{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# M-Estimators for Robust Linear Modeling" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from statsmodels.compat import lmap\n", "import numpy as np\n", "from scipy import stats\n", "import matplotlib.pyplot as plt\n", "\n", "import statsmodels.api as sm" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* An M-estimator minimizes the function \n", "\n", "$$Q(e_i, \\rho) = \\sum_i~\\rho \\left (\\frac{e_i}{s}\\right )$$\n", "\n", "where $\\rho$ is a symmetric function of the residuals \n", "\n", "* The effect of $\\rho$ is to reduce the influence of outliers\n", "* $s$ is an estimate of scale. \n", "* The robust estimates $\\hat{\\beta}$ are computed by the iteratively re-weighted least squares algorithm" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* We have several choices available for the weighting functions to be used" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "norms = sm.robust.norms" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def plot_weights(support, weights_func, xlabels, xticks):\n", " fig = plt.figure(figsize=(12,8))\n", " ax = fig.add_subplot(111)\n", " ax.plot(support, weights_func(support))\n", " ax.set_xticks(xticks)\n", " ax.set_xticklabels(xlabels, fontsize=16)\n", " ax.set_ylim(-.1, 1.1)\n", " return ax" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Andrew's Wave" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Help on function weights in module statsmodels.robust.norms:\n", "\n", "weights(self, z)\n", " Andrew's wave weighting function for the IRLS algorithm\n", " \n", " The psi function scaled by z\n", " \n", " Parameters\n", " ----------\n", " z : array_like\n", " 1d array\n", " \n", " Returns\n", " -------\n", " weights : array\n", " weights(z) = sin(z/a)/(z/a) for \\|z\\| <= a*pi\n", " \n", " weights(z) = 0 for \\|z\\| > a*pi\n", "\n" ] } ], "source": [ "help(norms.AndrewWave.weights)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "a = 1.339\n", "support = np.linspace(-np.pi*a, np.pi*a, 100)\n", "andrew = norms.AndrewWave(a=a)\n", "plot_weights(support, andrew.weights, ['$-\\pi*a$', '0', '$\\pi*a$'], [-np.pi*a, 0, np.pi*a]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Hampel's 17A" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Help on function weights in module statsmodels.robust.norms:\n", "\n", "weights(self, z)\n", " Hampel weighting function for the IRLS algorithm\n", " \n", " The psi function scaled by z\n", " \n", " Parameters\n", " ----------\n", " z : array_like\n", " 1d array\n", " \n", " Returns\n", " -------\n", " weights : array\n", " weights(z) = 1 for \\|z\\| <= a\n", " \n", " weights(z) = a/\\|z\\| for a < \\|z\\| <= b\n", " \n", " weights(z) = a*(c - \\|z\\|)/(\\|z\\|*(c-b)) for b < \\|z\\| <= c\n", " \n", " weights(z) = 0 for \\|z\\| > c\n", "\n" ] } ], "source": [ "help(norms.Hampel.weights)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "c = 8\n", "support = np.linspace(-3*c, 3*c, 1000)\n", "hampel = norms.Hampel(a=2., b=4., c=c)\n", "plot_weights(support, hampel.weights, ['3*c', '0', '3*c'], [-3*c, 0, 3*c]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Huber's t" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Help on function weights in module statsmodels.robust.norms:\n", "\n", "weights(self, z)\n", " Huber's t weighting function for the IRLS algorithm\n", " \n", " The psi function scaled by z\n", " \n", " Parameters\n", " ----------\n", " z : array_like\n", " 1d array\n", " \n", " Returns\n", " -------\n", " weights : array\n", " weights(z) = 1 for \\|z\\| <= t\n", " \n", " weights(z) = t/\\|z\\| for \\|z\\| > t\n", "\n" ] } ], "source": [ "help(norms.HuberT.weights)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "t = 1.345\n", "support = np.linspace(-3*t, 3*t, 1000)\n", "huber = norms.HuberT(t=t)\n", "plot_weights(support, huber.weights, ['-3*t', '0', '3*t'], [-3*t, 0, 3*t]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Least Squares" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Help on function weights in module statsmodels.robust.norms:\n", "\n", "weights(self, z)\n", " The least squares estimator weighting function for the IRLS algorithm.\n", " \n", " The psi function scaled by the input z\n", " \n", " Parameters\n", " ----------\n", " z : array_like\n", " 1d array\n", " \n", " Returns\n", " -------\n", " weights : array\n", " weights(z) = np.ones(z.shape)\n", "\n" ] } ], "source": [ "help(norms.LeastSquares.weights)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": true }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "support = np.linspace(-3, 3, 1000)\n", "lst_sq = norms.LeastSquares()\n", "plot_weights(support, lst_sq.weights, ['-3', '0', '3'], [-3, 0, 3]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Ramsay's Ea" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Help on function weights in module statsmodels.robust.norms:\n", "\n", "weights(self, z)\n", " Ramsay's Ea weighting function for the IRLS algorithm\n", " \n", " The psi function scaled by z\n", " \n", " Parameters\n", " ----------\n", " z : array_like\n", " 1d array\n", " \n", " Returns\n", " -------\n", " weights : array\n", " weights(z) = exp(-a*\\|z\\|)\n", "\n" ] } ], "source": [ "help(norms.RamsayE.weights)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": true }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "a = .3\n", "support = np.linspace(-3*a, 3*a, 1000)\n", "ramsay = norms.RamsayE(a=a)\n", "plot_weights(support, ramsay.weights, ['-3*a', '0', '3*a'], [-3*a, 0, 3*a]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Trimmed Mean" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Help on function weights in module statsmodels.robust.norms:\n", "\n", "weights(self, z)\n", " Least trimmed mean weighting function for the IRLS algorithm\n", " \n", " The psi function scaled by z\n", " \n", " Parameters\n", " ----------\n", " z : array_like\n", " 1d array\n", " \n", " Returns\n", " -------\n", " weights : array\n", " weights(z) = 1 for \\|z\\| <= c\n", " \n", " weights(z) = 0 for \\|z\\| > c\n", "\n" ] } ], "source": [ "help(norms.TrimmedMean.weights)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": true }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "c = 2\n", "support = np.linspace(-3*c, 3*c, 1000)\n", "trimmed = norms.TrimmedMean(c=c)\n", "plot_weights(support, trimmed.weights, ['-3*c', '0', '3*c'], [-3*c, 0, 3*c]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Tukey's Biweight" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Help on function weights in module statsmodels.robust.norms:\n", "\n", "weights(self, z)\n", " Tukey's biweight weighting function for the IRLS algorithm\n", " \n", " The psi function scaled by z\n", " \n", " Parameters\n", " ----------\n", " z : array_like\n", " 1d array\n", " \n", " Returns\n", " -------\n", " weights : array\n", " psi(z) = (1 - (z/c)**2)**2 for \\|z\\| <= R\n", " \n", " psi(z) = 0 for \\|z\\| > R\n", "\n" ] } ], "source": [ "help(norms.TukeyBiweight.weights)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": true }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "c = 4.685\n", "support = np.linspace(-3*c, 3*c, 1000)\n", "tukey = norms.TukeyBiweight(c=c)\n", "plot_weights(support, tukey.weights, ['-3*c', '0', '3*c'], [-3*c, 0, 3*c]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Scale Estimators" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Robust estimates of the location" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": true }, "outputs": [], "source": [ "x = np.array([1, 2, 3, 4, 500])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* The mean is not a robust estimator of location" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": true }, "outputs": [ { "data": { "text/plain": [ "102.0" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x.mean()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* The median, on the other hand, is a robust estimator with a breakdown point of 50%" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": true }, "outputs": [ { "data": { "text/plain": [ "3.0" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.median(x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Analogously for the scale\n", "* The standard deviation is not robust" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": true }, "outputs": [ { "data": { "text/plain": [ "199.00251254695254" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x.std()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Median Absolute Deviation\n", "\n", "$$ median_i |X_i - median_j(X_j)|) $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Standardized Median Absolute Deviation is a consistent estimator for $\\hat{\\sigma}$\n", "\n", "$$\\hat{\\sigma}=K \\cdot MAD$$\n", "\n", "where $K$ depends on the distribution. For the normal distribution for example,\n", "\n", "$$K = \\Phi^{-1}(.75)$$" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": true }, "outputs": [ { "data": { "text/plain": [ "0.6744897501960817" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stats.norm.ppf(.75)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 1 2 3 4 500]\n" ] } ], "source": [ "print(x)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": true }, "outputs": [ { "data": { "text/plain": [ "1.482602218505602" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sm.robust.scale.mad(x)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": true }, "outputs": [ { "data": { "text/plain": [ "1.4142135623730951" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.array([1,2,3,4,5.]).std()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* The default for Robust Linear Models is MAD\n", "* another popular choice is Huber's proposal 2" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": true }, "outputs": [], "source": [ "np.random.seed(12345)\n", "fat_tails = stats.t(6).rvs(40)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": true }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "kde = sm.nonparametric.KDEUnivariate(fat_tails)\n", "kde.fit()\n", "fig = plt.figure(figsize=(12,8))\n", "ax = fig.add_subplot(111)\n", "ax.plot(kde.support, kde.density);" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.0688231044810875 1.3471633229698652\n" ] } ], "source": [ "print(fat_tails.mean(), fat_tails.std())" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(0.0688231044810875, 1.3471633229698652)\n" ] } ], "source": [ "print(stats.norm.fit(fat_tails))" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(6, 0.03900835312789366, 1.0563837144431252)\n" ] } ], "source": [ "print(stats.t.fit(fat_tails, f0=6))" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.04048984333271795 1.1557140047569665\n" ] } ], "source": [ "huber = sm.robust.scale.Huber()\n", "loc, scale = huber(fat_tails)\n", "print(loc, scale)" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": true }, "outputs": [ { "data": { "text/plain": [ "1.115335001165415" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sm.robust.mad(fat_tails)" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": true }, "outputs": [ { "data": { "text/plain": [ "1.0483916565928972" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sm.robust.mad(fat_tails, c=stats.t(6).ppf(.75))" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": true }, "outputs": [ { "data": { "text/plain": [ "1.115335001165415" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sm.robust.scale.mad(fat_tails)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Duncan's Occupational Prestige data - M-estimation for outliers" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from statsmodels.graphics.api import abline_plot\n", "from statsmodels.formula.api import ols, rlm" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": true }, "outputs": [], "source": [ "prestige = sm.datasets.get_rdataset(\"Duncan\", \"carData\", cache=True).data" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " type income education prestige\n", "accountant prof 62 86 82\n", "pilot prof 72 76 83\n", "architect prof 75 92 90\n", "author prof 55 90 76\n", "chemist prof 64 86 90\n", "minister prof 21 84 87\n", "professor prof 64 93 93\n", "dentist prof 80 100 90\n", "reporter wc 67 87 52\n", "engineer prof 72 86 88\n" ] } ], "source": [ "print(prestige.head(10))" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": true }, "outputs": [ { "data": { "image/png": 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0JEmS1CDDtCRJktQgw7QkSZLUoELCdEQMRcRVEXF7RNwWES+MiCMi4rqIuKP6+fAiapMkSZJqVdTM9AeBz2fmM4ETgduAC4HrM/N44PrqbUmSJKljtT1MR8RhwIuBywAy86eZuQicCWyu3m0zMNnu2iRJkqR6HFTAz3wqsBP4eEScCGwDLgCenJn3AmTmvRHxpNUeHBHnA+cDHHvsse2pWJJabGauzPTsAjsWKwwPlZiaGGVybKTosiRJayiizeMg4CTgI5k5BvwXdbR0ZOalmTmemeMbNmxoVY2S1DYzc2U2bZmnvFghgfJihU1b5pmZKxddmiRpDUWE6e3A9sy8pXr7KpbC9fci4iiA6uf7CqhNktpuenaByq7dK8Yqu3YzPbtQUEWSpFq1PUxn5neB70TEaHXoNOBfgc8B51bHzgWubndtklSEHYuVusYlSZ2jiJ5pgN8BroiIg4G7gLewFOw/HRHnAfcAZxdUmyS11fBQifIqwXl4qFRANZKkehQSpjPz68D4Kt86rd21SFLRpiZG2bRlfkWrR2lwgKmJ0QM8SpLUCYqamZaktun0lTKWazlQjZ3+HCSpXxmmJfW05ZUylmd9l1fKADoqjE6Ojey3nm55DpLUj4raAVGS2qIXVsrohecgSb3KMC2pp/XCShm98BwkqVcZpiX1tP2tiNFNK2X0wnOQpF5Vc5iOiNJea0NLUleYmhilNDiwYqzbVsrohecgSb2qpjAdEa8Fvg58vnr7eRHxuVYWJknNMDk2wsVnncDIUIkARoZKXHzWCV114V4vPAdJ6lWRmWvfKWIbcCpwU2aOVce+kZnPbXF9BzQ+Pp5bt24tsgRJkiT1gYjYlpmP2iel1jaPhzLz/ibXJEmSJHW1WteZvjUifg0YiIjjgd8F/qF1ZUmSJEmdr9aZ6d8BngM8CFwJPAD8XquKkiRJkrpBTTPTmflj4I+qH5IkrcptzyX1m5rCdERcA+x7peL9wFbgLzLzJ80uTJLUXdz2XFI/qrXN4y7gP4GPVj8eAL4HPKN6W5LU59z2XFI/qvUCxLHMfPFet6+JiC9l5osj4putKEyS1F3c9lydxrYjtUOtM9MbIuLY5RvVr4+s3vxp06uSJHUdtz1XJ1luOyovVkgeaTuamSsXXZp6TK1h+u3AVyLixoi4CfgyMBURjwc2t6o4SVL3