Statsmodels example: Generalized Linear Models

example_glm.ipynb

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   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Generalized Linear Models"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import statsmodels.api as sm\n",
      "from scipy import stats\n",
      "from matplotlib import pyplot as plt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## GLM: Binomial response data\n",
      "\n",
      "### Load data\n",
      "\n",
      " In this example, we use the Star98 dataset which was taken with permission\n",
      " from Jeff Gill (2000) Generalized linear models: A unified approach. Codebook\n",
      " information can be obtained by typing: "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print sm.datasets.star98.NOTE"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Number of Observations - 303 (counties in California).\n",
        "\n",
        "Number of Variables - 13 and 8 interaction terms.\n",
        "\n",
        "Definition of variables names::\n",
        "\n",
        "    NABOVE   - Total number of students above the national median for the math\n",
        "               section.\n",
        "    NBELOW   - Total number of students below the national median for the math\n",
        "               section.\n",
        "    LOWINC   - Percentage of low income students\n",
        "    PERASIAN - Percentage of Asian student\n",
        "    PERBLACK - Percentage of black students\n",
        "    PERHISP  - Percentage of Hispanic students\n",
        "    PERMINTE - Percentage of minority teachers\n",
        "    AVYRSEXP - Sum of teachers' years in educational service divided by the\n",
        "               number of teachers.\n",
        "    AVSALK   - Total salary budget including benefits divided by the number of\n",
        "               full-time teachers (in thousands)\n",
        "    PERSPENK - Per-pupil spending (in thousands)\n",
        "    PTRATIO  - Pupil-teacher ratio.\n",
        "    PCTAF    - Percentage of students taking UC/CSU prep courses\n",
        "    PCTCHRT  - Percentage of charter schools\n",
        "    PCTYRRND - Percentage of year-round schools\n",
        "\n",
        "    The below variables are interaction terms of the variables defined above.\n",
        "\n",
        "    PERMINTE_AVYRSEXP\n",
        "    PEMINTE_AVSAL\n",
        "    AVYRSEXP_AVSAL\n",
        "    PERSPEN_PTRATIO\n",
        "    PERSPEN_PCTAF\n",
        "    PTRATIO_PCTAF\n",
        "    PERMINTE_AVTRSEXP_AVSAL\n",
        "    PERSPEN_PTRATIO_PCTAF\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Load the data and add a constant to the exogenous (independent) variables:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = sm.datasets.star98.load()\n",
      "data.exog = sm.add_constant(data.exog)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "/usr/local/lib/python2.7/dist-packages/statsmodels-0.5.0-py2.7-linux-x86_64.egg/statsmodels/tools/tools.py:306: FutureWarning: The default of `prepend` will be changed to True in 0.5.0, use explicit prepend\n",
        "  FutureWarning)\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      " The dependent variable is N by 2 (Success: NABOVE, Failure: NBELOW): "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print data.endog[:5,:]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[ 452.  355.]\n",
        " [ 144.   40.]\n",
        " [ 337.  234.]\n",
        " [ 395.  178.]\n",
        " [   8.   57.]]\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      " The independent variables include all the other variables described above, as\n",
      " well as the interaction terms:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print data.exog[:2,:]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[    34.3973       23.2993       14.23528      11.41112      15.91837\n",
        "      14.70646      59.15732       4.445207     21.71025      57.03276\n",
