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>24</td>\n",
       "      <td>71</td>\n",
       "      <td>177</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>13</td>\n",
       "      <td>64</td>\n",
       "      <td>145</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>21</td>\n",
       "      <td>84</td>\n",
       "      <td>197</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>16</td>\n",
       "      <td>86</td>\n",
       "      <td>184</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>22</td>\n",
       "      <td>72</td>\n",
       "      <td>172</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>18</td>\n",
       "      <td>84</td>\n",
       "      <td>187</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>20</td>\n",
       "      <td>71</td>\n",
       "      <td>157</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>16</td>\n",
       "      <td>75</td>\n",
       "      <td>169</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>28</td>\n",
       "      <td>84</td>\n",
       "      <td>200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>27</td>\n",
       "      <td>79</td>\n",
       "      <td>193</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>13</td>\n",
       "      <td>80</td>\n",
       "      <td>167</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>22</td>\n",
       "      <td>76</td>\n",
       "      <td>170</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>23</td>\n",
       "      <td>88</td>\n",
       "      <td>192</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Temperatura  Humedad  Conteo\n",
       "0            15       70     156\n",
       "1            16       65     157\n",
       "2            24       71     177\n",
       "3            13       64     145\n",
       "4            21       84     197\n",
       "5            16       86     184\n",
       "6            22       72     172\n",
       "7            18       84     187\n",
       "8            20       71     157\n",
       "9            16       75     169\n",
       "10           28       84     200\n",
       "11           27       79     193\n",
       "12           13       80     167\n",
       "13           22       76     170\n",
       "14           23       88     192"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "parasitos = {'Temperatura':[15,16,24,13,21,16,22,18,20,16,28,27,13,22,23],\n",
    "             'Humedad': [70,65,71,64,84,86,72,84,71,75,84,79,80,76,88],\n",
    "             'Conteo':[156,157,177,145,197,184,172,187,157,169,200,193,167,170,192]}\n",
    "parasitos = pd.DataFrame(parasitos)\n",
    "parasitos "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <span style=\"color:#4CC9F0\">Estadísticas Descriptivas</span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 750x750 with 12 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "sns.pairplot(parasitos, diag_kind=\"kde\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <span style=\"color:#4CC9F0\">Planteamiento del problema</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Por razones de claridad denotaremos Temperatura, Humedad y Conteo respectivamente como $\\mathbf{x}_1,\\mathbf{x}_2$ y $\\mathbf{y}$. Supondremos que tenemos una muestra de vectores independientes $(y_i,x_{1i}, x_{2i})^t$, $i=1, 2, \\ldots, n$. Las gráficas descriptivas revelan una relación lineal entre la variable de Conteo y las variables Temperatura y Humedad. Como Conteo es realmente una variable de conteo, la relación entre las variables se plantea de la siguiente forma.\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "y_i &\\sim \\text{Poi}(\\mu_i)\\\\\n",
    "\\log  \\mu_i &=  w_1x_{1i} + w_2x_{2i} + b\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "La razón de escribir $\\log \\mu_i$, en lugar de simplemente $\\mu_i$ es la siguiente. Todos los $\\mu_i>0$, pero las expresiones lineales $w_1x_{1i} + w_2x_{2i} + b$ pueden toma cualquier valor real. Al tomar $\\log \\mu_i$ desaparece el problema. La función $\\log$ en este caso se llama función de enlace. Esta función pone en comunicación el predictor lineal $w_1x_{1i} + w_2x_{2i} + b$ con la esperanza $\\mu_i$ de las variables $y_i$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <span style=\"color:#4CC9F0\">Modelo estadístico</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vamos a denotar $\\mathbf{y} = (y_1, y_2,  \\ldots, y_n)$, $\\mathbf{x} = [x_{ij}]_{n\\times 2}$,  $\\mathbf{w} = (w_1, w_2)$, $\\mathbf{x}_i =(x_{1i}, x_{2i})^t$\n",