cNtzdRLbjtQuta7m8XfV9aWfCQRw+14XHX6gVcVJkrrH8ulzT6urE9h2pHY5YJiOiFMz84aIOGufbz01IsjMLS2sTZLUZSbHRgzP6gjDQyXKqwRn247UbGu1ebyk+vm1q3y8poV1SZIkNcy2I7XLAWemM/Oi6pfvzsxv7f29iDiuZVVJkiStg21Hapdal8b7DHDSPmNXAT/X3HIkSZKaw7YjtcNaPdPPBJ4D/Ld9+qYPAw5pZWGSJElSp1trZnqUpd7oIZb6pJf9CPjvrSpKkiRJ6gZr9UxfDVwdES/MzJvbVJMkSZLUFWrdtOUXI+KwiBiMiOsj4vsR8estrUySJEnqcLWG6Vdk5gMstXxsB54BTLWsKkmSJKkL1BqmB6ufXwVcmZk/aFE9kiRJUteodWm8ayLidqACvDUiNgA/WeMxkiRJUk+raWY6My8EXgiMZ+Yu4MfAma0sTJIkSep0NYXpiHgc8DbgI9WhYWC8VUVJkiRJ3aDWnumPAz8FXlS9vR34Xy2pSJIkSeoStYbpp2XmnwK7ADKzAkTLqpIkSZK6QK1h+qcRUQISICKeBjzYsqokSZKkLlDrah4XAZ8HjomIK4BTgDe3qihJ0kozc2WmZxfYsVhheKjE1MQok2MjRZclSX1vzTAdEQHcDpwFnMxSe8cFmfn9FtcmSWIpSG/aMk9l124AyosVNm2ZBzBQS1LB1mzzyMwEZjLzPzLz2sz8W4O0JLXP9OzCniC9rLJrN9OzCwVVJElaVmvP9D9GxPNbWokkaVU7Fit1jUuS2qfWMP0ylgL1v0fENyJiPiK+0crCJElLhodKdY1Lktqn1gsQz2hpFZKk/ZqaGF3RMw1QGhxgamK0wKokSbBGmI6IQ4DfBJ4OzAOXZeZD7ShMkrRk+SJDV/OQpM6z1sz0ZpY2avkyS7PTzwYuaHVRkqSVJsdGDM+S1IHWCtPPzswTACLiMuBrrS9JkiRJ6g5rXYC4a/kL2zskSZKkldaamT4xIh6ofh1AqXo7WFqC+rCWVidJkiR1sAOG6cwcaFchkiRJUrepdWk8SSrMzFzZlSzUNXy9Sv3FMC2po83MlVessVxerLBpyzyAAUUdx9er1H9q3QGx6SJiICLmIuJvq7ePi4hbIuKOiPhURBxcVG2SOsf07MKKzUoAKrt2Mz27UFBF0v75epX6T2FhmqX1qm/b6/Z7gfdn5vHAD4HzCqlKUkfZsVipa1wqkq9Xqf8UEqYj4mjg1cBfVm8HcCpwVfUum4HJImqT1FmGh0p1jUtF8vUq9Z+iZqY/APwh8HD19hOBxb3Wst4OrNpcFhHnR8TWiNi6c+fO1lcq9bCZuTKnXHIDx114LadccgMzc+WiS3qUqYlRSoMrFxYqDQ4wNTFaUEXS/vl6lfpP28N0RLwGuC8zt+09vMpdc7XHZ+almTmemeMbNmxoSY1SP1i+UKq8WCF55EKpTgvUk2MjXHzWCYwMlQhgZKjExWed4MVc6ki+XqX+U8RqHqcAr4uIVwGHAIexNFM9FBEHVWenjwZ2FFCb1DcOdKFUp/3DPzk20nE1Sfvj61XqL22fmc7MTZl5dGZuBN4A3JCZ5wA3Ar9Uvdu5wNXtrk3qJ14oJUmC7mj562RFruaxr3cAfxARd7LUQ31ZwfVIPc0LpSRJ3dLy18kKDdOZeVNmvqb69V2Z+YLMfHpmnp2ZDxZZm9TrvFBKkuTa6OvnDohSn1ru6XTbY0nqX7b8rZ9hWupjXiglSf1teKhEeZXgbMtf7TqpZ1qSJEltZMvf+jkzLUmS1Kds+Vs/w7QkSVIfs+VvfWzzkCRJkhpkmJYkSZIaZJiWJEmSGmSYliRJkhrkBYiSpLaZmSu7aoCknmKYliS1xcxcmU1b5vdsXVxerLBpyzyAgVpS1zJMq285Qya11/Tswp4gvayyazfTswv+7knqWoZp9SVnyKT227HKlsUHGpekbuAFiOpLB5ohk9Qaw0OlusYlqRsYptWXnCGT2m9qYpTS4MCKsdLgAFMTowVVJEnrZ5hWX3KGTGq/ybERLj7rBEaGSgQwMlTi4rNOsLVKUlezZ1p9aWpidEXPNDhDJrXD5NiI4VlSTzFMqy8t/2Puah6SJGk9DNPqW86QSZKk9bJnWpIkSWqQYVqSJElqkGFakiRJapBhWpIkSWqQFyBKUp+YmSu7go0kNZlhWpL6wMxcecXa6uXFCpu2zAMYqCVpHWzzkKQ+MD27sGKTIoDKrt1Mzy4UVJEk9QbDtCT1gR2LlbrGJUm1MUxLUh8YHirVNS5Jqo1hWpL6wNTEKKXBgRVjpcEBpiZGC6pIknqDFyBKUh9YvsjQ1TwkqbkM05LUJybHRgzPktRktnlIkiRJDXJmWtoPN7iQJElrMUxLq3CDC0mSVAvbPKRVuMGFJEmqhWFaWoUbXEiSpFoYpqVVuMGFJEmqhWFafWtmrswpl9zAcRdeyymX3MDMXHnP99zgQpIk1cILENWX1rrA0A0uJElSLQzT6ksHusBwOTC7wYUkSVqLbR7qS15gKEmSmsEwrb7kBYaSJKkZDNPqS15gKEmSmsGeafUlLzCUJEnNYJhW3/ICQ0mStF62eUiSJEkNMkxLkiRJDTJMS5IkSQ1qe5iOiGMi4saIuC0ivhkRF1THj4iI6yLijurnw9tdmyRJklSPImamHwLenpnPAk4G3hYRzwYuBK7PzOOB66u31aVm5sqccskNHHfhtZxyyQ3MzJWLLkmSJKnp2h6mM/PezPzn6tc/Am4DRoAzgc3Vu20GJttdm5pjZq7Mpi3zlBcrJFBerLBpy7yBWpIk9ZxCe6YjYiMwBtwCPDkz74WlwA08qbjKtB7TswtUdu1eMVbZtZvp2YWCKpIkSWqNwtaZjognAJ8Bfi8zH4iIWh93PnA+wLHHHtu6AtWwHYuVusYlrW1mruwmQ5LUgQqZmY6IQZaC9BWZuaU6/L2IOKr6/aOA+1Z7bGZempnjmTm+YcOG9hSsugwPleoal3Rgtk5JUucqYjWPAC4DbsvM/73Xtz4HnFv9+lzg6nbXpuaYmhilNDiwYqw0OMDUxGhBFUndzdYpSepcRbR5nAK8EZiPiK9Xx/4ncAnw6Yg4D7gHOLuA2tQEy6eePSUtNYetU5LUudoepjPzK8D+GqRPa2ctap3JsRHDs9Qkw0MlyqsEZ1unJKl47oAoSR3O1ilJ6lyFreYhSaqNrVOS1LkM05LUBWydkqTOZJjWo7iebf/w71qSpPUxTGuF5fVsl5fhWl7PFjBk9Rj/riVJWj8vQNQKrmfbP/y7liRp/ZyZrlOvnxZ3Pdv+4d+1JEnr58x0HfphS1+3Au8f/l1LkrR+huk69MNpcdez7R/+XUuStH62edShH06Lu55t//DvWpKk9TNM16FftvR1Pdv+4d+1JEnrY5tHHTwtLkmSpL05M10HT4v3ll5fmUWSJLWeYbpOnhbvDW5YIkmSmsE2D/WlfliZRZIktZ5hWn2pH1ZmkSRJrWeYVl9ywxJJktQMhmn1JVdmkSRJzeAFiCpE0StpuDKLJElqBsO02q5TVtJwZRZJkrRehukmW2vGtegZ2WZY73M40Eoa3XYsJElSfzNMN9FaM66dMiO7Hs14Dq6kIUmSeoUXIDbRWmsX98Laxs14Dq6kIUmSeoVhuonWmnHthRnZZjwHV9KQJEm9wjDdRGvNuPbCjGwznsPk2AgXn3UCI0MlAhgZKnHxWSd0TauLJEnSMsN0E60149oLM7LNeg6TYyN89cJT+dYlr+arF55qkJYkSV3JCxDrdKCVLNZau7gX1jbuhecgSZLULJGZRdfQsPHx8dy6dWvbft6+K1nA0qysLQqSJEm9LSK2Zeb4vuO2edShF1bjkCRJUvPY5lGHXliNo116YXMaSZKktTgzXYdeWI2jHZbbYcqLFZJHNnaZmSsXXZokSVJTGabr0AurcbSD7TCSJKlf2OZRh25ZyaLoFgvbYSRJUr8wTNdpcmyk48Lz3vZdcWS5xQJoW93DQyXKqwRn22EkSVKvsc2jx3RCi4XtMJIkqV84M91jOqHFolvaYSRJktbLMN1jOqXFotPbYSRJkprBNo8eY4uFJElS+zgz3WNssZAkSWofw3QPssVCkiSpPQzTbVb0GtCSJElqHsN0G3XCGtCSJElqHi9AbKNOWANakiRJzWOYbqNOWANakiRJzWOYbqP9rfXsNtuSJEndyTDdRq4BLUmS1Fu8ALGNXANakiSptxim28w1oCVJknqHbR6SJElSgzoqTEfEKyNiISLujIgLi65HkiRJOpCOCdMRMQB8GDgDeDbwqxHx7GKrkiRJkvavY8I08ALgzsy8KzN/CvwNcGbBNUmSJEn71UlhegT4zl63t1fHVoiI8yNia0Rs3blzZ9uKkyRJkvbVSWE6VhnLRw1kXpqZ45k5vmHDhjaUJUmSJK2uk8L0duCYvW4fDewoqBZJkiRpTZ0Upv8JOD4ijouIg4E3AJ8ruCZJkiRpvzpm05bMfCgifhuYBQaAj2XmNwsuS5IkSdqvyHxUW3LXiIidwLeLrqNFjgS+X3QRPcDj2Dwey+bwODaHx7E5PI7N47Fsjk4+jk/JzEddsNfVYbqXRcTWzBwvuo5u53FsHo9lc3gcm8Pj2Bwex+bxWDZHNx7HTuqZliRJkrqKYVqSJElqkGG6c11adAE9wuPYPB7L5vA4NofHsTk8js3jsWyOrjuO9kxLkiRJDXJmWpIkSWqQYVqSJElqkGG6A0TExyLivoi4da+xIyLiuoi4o/r58CJr7AYRcUxE3BgRt0XENyPiguq4x7IOEXFIRHwtIv6lehz/pDp+XETcUj2On6ruVKo1RMRARMxFxN9Wb3scGxARd0fEfER8PSK2Vsf83a5TRAxFxFURcXv1vfKFHsf6RMRo9XW4/PFARPyex7F+EfH71X9nbo2IKxJ6gzoAACAASURBVKv//nTde6RhujNcDrxyn7ELgesz83jg+uptHdhDwNsz81nAycDbIuLZeCzr9SBwamaeCDwPeGVEnAy8F3h/9Tj+EDivwBq7yQXAbXvd9jg27mWZ+by91qD1d7t+HwQ+n5nPBE5k6bXpcaxDZi5UX4fPA34O+DHwWTyOdYmIEeB3gfHM/FmWdr9+A134HmmY7gCZ+SXgB/sMnwlsrn69GZhsa1FdKDPvzcx/rn79I5b+kRjBY1mXXPKf1ZuD1Y8ETgWuqo57HGsQEUcDrwb+sno78Dg2k7/bdYiIw4AXA5cBZOZPM3MRj+N6nAb8e2Z+G49jIw4CShFxEPA44F668D3SMN25npyZ98JSSASeVHA9XSUiNgJjwC14LOtWbU34OnAfcB3w78BiZj5Uvct2lv6jogP7APCHwMPV20/E49ioBL4QEdsi4vzqmL/b9XkqsBP4eLX16C8j4vF4HNfjDcCV1a89jnXIzDLwPuAelkL0/cA2uvA90jCtnhMRTwA+A/xeZj5QdD3dKDN3V09hHg28AHjWandrb1XdJSJeA9yXmdv2Hl7lrh7H2pySmScBZ7DUwvXiogvqQgcBJwEfycwx4L+wFaFh1V7e1wH/r+haulG1p/xM4DhgGHg8S7/f++r490jDdOf6XkQcBVD9fF/B9XSFiBhkKUhfkZlbqsMeywZVTwHfxFIP+lD1VBwshewdRdXVJU4BXhcRdwN/w9Kpyw/gcWxIZu6ofr6Ppf7UF+Dvdr22A9sz85bq7atYCtcex8acAfxzZn6vetvjWJ+XA9/KzJ2ZuQvYAryILnyPNEx3rs8B51a/Phe4usBaukK1H/Uy4LbM/N97fctjWYeI2BARQ9WvSyy94d0G3Aj8UvVuHsc1ZOamzDw6MzeydCr4hsw8B49j3SLi8RFx6PLXwCuAW/F3uy6Z+V3gOxExWh06DfhXPI6N+lUeafEAj2O97gFOjojHVf/9Xn49dt17pDsgdoCIuBJ4KXAk8D3gImAG+DRwLEsvuLMzc9+LFLWXiPgF4MvAPI/0qP5PlvqmPZY1iojnsnTRxwBL/+H+dGa+OyKeytIM6xHAHPDrmflgcZV2j4h4KfA/MvM1Hsf6VY/ZZ6s3DwL+OjP/v4h4Iv5u1yUinsfSBbEHA3cBb6H6e47HsWYR8TjgO8BTM/P+6pivxzpVl179FZZW45oDfoOlHumueo80TEuSJEkNss1DkiRJapBhWpIkSWqQYVqSJElqkGFakiRJapBhWpIkSWqQYVqSukhE/GfRNUiSHmGYliRJkhpkmJakLhQRL42ImyLiqoi4PSKuqO4iRkQ8PyL+ISL+JSK+FhGHRsQhEfHxiJiPiLmIeFn1vm+OiJmIuCYivhURvx0Rf1C9zz9GxBHV+z0tIj4fEdsi4ssR8cwin78kdYqD1r6LJKlDjQHPAXYAXwVOiYivAZ8CfiUz/ykiDgMqwAUAmXlCNQh/ISKeUf1zfrb6Zx0C3Am8IzPHIuL9wJuADwCXAr+ZmXdExM8D/xc4tV1PVJI6lWFakrrX1zJzO0BEfB3YCNwP3JuZ/wSQmQ9Uv/8LwP+pjt0eEd8GlsP0jZn5I+BHEXE/cE11fB54bkQ8AXgR8P+qk98Aj23xc5OkrmCYlqTu9eBeX+9m6T09gFzlvrHK2Gp/zsN73X64+mc+BljMzOc1Xqok9SZ7piWpt9wODEfE8wGq/dIHAV8CzqmOPQM4Flio5Q+szm5/KyLOrj4+IuLEVhQvSd3GMC1JPSQzfwr8CvB/IuJfgOtY6oX+v8BARMyz1FP95sx8cP9/0qOcA5xX/TO/CZzZ3MolqTtF5mpnAyVJkiStxZlpSZIkqUGGaUmSJKlBhmlJkiSpQYZpSZIkqUGGaUmSJKlBhmlJkiSpQYZpSZIkqUGGaUmSJKlBhmlJkiSpQYZpSZIkqUGGaUmSJKlBhmlJkiSpQYZpSZIkqUGGaUmSJKlBhmlJkiSpQYZpSZIkqUGGaUmSJKlBhmlJkiSpQYZpSZIkqUGGaUmSJKlBhmlJkiSpQYZpSZIkqUGGaUmSJKlBhmlJkiSpQYZpSZIkqUGGaUmSJKlBhmlJkiSpQYZpSZIkqUEHFV3Aehx55JG5cePGosuQJElSj9u2bdv3M3PDvuNdHaY3btzI1q1biy5DkiRJPS4ivr3aeMvaPCLiYxFxX0TcutfYERFxXUTcUf18eHU8IuJDEXFnRHwjIk5qVV2SJElSs7SyZ/py4JX7jF0IXJ+ZxwPXV28DnAEcX/04H/hIC+uSJEmSmqJlYTozvwT8YJ/hM4HN1a83A5N7jX8il/wjMBQRR7WqNkmSJKkZ2r2ax5Mz816A6ucnVcdHgO/sdb/t1bFHiYjzI2JrRGzduXNnS4uVJEmSDqRTlsaLVcZytTtm5qWZOZ6Z4xs2POqCSkmSJKlt2h2mv7fcvlH9fF91fDtwzF73OxrY0ebaJEmSpLq0O0x/Dji3+vW5wNV7jb+puqrHycD9y+0gkiRJUqdq2TrTEXEl8FLgyIjYDlwEXAJ8OiLOA+4Bzq7e/e+AVwF3Aj8G3tKquiRJkqRmaVmYzsxf3c+3Tlvlvgm8rVW1SJIkSa3Q1TsgSpIkqTPNzJWZnl1gx2KF4aESUxOjTI6tulhbVzNMS5Ikqalm5sps2jJPZdduAMqLFTZtmQfouUDdKUvjSZIkqUdMzy7sCdLLKrt2Mz27UFBFrWOYliRJUlPtWKzUNd7NDNOSJElqquGhUl3j3cwwLUmSpKaamhilNDiwYqw0OMDUxGhBFbWOFyBKkiSpqZYvMnQ1D0mSJKkBk2MjPRme92WbhyRJktQgw7QkSZLUIMO0JEmS1CB7piVJkvpEv2zx3U6GaUmSpD7QT1t8t5NtHpIkSX2gn7b4bidnpiVJUs+wjWH/+mmL73ZyZlqSJPWE5TaG8mKF5JE2hpm5ctGldYR+2uK7nQzTkiSpJ9jGcGD9tMV3O9nmIUmSeoJtDAfWT1t8t5NhWpIk9YThoRLlVYKzbQyP6JctvtvJNg9JktQTbGNQEZyZliRJPaHdbQydvHJIJ9fWiE5+PoZpSZLUM9rVxtDJG6B0cm2N6PTnY5uHJElSnTp55ZBOrq0Rnf58nJmWJEmqUyevHNLJtUH9LRud/nycmZYkSapTJ2+A0sm1NbKxTic/HzBMS5Ik1a2TVw7p5Noaadno5OcDhmlJkqS6TY6N8PqfG2EgAoCBCF7/c52xhvPk2AgXn3UCI0MlAhgZKnHxWSd0RG2NtGx08vMBe6YlSZLqNjNX5jPbyuzOBGB3Jp/ZVmb8KUd0RMjr1M1ZGt1Yp1OfDzgzLUmS+tzMXJlTLrmB4y68llMuueGA/bvLOn2FiU7V6S0bjXBmWpIk9a1G1zDu9BUmOlW7N9ZpB8O0JEnqWweaYT5QwGu0XUGd3bLRCNs8JElS32p0hrkX2xXUGMO0JEnqW42uYdzpK0yofWzzkCRJfWtqYnRFzzTUPsPca+0KaoxhWpIk9a1evCBO7WWYliRJfc0ZZq2HPdOSJElSgwzTkiRJUoMM05IkSVKDDNOSJElSg7wAUZIk1WVmruzqF1KVYVqSJNVsZq68Yl3m8mKFTVvmAQzU6ku2eUiSpJpNzy6s2OAEoLJrN9OzCwVVJBXLmWlJklSzHYuVusZ7me0uAmemJUlSHYaHSnWN96rldpfyYoXkkXaXmbly0aWpzQzTkiSpZlMTo5QGB1aMlQYHmJoYLaiiYtjuomW2eUiSauIpbcEjFxn2+2vBdhctM0xLktbkCg7a2+TYSN//vQ8PlSivEpz7rd1FBbV5RMTvR8Q3I+LWiLgyIg6JiOMi4paIuCMiPhURBxdRmyTp0TylLa1ku4uWtT1MR8QI8LvAeGb+LDAAvAF4L/D+zDwe+CFwXrtrkyStzlPa0kqTYyNcfNYJjAyVCGBkqMTFZ53Q9zP2/aioNo+DgFJE7AIeB9wLnAr8WvX7m4E/Bj5SSHWSpBU8pS09mu0uggJmpjOzDLwPuIelEH0/sA1YzMyHqnfbDvjqlKQO4SltSVpdEW0ehwNnAscBw8DjgTNWuWvu5/HnR8TWiNi6c+fO1hUqSdrDU9qStLoi2jxeDnwrM3cCRMQW4EXAUEQcVJ2dPhrYsdqDM/NS4FKA8fHxVQO3JKn5PKUtSY9WxGoe9wAnR8TjIiKA04B/BW4Efql6n3OBqwuoTZIkSapZET3TtwBXAf8MzFdruBR4B/AHEXEn8ETgsnbXJkmSJNWjkNU8MvMi4KJ9hu8CXlBAOZIkSVJDCtm0RZIkSeoFhmlJkiSpQYZpSZIkqUFF7YAoSR1nZq7M9OwCOxYrDA+VmJoYdSk4SYXzvamzGaYliaV/rDZtmaeyazcA5cUKm7bMA/iPlqTC+N7U+WzzkCRgenZhzz9Wyyq7djM9u1BQRZLke1M3MExLErBjsVLXuCS1g+9Nnc8wLUnA8FCprnFJagffmzqfYVqSgKmJUUqDAyvGSoMDTE2MFlSRJPne1A28AFGSeORCHq+Yl9RJfG/qfJGZRdfQsPHx8dy6dWvRZUiSJKnHRcS2zBzfd9w2D0mSJKlBtnlIkiR1ITdz6QyGaUmSpC7jZi6dwzYPSZKkLuNmLp3DMC1JktRl3MylcximJUmSuoybuXQOw7QkSVKXcTOXzuEFiJIkSV3GzVw6h2FakiSpC02OjRieO4BtHpIkSVKDDNOSJElSgwzTkiRJUoMM05IkSVKDDNOSJElSgwzTkiRJUoMM05IkSVKDDNOSJElSgwzTkiRJUoPcAVFqspm5stu7SpLUJwzTUhPNzJXZtGWeyq7dAJQXK2zaMg9goJYkqQfZ5iE10fTswp4gvayyazfTswsFVSRJklrJMC010Y7FSl3jkiSpuxmmpSYaHirVNS5JkrqbYVpqoqmJUUqDAyvGSoMDTE2MFlSRJElqJS9AlJpo+SJDV/OQJKk/GKalJpscGzE8S5LUJ2zzkCRJkhpkmJYkSZIaZJiWJEmSGmSYliRJkhpkmJYkSZIaZJiWJEmSGmSYliRJkhpkmJYkSZIaZJiWJEmSGmSYliRJkhpkmJYkSZIaZJiWJEmSGlRImI6IoYi4KiJuj4jbIuKFEXFERFwXEXdUPx9eRG2SJElSrYqamf4g8PnMfCZwInAbcCFwfWYeD1xfvS1JkiR1rLaH6Yg4DHgxcBlAZv40MxeBM4HN1bttBibbXZskSZJUj4MK+JlPBXYCH4+IE4FtwAXAkzPzXoDMvDcinrTagyPifOB8gGOPPbY9FUuSpJ41M1dmenaBHYsVhodKTE2MMjk2UnRZ6hJFtHkcBJwEfCQzx4D/oo6Wjsy8NDPHM3N8w4YNrapRkiT1gZm5Mpu2zFNerJBAebHCpi3zzMyViy5NXaKIML0d2J6Zt1RvX8VSuP5eRBwFUP18XwG1SZKkPjI9u0Bl1+4VY5Vdu5meXSioInWbtofpzPwu8J2IGK0OnQb8K/A54Nzq2LnA1e2uTZIk9Zcdi5W6xqV9FdEzDfA7wBURcTBwF/AWloL9pyPiPOAe4OyCapMkSX1ieKhEeZXgPDxUKqAadaNCwnRmfh0YX+Vbp7W7FqlbecGMpGbo9/eSqYlRNm2ZX9HqURocYGpi9ACPkh5R1My0pHVYvmBm+c1/+YIZoK/+EZS0Pr6XPPI8+/k/FFofw7TUhQ50wYz/AEiqle8lSybHRvrq+aq5itoBUdI6eMGMpGbwvURaP8O01IX2d2GMF8xIqofvJdL6GaalLjQ1MUppcGDFmBfMSKqX7yXS+tXcMx0RJeDYzHQVc6lgXjAjqRl8L5HWLzJz7TtFvBZ4H3BwZh4XEc8D3p2Zr2t1gQcyPj6eW7duLbIESZIk9YGI2JaZj1raudY2jz8GXgAswp51ojc2qzhJkiSpG9Uaph/KzPtbWokkSZLUZWrtmb41In4NGIiI44HfBf6hdWVJkiRJna/WmenfAZ4DPAhcCTwA/F6ripIkSZK6QU0z05n5Y+CPqh+S1LCZubIrB0iSekZNYToirgH2XfbjfmAr8BeZ+ZNmFyap98zMldm0ZX7P9sXlxQqbtswDGKglSV2p1jaPu4D/BD5a/XgA+B7wjOptSVrT9OzCniC9rLJrN9OzLl8vSepOtV6AOJaZL97r9jUR8aXMfHFEfLMVhUnqPTsWK3WNS1I3sp2tv9Q6M70hIo5dvlH9+sjqzZ82vSpJPWl4qFTXuCR1m+V2tvJiheSRdraZuXLRpalFag3Tbwe+EhE3RsRNwJeBqYh4PLC5VcVJ6i1TE6OUBgdWjJUGB5iaGC2oIklqLtvZ+k+tq3n8XXV96WcCAdy+10WHH2hVcZJ6y/JpTk9/SupVtrP1nwOG6Yg4NTNviIiz9vnWUyOCzNzSwtok9aDJsRHDs6SeNTxUorxKcLadrXet1ebxkurn167y8ZoW1iVJktR1bGfrPwecmc7Mi6pfvjszv7X39yLiuJZVJUmS1IVsZ+s/tS6N9xngpH3GrgJ+rrnlSJIkdTfb2frLWj3TzwSeA/y3ffqmDwMOaWVhkiRJUqdba2Z6lKXe6CGW+qSX/Qj4760qSpIkSeoGa/VMXw1cHREvzMyb21STJEmS1BVq3bTlFyPisIgYjIjrI+L7EfHrLa1MkiRJ6nC1hulXZOYDLLV8bAeeAUy1rCpJkiSpC9Qapgern18FXJmZP2hRPZIkSVLXqHVpvGsi4nagArw1IjYAP1njMZIkSVJPq2lmOjMvBF4IjGfmLuDHwJmtLEySJEnqdDWF6Yh4HPA24CPVoWFgvFVFSZIkSd2g1p7pjwM/BV5Uvb0d+F8tqUiSJEnqErWG6adl5p8CuwAyswJEy6qSJEmSukCtYfqnEVECEiAingY82LKqJEmSpC5Q62oeFwGfB46JiCuAU4A3t6ooSWqlmbky07ML7FisMDxUYmpilMmxkaLLkiR1oTXDdEQEcDtwFnAyS+0dF2Tm91tcmyQ13cxcmU1b5qns2g1AebHCpi3zAAZqSVLd1mzzyMwEZjLzPzLz2sz8W4O0pG41PbuwJ0gvq+zazfTsQkEVSZK6Wa090/8YEc9vaSWS1AY7Fit1jUuSdCC1humXsRSo/z0ivhER8xHxjVYWJkmtMDxUqmtckqQDqfUCxDNaWoUktcnUxOiKnmmA0uAAUxOjBVYlSepWBwzTEXEI8JvA04F54LLMfKgdhUlSKyxfZOhqHpKkZlhrZnozSxu1fJml2elnAxe0uihJaqXJsRHDsySpKdYK08/OzBMAIuIy4GutL0mSJEnqDmtdgLhr+QvbOyRJkqSV1pqZPjEiHqh+HUCpejtYWoL6sJZWJ0mSJHWwA4bpzBxoVyGS1I3cmlzt5mtO6iy1Lo0nSdqHW5Or3XzNSZ2n1k1bJEn7cGtytZuvOanzFBamI2IgIuYi4m+rt4+LiFsi4o6I+FREHFxUbZJUC7cmV7v5mpM6T5Ez0xcAt+11+73A+zPzeOCHwHmFVCVJNXJrcrWbrzmp8xQSpiPiaODVwF9WbwdwKnBV9S6bgckiapOkWk1NjFIaXHmdtluTq5V8zUmdp6gLED8A/CFwaPX2E4HFvday3g6seiVFRJwPnA9w7LHHtrhMSdo/tyZXu631mnOlD6n9IjPb+wMjXgO8KjPfGhEvBf4H8Bbg5sx8evU+xwB/t7z74v6Mj4/n1q1bW12yJEkdb9+VPmBp1vris04wUEtNEBHbMnN83/Ei2jxOAV4XEXcDf8NSe8cHgKGIWJ4pPxrYUUBtkiR1JVf6kIrR9jCdmZsy8+jM3Ai8AbghM88BbgR+qXq3c4Gr212b1Otm5sqccskNHHfhtZxyyQ3MzJWLLklSk7jSh1SMTlpn+h3AH0TEnSz1UF9WcD1ST1k+BVxerJA8stmDgVrqDa70IRWj0DCdmTdl5muqX9+VmS/IzKdn5tmZ+WCRtUm9xlPAUm9zpQ+pGG4nLvUJTwFLvc3VZaRiGKalPjE8VKK8SnD2FLDUOybHRgzPUpt1Us+0pBbyFLAkSc3nzLTUJzwFLElS8xmmpT7iKWBJkprLNg9JkiSpQYZpSZIkqUGGaUmSJKlB9kxLklaYmSt7oaok1cgwLUnaY3nb+eXdMpe3nQcM1JK0Cts8JEl7uO28JNXHmWn1FE9PS+vjtvOSVB9nptUzlk9PlxcrJI+cnp6ZKxddmtQ19re9vNvOS9LqDNPqGZ6eltbPbeclqT62eahneHpaWj+3nZek+him1TOGh0qUVwnOnp6W6uO285JUO9s81DM8PS1JktrNmWn1DE9PS5KkdjNMq6d4elqSJLWTbR6SJElSgwzTkiRJUoMM05IkSVKDDNOSJElSg7wAUX1vZq7sCiCSJKkhhmn1tZm5Mpu2zO/Zhry8WGHTlnkAA7UkSVqTbR7qa9OzC3uC9LLKrt1Mzy4UVJEkSeomhmn1tR2rbD9+oHFJkqS9GabV14aHSnWNS5Ik7c0wrb42NTFKaXBgxVhpcICpidGCKpIkSd3ECxDV15YvMnQ1D0mS1AjDtPre5NiI4VmSJDXEMK2u5NrQkiSpExim1XVcG1qSJHUKL0BU13FtaEmS1CkM0+o6rg0tSZI6hWFaXce1oSVJUqcwTKvruDa0JEnqFF6AqMLVuzKHa0NLkqROYZhWoRpdmcO1oSVJUiewzUOFcmUOSZLUzQzTKpQrc0iSpG5mmFahXJlDkiR1M8O0CuXKHJIkqZt5AaIK5cockiSpmxmmVThX5pAkSd3KNg9JkiSpQYZpSZIkqUGGaUmSJKlBbQ/TEXFMRNwYEbdFxDcj4oLq+BERcV1E3FH9fHi7a5MkSfr/27v/WLvvuo7jz1fakRVQyqDMrZ22mGUyRdqlIZM60wzJhoKdRAWirCGaicG4ERh2+gdoYizBDFQMZDJ0KAFkq2WyRKIbzi2Gaccd++EGW9hgvatbF+mYWmGtb/8438s9vetpOae353vO+T4fyc0938/53nM//eaTz333831/3x9pGG2sTB8C3llVLwPOB96e5FxgB3BzVZ0N3NwcS63aPTfPlp23sGHHTWzZeQu75+bb7pIkSZogYw+mq2pfVX2pef00cD+wFtgGXNecdh1wybj7JvXbPTfPVbvuYf7AQQqYP3CQq3bdY0AtSZK+q9Wc6STrgU3AHcDpVbUPegE38JL2eib1al8ffObwEW0HnznM+z//lZZ6JEmSJk1rwXSS5wM3AFdU1beG+LnLkuxJsmf//v0nr4PqvPkDB4dqlyRJ3dNKMJ3kFHqB9CeqalfT/HiSM5r3zwCeONrPVtU1VbW5qjavWbNmPB1WJ61IhmqXJEnd00Y1jwDXAvdX1dV9b90IbG9ebwc+O+6+Sf0OVw3VLkmSuqeNlektwFuAC5Pc1Xz9DLATeE2SB4HXNMdSa9auXjVUuyRJ6p6V4/6FVXU7MOg++avH2RfpWK686Byu2nXPEQ8hrjplBVdedE6LvZIkSZNk7MG0NC0u2bQW6FX1eOzAQc5cvYorLzrnu+2SJEkG09IxXLJprcGzJEkaqNU605IkSdI0c2VaU2n33LzpF5pJjm1Jmi4G05o6C9t8LzwYuLDNN2DQoanm2Jak6WOah6aO23xrVjm2JWn6uDI9JG/Btu+xAdt5D2qXpoVjW5KmjyvTQ1i4BTt/4CDF4i3Y3XPzbXetU84csGnKoHZpWji2JWn6GEwPwVuwk+HKi85h1SkrjmhzMxXNAse2JE0f0zyG4C3YyeBmKppVjm1Jmj4G00M4c/Uq5o8SOHsLdvzcTEWzyrEtSdPFNI8heAtWkiRJ/VyZHsIs3oK1OokkSdLoDKaHNEu3YN0gQpIk6cSY5tFhVieRJEk6MQbTHWZ1EkmSpBNjMN1hbhAhSZJ0YgymO8zqJD275+bZsvMWNuy4iS07b3FHS0mS9D3zAcQOm8XqJMPyIUxJknQiDKY7bpaqk4ziWA9hdvm6SJKk743BtMZiUutZj/shzOW8DpN6TSVJ6hKDaZ10k5xKMc4t4pfzOkzyNZUkqUt8AFEn3STXsx7nQ5jLeR0m+ZpKktQlrkzrpJvketbjfAhzOa/DJF9TSZK6xGBaJ904UylGMa6HMJfzOkz6NZUkqStM89BJZz3rnuW8Dl5TSZImgyvTOumOl0rRlaoUy5lSYo1wSZImQ6qq7T6MbPPmzbVnz562u6ETsLQqBfRWWP/wDS83MJQkSRMjyZ1VtXlpu2keapVVKSRJ0jQzzUOtmsWqFF1JW5EkSa5Mq2WDqk9Ma1WKhbSV+QMHKRY3U9k9N9921yRJ0klgMK1WzVpVCtNWJEnqFtM81KpZq0oxatqKqSGSJE0ng2m1blybpozDKJupLK1ospAaAszMdZEkaVaZ5iEto1HSVkwNkSRperkyLS2jUdJWZrGiiSRJXWEwLS2zYdNWRkkNkSRJk8E0D6lls1bRRJKkLnFlWmrZrFU0kSSpSwympQkwSxVNJEnqEoNpDc2ayJIkST0G0xqKNZElSZIW+QCihmJNZEmSpEUG0xqKNZElSZIWGUxrKINqH1sTWZIkdZHBtIZiTWRJkqRFPoCooVgTWZIkaZHBtIZmTWRJkqQe0zwkSZKkEU1UMJ3k4iRfSfJQkh1t90eSJEk6lokJppOsAP4MeC1wLvDmJOe22ytJkiRpsIkJpoFXAg9V1deq6jvAp4BtLfdJkiRJGmiSgum1wKN9x3ubtiMkuSzJniR79u/fP7bOSZIkSUtNUjCdo7TVsxqqrqmqzVW1ec2aNWPoliRJknR0kxRM7wXO6jteBzzWUl8kSZKk45qkYPrfgLOTbEjyHOBNwI0t90mSJEkaaGI2bamqQ0l+E/g8sAL4WFXd13K3JEmSpIFS9ay05KmRZD/w9bb7oWXzYuDJtjuhieBYEDgOtMixoAVtjoUfqqpnPbA31cG0ZkuSPVW1ue1+qH2OobZxqAAABdRJREFUBYHjQIscC1owiWNhknKmJUmSpKliMC1JkiSNyGBak+SatjugieFYEDgOtMixoAUTNxbMmZYkSZJG5Mq0JEmSNCKDaUmSJGlEBtMauyRnJflCkvuT3Jfk8qb9tCT/kOTB5vsL2+6rxiPJiiRzST7XHG9IckczFj7d7IqqGZdkdZLrkzzQzA8/4bzQTUne0fx9uDfJJ5Oc6rzQDUk+luSJJPf2tR11HkjPnyR5KMndSc5ro88G02rDIeCdVfUy4Hzg7UnOBXYAN1fV2cDNzbG64XLg/r7j9wEfaMbCN4FfbaVXGrc/Bv6+qn4EeAW9MeG80DFJ1gK/BWyuqh+jtyvym3Be6Iq/BC5e0jZoHngtcHbzdRnw4TH18QgG0xq7qtpXVV9qXj9N7w/mWmAbcF1z2nXAJe30UOOUZB3ws8BHm+MAFwLXN6c4FjogyfcDPwVcC1BV36mqAzgvdNVKYFWSlcBzgX04L3RCVf0z8J9LmgfNA9uAj1fPF4HVSc4YT08XGUyrVUnWA5uAO4DTq2of9AJu4CXt9Uxj9EHg3cD/NccvAg5U1aHmeC+9/2xptr0U2A/8RZPy89Ekz8N5oXOqah74I+Ab9ILop4A7cV7oskHzwFrg0b7zWhkXBtNqTZLnAzcAV1TVt9ruj8YvyeuAJ6rqzv7mo5xqDc/ZtxI4D/hwVW0C/htTOjqpyYfdBmwAzgSeR+92/lLOC5qIvxcG02pFklPoBdKfqKpdTfPjC7dnmu9PtNU/jc0W4OeSPAJ8it5t3A/Su1W3sjlnHfBYO93TGO0F9lbVHc3x9fSCa+eF7vlp4OGq2l9VzwC7gFfhvNBlg+aBvcBZfee1Mi4MpjV2TU7stcD9VXV131s3Atub19uBz467bxqvqrqqqtZV1Xp6DxjdUlW/DHwB+IXmNMdCB1TVfwCPJjmnaXo18O84L3TRN4Dzkzy3+XuxMBacF7pr0DxwI3BpU9XjfOCphXSQcXIHRI1dkp8EbgPuYTFP9nfo5U3/DfCD9CbTX6yqpQ8haEYl2Qq8q6pel+Sl9FaqTwPmgF+pqm+32T+dfEk20nsQ9TnA14C30lv0cV7omCS/B7yRXvWnOeDX6OXCOi/MuCSfBLYCLwYeB94D7OYo80Dzn60P0av+8T/AW6tqz9j7bDAtSZIkjcY0D0mSJGlEBtOSJEnSiAymJUmSpBEZTEuSJEkjMpiWJEmSRmQwLUkTJsnhJHf1fT1rJ8AkW5N8bpl/79Ykr+o7fluSS5fzd0jSrFl5/FMkSWN2sKo2tvB7twL/BfwLQFV9pIU+SNJUcWVakqZEkouTPJDkduANfe3vTfKuvuN7k6xvXl+a5O4kX07yV03b65PckWQuyT8mOb05/23AO5rV8Av6PzfJxiRfbD7rb5O8sGn/pyTvS/KvSb6a5IIxXQ5JmggG05I0eVYtSfN4Y5JTgT8HXg9cAPzA8T4kyY8CvwtcWFWvAC5v3rodOL+qNtHbUe7dVfUI8BHgA1W1sapuW/JxHwd+u6p+nN7upe/pe29lVb0SuGJJuyTNPNM8JGnyPCvNo9lq++GqerA5/mvgsuN8zoXA9VX1JEDfNtzrgE8nOYPe1t0PH+tDkrwAWF1VtzZN1wGf6TtlV/P9TmD9cfokSTPFlWlJmh41oP0QR87npzbfM+Bn/hT4UFW9HPj1vvNH9e3m+2FcpJHUMQbTkjQdHgA2JPnh5vjNfe89ApwHkOQ8YEPTfjPwS0le1Lx3WtP+AmC+eb2973OeBr5v6S+uqqeAb/blQ78FuHXpeZLURQbTkjR5luZM76yq/6WX1nFT8wDi1/vOvwE4LcldwG8AXwWoqvuAPwBuTfJl4Orm/PcCn0lyG/Bk3+f8HfDzCw8gLunTduD9Se4GNgK/v5z/YEmaVqkadNdQkiRJ0rG4Mi1JkiSNyGBakiRJGpHBtCRJkjQig2lJkiRpRAbTkiRJ0ogMpiVJkqQRGUxLkiRJI/p/S9biWal8MpYAAAAASUVORK5CYII=\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(12,12))\n", "ax1 = fig.add_subplot(211, xlabel='Income', ylabel='Prestige')\n", "ax1.scatter(prestige.income, prestige.prestige)\n", "xy_outlier = prestige.loc['minister', ['income','prestige']]\n", "ax1.annotate('Minister', xy_outlier, xy_outlier+1, fontsize=16)\n", "ax2 = fig.add_subplot(212, xlabel='Education',\n", " ylabel='Prestige')\n", "ax2.scatter(prestige.education, prestige.prestige);" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: prestige R-squared: 0.828\n", "Model: OLS Adj. R-squared: 0.820\n", "Method: Least Squares F-statistic: 101.2\n", "Date: Tue, 17 Dec 2019 Prob (F-statistic): 8.65e-17\n", "Time: 23:39:15 Log-Likelihood: -178.98\n", "No. Observations: 45 AIC: 364.0\n", "Df Residuals: 42 BIC: 369.4\n", "Df Model: 2 \n", "Covariance Type: nonrobust \n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "Intercept -6.0647 4.272 -1.420 0.163 -14.686 2.556\n", "income 0.5987 0.120 5.003 0.000 0.357 0.840\n", "education 0.5458 0.098 5.555 0.000 0.348 0.744\n", "==============================================================================\n", "Omnibus: 1.279 Durbin-Watson: 1.458\n", "Prob(Omnibus): 0.528 Jarque-Bera (JB): 0.520\n", "Skew: 0.155 Prob(JB): 0.771\n", "Kurtosis: 3.426 Cond. No. 163.\n", "==============================================================================\n", "\n", "Warnings:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n" ] } ], "source": [ "ols_model = ols('prestige ~ income + education', prestige).fit()\n", "print(ols_model.summary())" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "collapsed": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "accountant 0.303900\n", "pilot 0.340920\n", "architect 0.072256\n", "author 0.000711\n", "chemist 0.826578\n", "minister 3.134519\n", "professor 0.768277\n", "dentist -0.498082\n", "reporter -2.397022\n", "engineer 0.306225\n", "undertaker -0.187339\n", "lawyer -0.303082\n", "physician 0.355687\n", "welfare.worker -0.411406\n", "teacher 0.050510\n", "conductor -1.704032\n", "contractor 2.043805\n", "factory.owner 1.602429\n", "store.manager 0.142425\n", "banker 0.508388\n", "bookkeeper -0.902388\n", "mail.carrier -1.433249\n", "insurance.agent -1.930919\n", "store.clerk -1.760491\n", "carpenter 1.068858\n", "electrician 0.731949\n", "RR.engineer 0.808922\n", "machinist 1.887047\n", "auto.repairman 0.522735\n", "plumber -0.377954\n", "gas.stn.attendant -0.666596\n", "coal.miner 1.018527\n", "streetcar.motorman -1.104485\n", "taxi.driver 0.023322\n", "truck.driver -0.129227\n", "machine.operator 0.499922\n", "barber 0.173805\n", "bartender -0.902422\n", "shoe.shiner -0.429357\n", "cook 