        "       0.           22.22222     234.102872    941.68811     869.9948\n",
        "      96.50656     253.52242    1238.1955    13848.8985     5504.0352\n",
        "       1.      ]\n",
        " [    17.36507      29.32838       8.234897      9.314884     13.63636\n",
        "      16.08324      59.50397       5.267598     20.44278      64.62264\n",
        "       0.            0.          219.316851    811.41756     957.0166\n",
        "     107.68435     340.40609    1321.0664    13050.2233     6958.8468\n",
        "       1.      ]]\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Fit and summary"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "glm_binom = sm.GLM(data.endog, data.exog, family=sm.families.Binomial())\n",
      "res = glm_binom.fit()\n",
      "print res.summary()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "                 Generalized Linear Model Regression Results                  \n",
        "==============================================================================\n",
        "Dep. Variable:           ['y1', 'y2']   No. Observations:                  303\n",
        "Model:                            GLM   Df Residuals:                      282\n",
        "Model Family:                Binomial   Df Model:                           20\n",
        "Link Function:                  logit   Scale:                             1.0\n",
        "Method:                          IRLS   Log-Likelihood:                -2998.6\n",
        "Date:                Sun, 26 Aug 2012   Deviance:                       4078.8\n",
        "Time:                        20:49:59   Pearson chi2:                 4.05e+03\n",
        "No. Iterations:                     6                                         \n",
        "==============================================================================\n",
        "                 coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
        "------------------------------------------------------------------------------\n",
        "x1            -0.0168      0.000    -38.749      0.000        -0.018    -0.016\n",
        "x2             0.0099      0.001     16.505      0.000         0.009     0.011\n",
        "x3            -0.0187      0.001    -25.182      0.000        -0.020    -0.017\n",
        "x4            -0.0142      0.000    -32.818      0.000        -0.015    -0.013\n",
        "x5             0.2545      0.030      8.498      0.000         0.196     0.313\n",
        "x6             0.2407      0.057      4.212      0.000         0.129     0.353\n",
        "x7             0.0804      0.014      5.775      0.000         0.053     0.108\n",
        "x8            -1.9522      0.317     -6.162      0.000        -2.573    -1.331\n",
        "x9            -0.3341      0.061     -5.453      0.000        -0.454    -0.214\n",
        "x10           -0.1690      0.033     -5.169      0.000        -0.233    -0.105\n",
        "x11            0.0049      0.001      3.921      0.000         0.002     0.007\n",
        "x12           -0.0036      0.000    -15.878      0.000        -0.004    -0.003\n",
        "x13           -0.0141      0.002     -7.391      0.000        -0.018    -0.010\n",
        "x14           -0.0040      0.000     -8.450      0.000        -0.005    -0.003\n",
        "x15           -0.0039      0.001     -4.059      0.000        -0.006    -0.002\n",
        "x16            0.0917      0.015      6.321      0.000         0.063     0.120\n",
        "x17            0.0490      0.007      6.574      0.000         0.034     0.064\n",
        "x18            0.0080      0.001      5.362      0.000         0.005     0.011\n",
        "x19            0.0002   2.99e-05      7.428      0.000         0.000     0.000\n",
        "x20           -0.0022      0.000     -6.445      0.000        -0.003    -0.002\n",
        "const          2.9589      1.547      1.913      0.057        -0.073     5.990\n",