    "\n",
    "\n",
    "Asumiremos que las variables $[y_i|x_{1i},x_{2i}, w_1,w_2,b ]$ son independientes. En consecuencia la distribución conjunta es dada por\n",
    "\n",
    "$$\n",
    "p(\\mathbf{y}|, \\mathbf{w}, b) = \\prod_{i=1}^n \\frac{e^{-\\mu_i} \\mu_i^{y_i}}{y_i!}\n",
    "$$\n",
    "\n",
    "\n",
    "La estimación máximo verosímil es el valor en donde se maximiza la función de log-verosimiltud  $\\mathcal{L} = \\log f(\\mathbf{w}, b |\\mathbf{x})$.\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "\\mathcal{L}(\\mathbf{w}, b) &=  \\sum_i \\left[ -(\\mu_i) + y_i \\log (\\mu_i) -\\log y_i! \\right]\\\\\n",
    "\\log \\mu_i &=  w_1x_{1i} + w_2x_{2i} + b,\n",
    "\\end{align} \n",
    "$$\n",
    "\n",
    "En el lenguaje de los modelos de regresión $\\mu_i$ es identificado como la variable predictora. Por esa razón tomamos la licencia de escribir\n",
    "\n",
    "$$\n",
    "\\hat{y_i} = \\mu_i\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "### <span style=\"color:#4CC9F0\">Deviance en el modelo de Poisson</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El modelo saturado o con el número máximo de parámetros es aquel en el cual $\\hat{y_i}= y_i$. Entonces un cálculo directo muestra que la deciance en este caso es\n",
    "\n",
    "$$\n",
    "\\text{Deviance} = -2\\left[\\sum_i \\left(-\\mu_i + y_i \\log \\mu_i \\right) - \\sum_i \\left(-y_i + y_i \\log y_i \\right) \\right] = 2 \\sum_i \\left[y_i \\log \\left(\\frac{y_i}{\\mu_i}\\right) - (y_i-\\mu_i)   \\right]\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <span style=\"color:#4CC9F0\">Modelos GLM con Statsmodels de Python</span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# conda install -c anaconda statsmodels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Número de valores únicos por variable\n",
      " Temperatura    11\n",
      "Humedad        12\n",
      "Conteo         14\n",
      "dtype: int64\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Generalized Linear Model Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>        <td>Conteo</td>      <th>  No. Observations:  </th>  <td>    15</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                  <td>GLM</td>       <th>  Df Residuals:      </th>  <td>    12</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model Family:</th>         <td>Poisson</td>     <th>  Df Model:          </th>  <td>     2</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Link Function:</th>          <td>Log</td>       <th>  Scale:             </th> <td>  1.0000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>                <td>IRLS</td>       <th>  Log-Likelihood:    </th> <td> -53.462</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>            <td>Sun, 20 Nov 2022</td> <th>  Deviance:          </th> <td>  1.9468</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                <td>16:03:14</td>     <th>  Pearson chi2:      </th>  <td>  1.94</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Iterations:</th>          <td>3</td>        <th>  Pseudo R-squ. (CS):</th>  <td>0.7536</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>     <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "       <td></td>          <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercepto</th>  <td>    5.1600</td> <td>    0.020</td> <td>  263.202</td> <td> 0.000</td> <td>    5.122</td> <td>    5.198</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Temperatura</th> <td>    0.0417</td> <td>    0.021</td> <td>    2.018</td> <td> 0.044</td> <td>    0.001</td> <td>    0.082</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Humedad</th>     <td>    0.0664</td> <td>    0.021</td> <td>    3.163</td> <td> 0.002</td> <td>    0.025</td> <td>    0.108</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                 Generalized Linear Model Regression Results                  \n",
       "==============================================================================\n",
       "Dep. Variable:                 Conteo   No. Observations:                   15\n",
       "Model:                            GLM   Df Residuals:                       12\n",
       "Model Family:                 Poisson   Df Model:                            2\n",
       "Link Function:                    Log   Scale:                          1.0000\n",
       "Method:                          IRLS   Log-Likelihood:                -53.462\n",
       "Date:                Sun, 20 Nov 2022   Deviance:                       1.9468\n",
       "Time:                        16:03:14   Pearson chi2:                     1.94\n",
       "No. Iterations:                     3   Pseudo R-squ. (CS):             0.7536\n",
       "Covariance Type:            nonrobust                                         \n",
       "===============================================================================\n",
       "                  coef    std err          z      P>|z|      [0.025      0.975]\n",
       "-------------------------------------------------------------------------------\n",
       "Intercepto      5.1600      0.020    263.202      0.000       5.122       5.198\n",
       "Temperatura     0.0417      0.021      2.018      0.044       0.001       0.082\n",
       "Humedad         0.0664      0.021      3.163      0.002       0.025       0.108\n",
       "===============================================================================\n",
       "\"\"\""
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# librerías\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "import statsmodels.api as sm\n",
    "\n",
    "# datos\n",
    "parasitos = {'Temperatura':[15,16,24,13,21,16,22,18,20,16,28,27,13,22,23],\n",
    "             'Humedad': [70,65,71,64,84,86,72,84,71,75,84,79,80,76,88],\n",
    "             'Conteo':[156,157,177,145,197,184,172,187,157,169,200,193,167,170,192]}\n",
    "parasitos = pd.DataFrame(parasitos)\n",
    "\n",
    "# prepara los datos para la regresión\n",
    "X = parasitos.drop(\"Conteo\", axis=1)\n",
    "y = parasitos.Conteo\n",
    "nomb_caract = X.columns.to_list()\n",
    "\n",
    "# escala las características (variables)\n",
    "standizer = StandardScaler()\n",
    "X = standizer.fit_transform(X)\n",
    "\n",
    "# revisa número de valores únicos en cada característica\n",
    "print('Número de valores únicos por variable\\n', parasitos.select_dtypes(\"int\").nunique())\n",
    "\n",
    "# ajusta un modelo de regresión de Poisson a los datos\n",
    "exog = sm.add_constant(X)\n",
    "poission_model = sm.GLM(y, exog, family=sm.families.Poisson())\n",
    "result = poission_model.fit()\n",
    "result.summary(xname=['Intercepto'] + nomb_caract)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <span style=\"color:#4361EE\">Interpretación de la salida de la regresión </span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <span style=\"color:#4CC9F0\">Coeficientes y p-valores</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. La estimación de los coeficientes , `coef`, en la salida indica el cambio en el logaritmo de los $\\mu_i$, es decir en el logaritmo de la predicciones del modelos. Por ejemplo, un aumento de una unidad en la variable predictora *Temperatura* está asociado con un cambio promedio de 0.0417 en el logaritmo de la variable de respuesta *Conteo*, manteniendo la variable *Humedad* sin ningún cambio. Esto significa que los valores más altos de *Temperatura* están asociados con una mayor probabilidad de la variable *Conteo*.\n",
    "\n",
    "1. El error estándar, `std err` da una idea de la variabilidad asociada con la estimación del coeficiente. Puede interpretar el error estándar como una estimación  desviación estándar de la distribución posterior del respectivo coeficiente.\n",
    "\n",
    "1. `El valor z`. Se obtiene al dividir la estimación del coeficiente por el error estándar.\n",
    "1. El `p- valor` Pr(>|z|)  dice la probabilidad asociada con un valor *z* particular. Básicamente, esta probabilidad nos dice qué tan bien cada variable predictora puede predecir el valor de la variable de respuesta en el modelo. Por ejemplo, el p-valor asociado con el valor *z* para la variable *Temperatura* es .044. Dado que este valor es inferior a 0,05, diríamos que *Temperatura* es una variable predictora estadísticamente significativa en el modelo. \n",
    "1. `Intervalo de confianza`: [0.025, 0.975]. Es una estimación por intervalo del 95%. La salida en esta caso no puede interpretarse directamente como un intervalo de credibilidad, pero es una aproximación razonable. En el ejemplo el intervalos de confianza reportado para el parámetro *Temperatura* es [0.001, 0.082].\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <span style=\"color:#4CC9F0\">Bondad de ajuste</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Las medidas de bondad de ajuste indican que tan bien ajusta el modelo a los datos. Si no está acostubrado o acostumbrada a estas medidas revise las siguientes  secciones.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "### <span style=\"color:#4CC9F0\">Estadística Chi cuadrado de Person: $X^2$</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Si $y_i$ representan los valores observados y $\\hat{y}_i$ los valores predichos por el modelo, la estadísitca $X^2$ se define por\n",