0.127207\n", "soda.clerk -0.883095\n", "watchman -0.513502\n", "janitor -0.079890\n", "policeman 0.078847\n", "waiter -0.475972\n", "Name: student_resid, dtype: float64\n" ] } ], "source": [ "infl = ols_model.get_influence()\n", "student = infl.summary_frame()['student_resid']\n", "print(student)" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "collapsed": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "minister 3.134519\n", "reporter -2.397022\n", "contractor 2.043805\n", "Name: student_resid, dtype: float64\n" ] } ], "source": [ "print(student.loc[np.abs(student) > 2])" ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "collapsed": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "dfb_Intercept 0.144937\n", "dfb_income -1.220939\n", "dfb_education 1.263019\n", "cooks_d 0.566380\n", "standard_resid 2.849416\n", "hat_diag 0.173058\n", "dffits_internal 1.303510\n", "student_resid 3.134519\n", "dffits 1.433935\n", "Name: minister, dtype: float64\n" ] } ], "source": [ "print(infl.summary_frame().loc['minister'])" ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "collapsed": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " student_resid unadj_p sidak(p)\n", "minister 3.134519 0.003177 0.133421\n", "reporter -2.397022 0.021170 0.618213\n", "contractor 2.043805 0.047433 0.887721\n", "insurance.agent -1.930919 0.060428 0.939485\n", "machinist 1.887047 0.066248 0.954247\n", "store.clerk -1.760491 0.085783 0.982331\n", "conductor -1.704032 0.095944 0.989315\n", "factory.owner 1.602429 0.116738 0.996250\n", "mail.carrier -1.433249 0.159369 0.999595\n", "streetcar.motorman -1.104485 0.275823 1.000000\n", "carpenter 1.068858 0.291386 1.000000\n", "coal.miner 1.018527 0.314400 1.000000\n", "bartender -0.902422 0.372104 1.000000\n", "bookkeeper -0.902388 0.372122 1.000000\n", "soda.clerk -0.883095 0.382334 1.000000\n", "chemist 0.826578 0.413261 1.000000\n", "RR.engineer 0.808922 0.423229 1.000000\n", "professor 0.768277 0.446725 1.000000\n", "electrician 0.731949 0.468363 1.000000\n", "gas.stn.attendant -0.666596 0.508764 1.000000\n", "auto.repairman 0.522735 0.603972 1.000000\n", "watchman -0.513502 0.610357 1.000000\n", "banker 0.508388 0.613906 1.000000\n", "machine.operator 0.499922 0.619802 1.000000\n", "dentist -0.498082 0.621088 1.000000\n", "waiter -0.475972 0.636621 1.000000\n", "shoe.shiner -0.429357 0.669912 1.000000\n", "welfare.worker -0.411406 0.682918 1.000000\n", "plumber -0.377954 0.707414 1.000000\n", "physician 0.355687 0.723898 1.000000\n", "pilot 0.340920 0.734905 1.000000\n", "engineer 0.306225 0.760983 1.000000\n", "accountant 0.303900 0.762741 1.000000\n", "lawyer -0.303082 0.763360 1.000000\n", "undertaker -0.187339 0.852319 1.000000\n", "barber 0.173805 0.862874 1.000000\n", "store.manager 0.142425 0.887442 1.000000\n", "truck.driver -0.129227 0.897810 1.000000\n", "cook 0.127207 0.899399 1.000000\n", "janitor -0.079890 0.936713 1.000000\n", "policeman 0.078847 0.937538 1.000000\n", "architect 0.072256 0.942750 1.000000\n", "teacher 0.050510 0.959961 1.000000\n", "taxi.driver 0.023322 0.981507 1.000000\n", "author 0.000711 0.999436 1.000000\n" ] } ], "source": [ "sidak = ols_model.outlier_test('sidak')\n", "sidak.sort_values('unadj_p', inplace=True)\n", "print(sidak)" ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "collapsed": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " student_resid unadj_p fdr_bh(p)\n", "minister 3.134519 0.003177 0.142974\n", "reporter -2.397022 0.021170 0.476332\n", "contractor 2.043805 0.047433 0.596233\n", "insurance.agent -1.930919 0.060428 0.596233\n", "machinist 1.887047 0.066248 0.596233\n", "store.clerk -1.760491 0.085783 0.616782\n", "conductor -1.704032 0.095944 0.616782\n", "factory.owner 1.602429 0.116738 0.656653\n", "mail.carrier -1.433249 0.159369 0.796844\n", "streetcar.motorman -1.104485 0.275823 0.999436\n", "carpenter 1.068858 0.291386 0.999436\n", "coal.miner 1.018527 0.314400 0.999436\n", "bartender -0.902422 0.372104 0.999436\n", "bookkeeper -0.902388 0.372122 0.999436\n", "soda.clerk -0.883095 0.382334 0.999436\n", "chemist 0.826578 0.413261 0.999436\n", "RR.engineer 0.808922 0.423229 0.999436\n", "professor 0.768277 0.446725 0.999436\n", "electrician 0.731949 0.468363 0.999436\n", "gas.stn.attendant -0.666596 0.508764 0.999436\n", "auto.repairman 0.522735 0.603972 0.999436\n", "watchman -0.513502 0.610357 0.999436\n", "banker 0.508388 0.613906 0.999436\n", "machine.operator 0.499922 0.619802 0.999436\n", "dentist -0.498082 0.621088 0.999436\n", "waiter -0.475972 0.636621 0.999436\n", "shoe.shiner -0.429357 0.669912 0.999436\n", "welfare.worker -0.411406 0.682918 0.999436\n", "plumber -0.377954 0.707414 0.999436\n", "physician 0.355687 0.723898 0.999436\n", "pilot 0.340920 0.734905 0.999436\n", "engineer 0.306225 0.760983 0.999436\n", "accountant 0.303900 0.762741 0.999436\n", "lawyer -0.303082 0.763360 0.999436\n", "undertaker -0.187339 0.852319 0.999436\n", "barber 0.173805 0.862874 0.999436\n", "store.manager 0.142425 0.887442 0.999436\n", "truck.driver -0.129227 0.897810 0.999436\n", "cook 0.127207 0.899399 0.999436\n", "janitor -0.079890 0.936713 0.999436\n", "policeman 0.078847 0.937538 0.999436\n", "architect 0.072256 0.942750 0.999436\n", "teacher 0.050510 0.959961 0.999436\n", "taxi.driver 0.023322 0.981507 0.999436\n", "author 0.000711 0.999436 0.999436\n" ] } ], "source": [ "fdr = ols_model.outlier_test('fdr_bh')\n", "fdr.sort_values('unadj_p', inplace=True)\n", "print(fdr)" ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "collapsed": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " Robust linear Model Regression Results \n", "==============================================================================\n", "Dep. Variable: prestige No. Observations: 45\n", "Model: RLM Df Residuals: 42\n", "Method: IRLS Df Model: 2\n", "Norm: HuberT \n", "Scale Est.: mad \n", "Cov Type: H1 \n", "Date: Tue, 17 Dec 2019 \n", "Time: 23:39:15 \n", "No. Iterations: 18 \n", "==============================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "Intercept -7.1107 3.879 -1.833 0.067 -14.713 0.492\n", "income 0.7015 0.109 6.456 0.000 0.489 0.914\n", "education 0.4854 0.089 5.441 0.000 0.311 0.660\n", "==============================================================================\n", "\n", "If the model instance has been used for another fit with different fit parameters, then the fit options might not be the correct ones anymore .