        "==============================================================================\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Quantities of interest"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print 'Total number of trials:',  data.endog[0].sum()\n",
      "print 'Parameters: ', res.params\n",
      "print 'T-values: ', res.tvalues"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Total number of trials: 807.0\n",
        "Parameters:  [-0.01681504  0.00992548 -0.01872421 -0.01423856  0.25448717  0.24069366\n",
        "  0.08040867 -1.9521605  -0.33408647 -0.16902217  0.0049167  -0.00357996\n",
        " -0.01407656 -0.00400499 -0.0039064   0.0917143   0.04898984  0.00804074\n",
        "  0.00022201 -0.00224925  2.95887793]\n",
        "T-values:  [-38.74908321  16.50473627 -25.1821894  -32.81791308   8.49827113\n",
        "   4.21247925   5.7749976   -6.16191078  -5.45321673  -5.16865445\n",
        "   3.92119964 -15.87825999  -7.39093058  -8.44963886  -4.05916246\n",
        "   6.3210987    6.57434662   5.36229044   7.42806363  -6.44513698\n",
        "   1.91301155]\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "First differences: We hold all explanatory variables constant at their means and manipulate the percentage of low income households to assess its impact on the response variables: "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "means = data.exog.mean(axis=0)\n",
      "means25 = means.copy()\n",
      "means25[0] = stats.scoreatpercentile(data.exog[:,0], 25)\n",
      "means75 = means.copy()\n",
      "means75[0] = lowinc_75per = stats.scoreatpercentile(data.exog[:,0], 75)\n",
      "resp_25 = res.predict(means25)\n",
      "resp_75 = res.predict(means75)\n",
      "diff = resp_75 - resp_25"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The interquartile first difference for the percentage of low income households in a school district is:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print \"%2.4f%%\" % (diff*100)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "-11.8753%\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Plots\n",
      "\n",
      " We extract information that will be used to draw some interesting plots: "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "nobs = res.nobs\n",
      "y = data.endog[:,0]/data.endog.sum(1)\n",
      "yhat = res.mu"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Plot yhat vs y:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.figure()\n",
      "plt.scatter(yhat, y)\n",
      "line_fit = sm.OLS(y, sm.add_constant(yhat)).fit().params\n",
      "fit = lambda x: line_fit[1]+line_fit[0]*x  # better way in scipy?\n",
      "plt.plot(np.linspace(0,1,nobs), fit(np.linspace(0,1,nobs)))\n",
      "plt.title('Model Fit Plot')\n",
      "plt.ylabel('Observed values')\n",
      "plt.xlabel('Fitted values')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "<matplotlib.text.Text at 0x4788b90>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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BugCh6HTr6dXrRczmztjXbvoUvf5rxo0byMcfT6NLF3jlFReWL/fh0KHabNs2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\nFSz+mY4cOSKbN292Tje9JT09XZYuXSq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6iGRR823evJk2NqEFLr56qtU2TExM5LPPPk9L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\nMDsOtAAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Plot yhat vs. Pearson residuals:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.scatter(yhat, res.resid_pearson)\n",
      "plt.plot([0.0, 1.0],[0.0, 0.0], 'k-')\n",
      "plt.title('Residual Dependence Plot')\n",
      "plt.ylabel('Pearson Residuals')\n",
      "plt.xlabel('Fitted values')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "<matplotlib.text.Text at 0x477d610>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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BeKRb4o4nT+Jy+W0yMxgMOHbsGB4/foyaNWvC2dkZ48aNxI4dzXDtWiUAStjZ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      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Histogram of standardized deviance residuals:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.figure()\n",