    "\n",
    "$$\n",
    "X^2 = \\sum_i \\frac{(y_i -  \\hat{y}_i)^2}{\\hat{y}_i}\n",
    "$$\n",
    "\n",
    "Asintóticamente se tiene que si el modelo ajusta bien a los datos, entonces aproximadamente  $X^2 \\sim \\chi^2(p-1)$. En donde  $p$ el número de parámetros.\n",
    "\n",
    "La deviance del modelo y la estadística $X^2$ coinciden asintóticamente en distribución. En el ejemplo $p=3$, por lo que si las cosas van bien $X^2 \\sim \\chi^2(2) $. Por lo que una valor de 1.94 indica un bueb ajuste global del modelo a los datos."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <span style=\"color:#4CC9F0\">Pseudo $R^2$</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Si $l$ es la función log verosimiltud de un modelo, $\\tilde{\\mu}$ la estimación parámetro minimal de un modelo, por lo general el intercepto, $\\hat{\\mu}$ la estimación del modelo bajo estudio, entonces\n",
    "\n",
    "$$\n",
    "\\text{pseudo} R^2 = \\frac{l(\\tilde{\\mu},y) -l(\\hat{\\mu},y) }{l(\\tilde{\\mu},y)}\n",
    "$$\n",
    "\n",
    "$\\text{pseudo} R^2$ representa la mejora del modelo en relación con el modelo nulo. Es análogo al $R^2$ de la regresión lineal clasica. \n",
    "\n",
    "- **Interpretación**. Valores cercanos a 1, indican un buen ajuste del modelo.\n",
    "\n",
    "En ejemplo el valor el valor de 0.75 indican un ajuste aceptable del modelo a los datos.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <span style=\"color:#4CC9F0\">Deviance del modelo</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La \"deviance del modelo\" (model deviance) es una medida importante en modelos de regresión generalizada (GLM) que se utiliza para evaluar que tan bien el modelo se ajusta a los datos. La deviance del modelo se calcula como una medida de ajuste y se compara con la deviance nula (null deviance) para determinar si el modelo proporciona una mejora significativa en la explicación de la variabilidad en los datos en comparación con un modelo nulo (modelo que incluye solo el intercepto y no tiene covariables).\n",
    "\n",
    "Matemáticamente, la deviance del modelo se calcula como la diferencia entre el logaritmo de la verosimilitud (likelihood) bajo el modelo ajustado y el logaritmo de la verosimilitud bajo el modelo nulo, multiplicada por 2. La fórmula es la siguiente:\n",
    "\n",
    "$$\n",
    "D_{\\text{modelo}} = -2(\\mathfrak{l}(\\text{modelo nulo}) - \\mathfrak{l}(\\text{modelo ajustado}))\n",
    "$$\n",
    "en donde:\n",
    "\n",
    "* $D_{\\text{modelo}}$ es la deviance del modelo.\n",
    "* $\\mathfrak{l}(\\text{modelo nulo})$ es el logaritmo de la verosimilitud bajo el modelo nulo (modelo más simple). Usualmente un modelo con intercepto únicamente.\n",
    "* $\\mathfrak{l}(\\text{modelo ajustado})$ es el logaritmo de la verosimilitud bajo el modelo ajustado (modelo que incluye covariables).\n",
    "\n",
    "La deviance del modelo se utiliza para evaluar si el modelo ajustado proporciona una mejora significativa en la explicación de la variabilidad en los datos en comparación con el modelo nulo. En general, un valor más bajo de deviance del modelo indica un mejor ajuste del modelo a los datos. La diferencia entre la deviance nula y la deviance del modelo se utiliza para realizar pruebas estadísticas para determinar si el modelo es estadísticamente significativo.\n",
    "\n",
    "En resumen, la deviance del modelo es una medida que se utiliza para evaluar la calidad del ajuste de un modelo en comparación con un modelo nulo y determinar si el modelo proporciona una mejora significativa en la explicación de los datos.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### <span style=\"color:#4CC9F0\">Distribución asintótica de la Deviance del modelo</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Si el modelo ajusta bien a los datos se tiene que asintóticamente $D_{\\text{modelo}} \\sim \\chi^2(p-1)$. En donde  $p$ el número de parámetros.\n",
    "\n",
    "La deviance del modelo y la estadística $X^2$ coinciden asintóticamente en distribución. En el ejemplo $p=3$, por lo que si las cosas van bien $D_{\\text{modelo}} \\sim \\chi^2(2) $. Por lo que una valor de 1.9468 indica un buen ajuste global del modelo a los datos."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}