\n" ] } ], "source": [ "rlm_model = rlm('prestige ~ income + education', prestige).fit()\n", "print(rlm_model.summary())" ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "collapsed": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "accountant 1.000000\n", "pilot 1.000000\n", "architect 1.000000\n", "author 1.000000\n", "chemist 1.000000\n", "minister 0.344596\n", "professor 1.000000\n", "dentist 1.000000\n", "reporter 0.441669\n", "engineer 1.000000\n", "undertaker 1.000000\n", "lawyer 1.000000\n", "physician 1.000000\n", "welfare.worker 1.000000\n", "teacher 1.000000\n", "conductor 0.538445\n", "contractor 0.552262\n", "factory.owner 0.706169\n", "store.manager 1.000000\n", "banker 1.000000\n", "bookkeeper 1.000000\n", "mail.carrier 0.690764\n", "insurance.agent 0.533499\n", "store.clerk 0.618656\n", "carpenter 0.935848\n", "electrician 1.000000\n", "RR.engineer 1.000000\n", "machinist 0.570360\n", "auto.repairman 1.000000\n", "plumber 1.000000\n", "gas.stn.attendant 1.000000\n", "coal.miner 0.963821\n", "streetcar.motorman 0.832870\n", "taxi.driver 1.000000\n", "truck.driver 1.000000\n", "machine.operator 1.000000\n", "barber 1.000000\n", "bartender 1.000000\n", "shoe.shiner 1.000000\n", "cook 1.000000\n", "soda.clerk 1.000000\n", "watchman 1.000000\n", "janitor 1.000000\n", "policeman 1.000000\n", "waiter 1.000000\n", "dtype: float64\n" ] } ], "source": [ "print(rlm_model.weights)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Hertzprung Russell data for Star Cluster CYG 0B1 - Leverage Points" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Data is on the luminosity and temperature of 47 stars in the direction of Cygnus." ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "collapsed": true }, "outputs": [], "source": [ "dta = sm.datasets.get_rdataset(\"starsCYG\", \"robustbase\", cache=True).data" ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "collapsed": true }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from matplotlib.patches import Ellipse\n", "fig = plt.figure(figsize=(12,8))\n", "ax = fig.add_subplot(111, xlabel='log(Temp)', ylabel='log(Light)', title='Hertzsprung-Russell Diagram of Star Cluster CYG OB1')\n", "ax.scatter(*dta.values.T)\n", "# highlight outliers\n", "e = Ellipse((3.5, 6), .2, 1, alpha=.25, color='r')\n", "ax.add_patch(e);\n", "ax.annotate('Red giants', xy=(3.6, 6), xytext=(3.8, 6),\n", " arrowprops=dict(facecolor='black', shrink=0.05, width=2),\n", " horizontalalignment='left', verticalalignment='bottom',\n", " clip_on=True, # clip to the axes bounding box\n", " fontsize=16,\n", " )\n", "# annotate these with their index\n", "for i,row in dta.loc[dta['log.Te'] < 3.8].iterrows():\n", " ax.annotate(i, row, row + .01, fontsize=14)\n", "xlim, ylim = ax.get_xlim(), ax.get_ylim()" ] }, { "cell_type": "code", "execution_count": 50, "metadata": { "collapsed": true }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.display import Image\n", "Image(filename='star_diagram.png')" ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "collapsed": true }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/travis/miniconda/envs/statsmodels-test/lib/python3.7/site-packages/numpy/core/fromnumeric.py:2495: FutureWarning: Method .ptp is deprecated and will be removed in a future version. Use numpy.ptp instead.\n", " return ptp(axis=axis, out=out, **kwargs)\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" } ], "source": [ "y = dta['log.light']\n", "X = sm.add_constant(dta['log.Te'], prepend=True)\n", "ols_model = sm.OLS(y, X).fit()\n", "abline_plot(model_results=ols_model, ax=ax)" ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "collapsed": true }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rlm_mod = sm.RLM(y, X, sm.robust.norms.TrimmedMean(.5)).fit()\n", "abline_plot(model_results=rlm_mod, ax=ax, color='red')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Why? Because M-estimators are not robust to leverage points." ] }, { "cell_type": "code", "execution_count": 53, "metadata": { "collapsed": true }, "outputs": [], "source": [ "infl = ols_model.get_influence()" ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "collapsed": true }, "outputs": [ { "data": { "text/plain": [ "10 0.194103\n", "19 0.194103\n", "29 0.198344\n", "33 0.194103\n", "Name: hat_diag, dtype: float64" ] }, "execution_count": 54, "metadata": {}, "output_type": "execute_result" } ], "source": [ "h_bar = 2*(ols_model.df_model + 1 )/ols_model.nobs\n", "hat_diag = infl.summary_frame()['hat_diag']\n", "hat_diag.loc[hat_diag > h_bar]" ] }, { "cell_type": "code", "execution_count": 55, "metadata": { "collapsed": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " student_resid unadj_p sidak(p)\n", "16 -2.049393 0.046415 0.892872\n", "13 -2.035329 0.047868 0.900286\n", "33 1.905847 0.063216 0.953543\n", "18 -1.575505 0.122304 0.997826\n", "1 1.522185 0.135118 0.998911\n", "3 1.522185 0.135118 0.998911\n", "21 -1.450418 0.154034 0.999615\n", "17 -1.426675 0.160731 0.999735\n", "29 1.388520 0.171969 0.999859\n", "14 -1.374733 0.176175 0.999889\n", "35 1.346543 0.185023 0.999933\n", "34 -1.272159 0.209999 0.999985\n", "28 -1.186946 0.241618 0.999998\n", "20 -1.150621 0.256103 0.999999\n", "44 1.134779 0.262612 0.999999\n", "39 1.091886 0.280826 1.000000\n", "19 1.064878 0.292740 1.000000\n", "6 -1.026873 0.310093 1.000000\n", "30 -1.009096 0.318446 1.000000\n", "22 -0.979768 0.332557 1.000000\n", "8 0.961218 0.341695 1.000000\n", "5 0.913802 0.365801 1.000000\n", "11 0.871997 0.387943 1.000000\n", "12 0.856685 0.396261 1.000000\n", "46 -0.833923 0.408829 1.000000\n", "10 0.743920 0.460879 1.000000\n", "42 0.727179 0.470968 1.000000\n", "15 -0.689258 0.494280 1.000000\n", "43 0.688272 0.494895 1.000000\n", "7 0.655712 0.515424 1.000000\n", "40 -0.646396 0.521381 1.000000\n", "26 -0.640978 0.524862 1.000000\n", "25 -0.545561 0.588123 1.000000\n", "37 0.472819 0.638680 1.000000\n", "32 0.472819 0.638680 1.000000\n", "38 0.462187 0.646225 1.000000\n", "0 0.430686 0.668799 1.000000\n", "31 0.341726 0.734184 1.000000\n", "36 0.318911 0.751303 1.000000\n", "4 0.307890 0.759619 1.000000\n", "9 0.235114 0.815211 1.000000\n", "41 0.187732 0.851950 1.000000\n", "2 -0.182093 0.856346 1.000000\n", "23 -0.156014 0.876736 1.000000\n", "27 -0.147406 0.883485 1.000000\n", "24 0.065195 0.948314 1.000000\n", "45 0.045675 0.963776 1.000000\n" ] } ], "source": [ "sidak2 = ols_model.outlier_test('sidak')\n", "sidak2.sort_values('unadj_p', inplace=True)\n", "print(sidak2)" ] }, { "cell_type": "code", "execution_count": 56, "metadata": { "collapsed": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " student_resid unadj_p fdr_bh(p)\n", "16 -2.049393 0.046415 0.764747\n", "13 -2.035329 0.047868 0.764747\n", "33 1.905847 0.063216 0.764747\n", "18 -1.575505 0.122304 0.764747\n", "1 1.522185 0.135118 0.764747\n", "3 1.522185 0.135118 0.764747\n", "21 -1.450418 0.154034 0.764747\n", "17 -1.426675 0.160731 0.764747\n", "29 1.388520 0.171969 0.764747\n", "14 -1.374733 0.176175 0.764747\n", "35 1.346543 0.185023 0.764747\n", "34 -1.272159 0.209999 0.764747\n", "28 -1.186946 0.241618 0.764747\n", "20 -1.150621 0.256103 0.764747\n", "44 1.134779 0.262612 0.764747\n", "39 1.091886 0.280826 0.764747\n", "19 1.064878 