      "resid = res.resid_deviance.copy()\n",
      "resid_std = (resid - resid.mean())/resid.std()\n",
      "plt.hist(resid_std, bins=25)\n",
      "plt.title('Histogram of standardized deviance residuals')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "<matplotlib.text.Text at 0x4bd5bd0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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EMsTwJiKSIYY3EZEMMbyJiGSI4U1EJEMMbyIiGWr2PSzvR66uHigpKTCztTOA\nKluWQ62i/f8u12sepVKF4uJ8G9ZDdA+v520BeV5z25Z9O0odtuzb8jra2npPrcsq1/OeM2cO1Gq1\n0W3O8vPzERERgcDAQIwdOxaFhYUtr5aIiCxiMryfeeYZpKamGv0sISEBERERyMjIwJgxY5CQkGDT\nAomIqL4mh02ysrIQGRmJH374AQDQp08fnDp1Cmq1Grm5udBqtfjll1/qd8xhEwvaWtreUfp2lDps\n2TeHTah1mZudFu+wzMvLg1qtBgCo1Wrk5eU12jY+Pl56rtVqodVqLZ0dEVGbptPpoNPpLJ7O4i1v\nlUqFgoL/P+LCw8MD+fn1965zy9tRthxt2bej1GHLvrnlTa3LZjcgrh0uAQC9Xg8vLy/LqyMiohax\nOLyfeuopJCUlAQCSkpIwadIkqxdFRESmmRw2mTFjBk6dOoXbt29DrVbj9ddfx8SJEzF9+nTcuHED\n/v7+2Lt3L9zd3et3zGETC9pa2t5R+naUOmzZN4dNqHWZm508SccCDG9HrcOWfTO8qXXZbMybiIjs\nj+FNRCRDDG8iIhlieBMRyRDDm4hIhhjeREQyxPAmIpIhhjcRkQwxvImIZIjhTUQkQwxvIiIZYngT\nEckQw5uISIYY3kREMsTwJiKSIYY3EZEMWXz3+Lr8/f3h6uqKdu3awdnZGWlpadaqi4iITGhReCsU\nCuh0Onh4eFirHiIiMkOLh014yyciotbX4i3vxx57DO3atcNzzz2HZ5991uj9+Ph46blWq4VWq23J\n7IiI2hydTgedTmfxdC26AbFer4ePjw9u3bqFiIgIbN68GcOHD7/XMW9AbEFbS9s7St+OUoct++YN\niKl1tcoNiH18fAAAXbt2xeTJk7nDkoiolTQ7vMvLy1FSUgIAKCsrw7Fjx9CvXz+rFUZERI1r9ph3\nXl4eJk+eDACorq7G3//+d4wdO9ZqhRERUeNaNOZtsmOZjHm7unqgpKTAginkNmZry74dpQ5b9m1p\nHc4Aqs1qqVSqUFycb0HfdD8wNzvv+/C23U5IRwkfW/btKHXYsm/b1iGH7wi1rlbZYUlERPbB8CYi\nkiGGNxGRDLXoDMvWkpKSiv37j5jdfuBADebPn2vDiohanyU717kztO2TxQ7L6Ohn8cknpQAeNaP1\ndTz8sA4ZGV+b1Td3WLaFOmzZt+PssLR0XeXOUHkyNztlseV9z2gAzzbZCvgagM62pRAR2RnHvImI\nZIjhTUSiXagCAAAGRklEQVQkQzIaNjFXBK5cKfrf+CCRI2vvEOuppWcZc2eoY2iD4V0Ey3cwEdlD\nNRxhXb0X3ObXUVLC74wj4LAJEZEMMbyJiGSI4U1EJEMMb6I26d7OUHMetuzb1dXDop5dXT1s0rcl\n/TanbntgeMuCzt4FmEln7wLaGF0Lpq3dGWrOo6V9f9lo35ZdK7/uztOmH5b0fa9t43W2tG57aHZ4\np6amok+fPnj44Yexdu1aa9ZE9ejsXYCZdPYuoI3R2bsAM+nsXYCZdPYuwKqaFd4GgwEvvvgiUlNT\ncfnyZXzyySf4+eefrV0bERE1olnhnZaWhoCAAPj7+8PZ2RlRUVE4dOiQtWsjIqJGNOsknZs3b6JH\njx7Sa19fX1y4cKFeO+uePfZvAPPNbGvpfC1pb6u2TbVfbcO+rdn2r3W2Vh227NuedbTk996an7Hx\n37vlOWB+e8v6Xo2m18/m9t36mhXe5nwoXo6SiMh2mjVs0r17d2RnZ0uvs7Oz4evra7WiiIjItGaF\nd3h4OK5cuYKsrCxUVlZiz549eOqpp6xdGxERNaJZwybt27fHu+++i3HjxsFgMGDu3Lno27evtWsj\nIqJGNPs478cffxy//vorrl69ihUrVjTYZuXKlQgNDUVYWBjGjBljNNTiSJYsWYK+ffsiNDQUU6ZM\nQVFRkb1LatC+ffsQHByMdu3a4dtvv7V3OUbkctz/nDlzoFar0a9fP3uX0qjs7GyMGjUKwcHBCAkJ\nwaZNm+xdUoPu3r2LQYMGISwsDEFBQY3mgKMwGAzQaDSIjIy0dymN8vf3R//+/aHRaDBw4EDTjYUN\nFRcXS883bdok5s6da8vZNduxY8eEwWAQQgixbNkysWzZMjtX1LCff/5Z/Prrr0Kr1YpvvvnG3uVI\nqqurxUMPPSQyMzNFZWWlCA0NFZcvX7Z3WQ06ffq0+Pbbb0VISIi9S2mUXq8X6enpQgghSkpKRGBg\noMMuz7KyMiGEEFVVVWLQoEHizJkzdq6ocYmJiSI6OlpERkbau5RG+fv7izt37pjV1qanxyuVSul5\naWkpPD09bTm7ZouIiICT071FMWjQIOTk5Ni5oob16dMHgYGB9i6jHjkd9z98+HCoVCp7l2GSt7c3\nwsLCAACdO3dG37598fvvv9u5qoa5uLgAACorK2EwGODh4ZjXBMnJyUFKSgrmzZvn8EfCmVufza9t\n8sorr8DPzw9JSUlYvny5rWfXYh999BGeeOIJe5chKw0d93/z5k07VtR2ZGVlIT09HYMGDbJ3KQ2q\nqalBWFgY1Go1Ro0ahaCgIHuX1KCFCxdi/fr10kaao1IoFHjssccQHh6ODz/80GTbFn+SiIgI9OvX\nr97j8OHDAIA333wTN27cwOzZs7Fw4cKWzs5mddbW+sADDyA6Otqh63Q0jn4yg1yVlpbi6aefxsaN\nG9G5c2d7l9MgJycnXLp0CTk5OTh9+jR0Op29S6rnyJEj8PLygkajcfit7nPnziE9PR1Hjx7Fe++9\nhzNnzjTatsW3QTt+/LhZ7aKjo+26RdtUnTt27EBKSgpOnDjRShU1zNzl6Uh43L/1VVVVYerUqZg5\ncyYmTZpk73Ka5ObmhgkTJuDixYvQarX2LsfI+fPnkZycjJSUFNy9exfFxcWYNWsWdu7cae/S6vHx\n8QEAdO3aFZMnT0ZaWhqGDx/eYFub/g9x5coV6fmhQ4eg0WhsObtmS01Nxfr163Ho0CF07NjR3uWY\nxZG2IHjcv3UJITB37lwEBQUhLi7O3uU06vbt2ygsLAQAVFRU4Pjx4w75HV+zZg2ys7ORmZmJ3bt3\nY/To0Q4Z3OXl5SgpKQEAlJWV4dixY6aPirLdflMhpk6dKkJCQkRoaKiYMmWKyMvLs+Xsmi0gIED4\n+fmJsLAwERYWJhYsWGDvkhq0f/9+4evrKzp27CjUarUYP368vUuSpKSkiMDAQPHQQw+JNWvW2Luc\nRkVFRQkfHx/xwAMPCF9fX/HRRx/Zu6R6zpw5IxQKhQgNDZXWyaNHj9q7rHq+//57odFoRGhoqOjX\nr59Yt26dvUtqkk6nc9ijTX777TcRGhoqQkNDRXBwcJPfI4UQDrQJR0REZnHsXa9ERNQghjcRkQwx\nvImIZIjhTUQkQwxvIiIZYngTEcnQ/wFqI0jRU54CMQAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "QQ Plot of Deviance Residuals:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from statsmodels import graphics\n",
      "graphics.gofplots.qqplot(resid, line='r')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "png": 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APChcQWSdHnLDwgX6kU4Mp+nCPhbjz63cSQpNMDeZHUankoqUrtyRwtSpU/Hw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\nRETERqEgIiI2CgUREbFRKIi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       "prompt_number": 14,
       "text": [
        "<matplotlib.figure.Figure at 0x48019d0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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APChcQWSdHnLDwgX6kU4Mp+nCPhbjz63cSQpNMDeZHUankoqUrtyRwtSpU/Hw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\n"
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## GLM: Gamma for proportional count response\n",
      "\n",
      "### Load data\n",
      "\n",
      " In the example above, we printed the ``NOTE`` attribute to learn about the\n",
      " Star98 dataset. Statsmodels datasets ships with other useful information. For\n",
      " example: "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print sm.datasets.scotland.DESCRLONG"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "This data is based on the example in Gill and describes the proportion of\n",
        "voters who voted Yes to grant the Scottish Parliament taxation powers.\n",
        "The data are divided into 32 council districts.  This example's explanatory\n",
        "variables include the amount of council tax collected in pounds sterling as\n",
        "of April 1997 per two adults before adjustments, the female percentage of\n",
        "total claims for unemployment benefits as of January, 1998, the standardized\n",
        "mortality rate (UK is 100), the percentage of labor force participation,\n",
        "regional GDP, the percentage of children aged 5 to 15, and an interaction term\n",
        "between female unemployment and the council tax.\n",
        "\n",
        "The original source files and variable information are included in\n",
        "/scotland/src/\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      " Load the data and add a constant to the exogenous variables:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data2 = sm.datasets.scotland.load()\n",
      "data2.exog = sm.add_constant(data2.exog)\n",
      "print data2.exog[:5,:]\n",
      "print data2.endog[:5]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[   712.      21.     105.      82.4  13566.      12.3  14952.       1. ]\n",
        " [   643.      26.5     97.      80.2  13566.      15.3  17039.5      1. ]\n",
        " [   679.      28.3    113.      86.3   9611.      13.9  19215.7      1. ]\n",
        " [   801.      27.1    109.      80.4   9483.      13.6  21707.1      1. ]\n",
        " [   753.      22.     115.      64.7   9265.      14.6  16566.       1. ]]\n",
        "[ 60.3  52.3  53.4  57.   68.7]\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Fit and summary"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "glm_gamma = sm.GLM(data2.endog, data2.exog, family=sm.families.Gamma())\n",
      "glm_results = glm_gamma.fit()\n",
      "print glm_results.summary()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "                 Generalized Linear Model Regression Results                  \n",
        "==============================================================================\n",
        "Dep. Variable:                      y   No. Observations:                   32\n",
        "Model:                            GLM   Df Residuals:                       24\n",
        "Model Family:                   Gamma   Df Model:                            7\n",