0.292740 0.764747\n", "6 -1.026873 0.310093 0.764747\n", "30 -1.009096 0.318446 0.764747\n", "22 -0.979768 0.332557 0.764747\n", "8 0.961218 0.341695 0.764747\n", "5 0.913802 0.365801 0.768599\n", "11 0.871997 0.387943 0.768599\n", "12 0.856685 0.396261 0.768599\n", "46 -0.833923 0.408829 0.768599\n", "10 0.743920 0.460879 0.770890\n", "42 0.727179 0.470968 0.770890\n", "15 -0.689258 0.494280 0.770890\n", "43 0.688272 0.494895 0.770890\n", "7 0.655712 0.515424 0.770890\n", "40 -0.646396 0.521381 0.770890\n", "26 -0.640978 0.524862 0.770890\n", "25 -0.545561 0.588123 0.837630\n", "37 0.472819 0.638680 0.843682\n", "32 0.472819 0.638680 0.843682\n", "38 0.462187 0.646225 0.843682\n", "0 0.430686 0.668799 0.849556\n", "31 0.341726 0.734184 0.892552\n", "36 0.318911 0.751303 0.892552\n", "4 0.307890 0.759619 0.892552\n", "9 0.235114 0.815211 0.922751\n", "41 0.187732 0.851950 0.922751\n", "2 -0.182093 0.856346 0.922751\n", "23 -0.156014 0.876736 0.922751\n", "27 -0.147406 0.883485 0.922751\n", "24 0.065195 0.948314 0.963776\n", "45 0.045675 0.963776 0.963776\n" ] } ], "source": [ "fdr2 = ols_model.outlier_test('fdr_bh')\n", "fdr2.sort_values('unadj_p', inplace=True)\n", "print(fdr2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Let's delete that line" ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "collapsed": true }, "outputs": [], "source": [ "l = ax.lines[-1]\n", "l.remove()\n", "del l" ] }, { "cell_type": "code", "execution_count": 58, "metadata": { "collapsed": true }, "outputs": [ { "data": { "image/png": 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" ] }, "execution_count": 58, "metadata": {}, "output_type": "execute_result" } ], "source": [ "weights = np.ones(len(X))\n", "weights[X[X['log.Te'] < 3.8].index.values - 1] = 0\n", "wls_model = sm.WLS(y, X, weights=weights).fit()\n", "abline_plot(model_results=wls_model, ax=ax, color='green')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* MM estimators are good for this type of problem, unfortunately, we do not yet have these yet. \n", "* It's being worked on, but it gives a good excuse to look at the R cell magics in the notebook." ] }, { "cell_type": "code", "execution_count": 59, "metadata": { "collapsed": true }, "outputs": [], "source": [ "yy = y.values[:,None]\n", "xx = X['log.Te'].values[:,None]" ] }, { "cell_type": "code", "execution_count": 60, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%load_ext rpy2.ipython" ] }, { "cell_type": "code", "execution_count": 61, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%R library(robustbase)\n", "%Rpush yy xx\n", "%R mod <- lmrob(yy ~ xx);\n", "%R params <- mod$coefficients;\n", "%Rpull params" ] }, { "cell_type": "code", "execution_count": 62, "metadata": { "collapsed": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Call:\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "lmrob(formula = yy ~ xx)" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " \\--> method = \"" ] }, { "name": "stdout", "output_type": "stream", "text": [ "MM" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\"\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Coefficients:\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "(Intercept) " ] }, { "name": "stdout", "output_type": "stream", "text": [ " xx " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " -4.969 " ] }, { "name": "stdout", "output_type": "stream", "text": [ " 2.253 " ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] }, { "data": { "text/html": [ "\n", " ListVector with 22 elements.\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
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object with classes: ('matrix',) mapped to:\n", "[1.000000, 1.000000, 1.000000, 1.000000, ..., 4.450000, 4.550000, 4.450000, 4.420000]" ] }, "execution_count": 62, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%R print(mod)" ] }, { "cell_type": "code", "execution_count": 63, "metadata": { "collapsed": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " [RTYPES.REALSXP]\n" ] } ], "source": [ "print(params)" ] }, { "cell_type": "code", "execution_count": 64, "metadata": { "collapsed": true }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 64, "metadata": {}, "output_type": "execute_result" } ], "source": [ "abline_plot(intercept=params[0], slope=params[1], ax=ax, color='red')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise: Breakdown points of M-estimator" ] }, { "cell_type": "code", "execution_count": 65, "metadata": { "collapsed": true }, "outputs": [], "source": [ "np.random.seed(12345)\n", "nobs = 200\n", "beta_true = np.array([3, 1, 2.5, 3, -4])\n", "X = np.random.uniform(-20,20, size=(nobs, len(beta_true)-1))\n", "# stack a constant in front\n", "X = sm.add_constant(X, prepend=True) # np.c_[np.ones(nobs), X]\n", "mc_iter = 500\n", "contaminate = .25 # percentage of response variables to contaminate" ] }, { "cell_type": "code", "execution_count": 66, "metadata": { "collapsed": true }, "outputs": [], "source": [ "all_betas = []\n", "for i in range(mc_iter):\n", " y = np.dot(X, beta_true) + np.random.normal(size=200)\n", " random_idx = np.random.randint(0, nobs, size=int(contaminate * nobs))\n", " y[random_idx] = np.random.uniform(-750, 750)\n", " beta_hat = sm.RLM(y, X).fit().params\n", " all_betas.append(beta_hat)" ] }, { "cell_type": "code", "execution_count": 67, "metadata": { "collapsed": true }, "outputs": [], "source": [ "all_betas = np.asarray(all_betas)\n", "se_loss = lambda x : np.linalg.norm(x, ord=2)**2\n", "se_beta = lmap(se_loss, all_betas - beta_true)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Squared error loss" ] }, { "cell_type": "code", "execution_count": 68, "metadata": { "collapsed": true }, "outputs": [ { "data": { "text/plain": [ "0.4450294873068631" ] }, "execution_count": 68, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.array(se_beta).mean()" ] }, { "cell_type": "code", "execution_count": 69, "metadata": { "collapsed": true }, "outputs": [ { "data": { "text/plain": [ "array([ 2.99711706, 0.99898147, 2.49909344, 2.99712918, -3.99626521])" ] }, "execution_count": 69, "metadata": {}, "output_type": "execute_result" } ], "source": [ "all_betas.mean(0)" ] }, { "cell_type": "code", "execution_count": 70, "metadata": { "collapsed": true }, "outputs": [ { "data": { "text/plain": [ "array([ 3. , 1. , 2.5, 3. , -4. ])" ] }, "execution_count": 70, "metadata": {}, "output_type": "execute_result" } ], "source": [ "beta_true" ] }, { "cell_type": "code", "execution_count": 71, "metadata": { "collapsed": true }, "outputs": [ { "data": { "text/plain": [ "3.236091328676275e-05" ] }, "execution_count": 71, "metadata": {}, "output_type": "execute_result" } ], "source": [ "se_loss(all_betas.mean(0) - beta_true)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.7.5" } }, "nbformat": 4, "nbformat_minor": 1 }