        "Link Function:          inverse_power   Scale:                0.00358428317349\n",
        "Method:                          IRLS   Log-Likelihood:                -83.017\n",
        "Date:                Sun, 26 Aug 2012   Deviance:                     0.087389\n",
        "Time:                        20:50:10   Pearson chi2:                   0.0860\n",
        "No. Iterations:                     5                                         \n",
        "==============================================================================\n",
        "                 coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
        "------------------------------------------------------------------------------\n",
        "x1          4.962e-05   1.62e-05      3.060      0.005      1.78e-05  8.14e-05\n",
        "x2             0.0020      0.001      3.824      0.001         0.001     0.003\n",
        "x3         -7.181e-05   2.71e-05     -2.648      0.014        -0.000 -1.87e-05\n",
        "x4             0.0001   4.06e-05      2.757      0.011      3.23e-05     0.000\n",
        "x5         -1.468e-07   1.24e-07     -1.187      0.247     -3.89e-07  9.56e-08\n",
        "x6            -0.0005      0.000     -2.159      0.041        -0.001 -4.78e-05\n",
        "x7         -2.427e-06   7.46e-07     -3.253      0.003     -3.89e-06 -9.65e-07\n",
        "const         -0.0178      0.011     -1.548      0.135        -0.040     0.005\n",
        "==============================================================================\n"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## GLM: Gaussian distribution with a noncanonical link\n",
      "\n",
      "### Artificial data"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "nobs2 = 100\n",
      "x = np.arange(nobs2)\n",
      "np.random.seed(54321)\n",
      "X = np.column_stack((x,x**2))\n",
      "X = sm.add_constant(X)\n",
      "lny = np.exp(-(.03*x + .0001*x**2 - 1.0)) + .001 * np.random.rand(nobs2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Fit and summary"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "gauss_log = sm.GLM(lny, X, family=sm.families.Gaussian(sm.families.links.log))\n",
      "gauss_log_results = gauss_log.fit()\n",
      "print gauss_log_results.summary()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "                 Generalized Linear Model Regression Results                  \n",
        "==============================================================================\n",
        "Dep. Variable:                      y   No. Observations:                  100\n",
        "Model:                            GLM   Df Residuals:                       97\n",
        "Model Family:                Gaussian   Df Model:                            2\n",
        "Link Function:                    log   Scale:               1.05311425588e-07\n",
        "Method:                          IRLS   Log-Likelihood:                 662.92\n",
        "Date:                Sun, 26 Aug 2012   Deviance:                   1.0215e-05\n",
        "Time:                        20:50:12   Pearson chi2:                 1.02e-05\n",
        "No. Iterations:                     6                                         \n",
        "==============================================================================\n",
        "                 coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
        "------------------------------------------------------------------------------\n",
        "x1            -0.0300    5.6e-06  -5361.316      0.000        -0.030    -0.030\n",
        "x2         -9.939e-05   1.05e-07   -951.091      0.000     -9.96e-05 -9.92e-05\n",
        "const          1.0003   5.39e-05   1.86e+04      0.000         1.000     1.000\n",
        "==============================================================================\n"
       ]
      }
     ],
     "prompt_number": 19
    }
   ],
   "metadata": {}
  }
 ]
}