{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Robust Linear Models" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true, "execution": { "iopub.execute_input": "2021-02-02T06:52:43.864450Z", "iopub.status.busy": "2021-02-02T06:52:43.854563Z", "iopub.status.idle": "2021-02-02T06:52:44.316283Z", "shell.execute_reply": "2021-02-02T06:52:44.317428Z" } }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2021-02-02T06:52:44.322664Z", "iopub.status.busy": "2021-02-02T06:52:44.321196Z", "iopub.status.idle": "2021-02-02T06:52:45.371837Z", "shell.execute_reply": "2021-02-02T06:52:45.373271Z" } }, "outputs": [], "source": [ "import numpy as np\n", "import statsmodels.api as sm\n", "import matplotlib.pyplot as plt\n", "from statsmodels.sandbox.regression.predstd import wls_prediction_std" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Estimation\n", "\n", "Load data:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "execution": { "iopub.execute_input": "2021-02-02T06:52:45.379022Z", "iopub.status.busy": "2021-02-02T06:52:45.377497Z", "iopub.status.idle": "2021-02-02T06:52:45.394219Z", "shell.execute_reply": "2021-02-02T06:52:45.395448Z" } }, "outputs": [], "source": [ "data = sm.datasets.stackloss.load(as_pandas=False)\n", "data.exog = sm.add_constant(data.exog)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Huber's T norm with the (default) median absolute deviation scaling" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "execution": { "iopub.execute_input": "2021-02-02T06:52:45.400578Z", "iopub.status.busy": "2021-02-02T06:52:45.399226Z", "iopub.status.idle": "2021-02-02T06:52:45.445158Z", "shell.execute_reply": "2021-02-02T06:52:45.446289Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[-41.02649835 0.82938433 0.92606597 -0.12784672]\n", "[9.79189854 0.11100521 0.30293016 0.12864961]\n", " Robust linear Model Regression Results \n", "==============================================================================\n", "Dep. Variable: y No. Observations: 21\n", "Model: RLM Df Residuals: 17\n", "Method: IRLS Df Model: 3\n", "Norm: HuberT \n", "Scale Est.: mad \n", "Cov Type: H1 \n", "Date: Tue, 02 Feb 2021 \n", "Time: 06:52:45 \n", "No. Iterations: 19 \n", "==============================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "var_0 -41.0265 9.792 -4.190 0.000 -60.218 -21.835\n", "var_1 0.8294 0.111 7.472 0.000 0.612 1.047\n", "var_2 0.9261 0.303 3.057 0.002 0.332 1.520\n", "var_3 -0.1278 0.129 -0.994 0.320 -0.380 0.124\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": [ "huber_t = sm.RLM(data.endog, data.exog, M=sm.robust.norms.HuberT())\n", "hub_results = huber_t.fit()\n", "print(hub_results.params)\n", "print(hub_results.bse)\n", "print(hub_results.summary(yname='y',\n", " xname=['var_%d' % i for i in range(len(hub_results.params))]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Huber's T norm with 'H2' covariance matrix" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "execution": { "iopub.execute_input": "2021-02-02T06:52:45.451481Z", "iopub.status.busy": "2021-02-02T06:52:45.449839Z", "iopub.status.idle": "2021-02-02T06:52:45.471830Z", "shell.execute_reply": "2021-02-02T06:52:45.473063Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[-41.02649835 0.82938433 0.92606597 -0.12784672]\n", "[9.08950419 0.11945975 0.32235497 0.11796313]\n" ] } ], "source": [ "hub_results2 = huber_t.fit(cov=\"H2\")\n", "print(hub_results2.params)\n", "print(hub_results2.bse)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Andrew's Wave norm with Huber's Proposal 2 scaling and 'H3' covariance matrix" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "execution": { "iopub.execute_input": "2021-02-02T06:52:45.478005Z", "iopub.status.busy": "2021-02-02T06:52:45.476593Z", "iopub.status.idle": "2021-02-02T06:52:45.540820Z", "shell.execute_reply": "2021-02-02T06:52:45.542086Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Parameters: [-40.8817957 0.79276138 1.04857556 -0.13360865]\n" ] } ], "source": [ "andrew_mod = sm.RLM(data.endog, data.exog, M=sm.robust.norms.AndrewWave())\n", "andrew_results = andrew_mod.fit(scale_est=sm.robust.scale.HuberScale(), cov=\"H3\")\n", "print('Parameters: ', andrew_results.params)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "See ``help(sm.RLM.fit)`` for more options and ``module sm.robust.scale`` for scale options\n", "\n", "## Comparing OLS and RLM\n", "\n", "Artificial data with outliers:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "execution": { "iopub.execute_input": "2021-02-02T06:52:45.547143Z", "iopub.status.busy": "2021-02-02T06:52:45.545522Z", "iopub.status.idle": "2021-02-02T06:52:45.555580Z", "shell.execute_reply": "2021-02-02T06:52:45.556794Z" } }, "outputs": [], "source": [ "nsample = 50\n", "x1 = np.linspace(0, 20, nsample)\n", "X = np.column_stack((x1, (x1-5)**2))\n", "X = sm.add_constant(X)\n", "sig = 0.3 # smaller error variance makes OLS<->RLM contrast bigger\n", "beta = [5, 0.5, -0.0]\n", "y_true2 = np.dot(X, beta)\n", "y2 = y_true2 + sig*1. * np.random.normal(size=nsample)\n", "y2[[39,41,43,45,48]] -= 5 # add some outliers (10% of nsample)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example 1: quadratic function with linear truth\n", "\n", "Note that the quadratic term in OLS regression will capture outlier effects. " ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "execution": { "iopub.execute_input": "2021-02-02T06:52:45.561819Z", "iopub.status.busy": "2021-02-02T06:52:45.560248Z", "iopub.status.idle": "2021-02-02T06:52:45.572442Z", "shell.execute_reply": "2021-02-02T06:52:45.573608Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 4.9399875 0.54301113 -0.01461384]\n", "[0.44996437 0.06946843 0.00614688]\n", "[ 4.57464158 4.85349246 5.12747409 5.39658648 5.66082961 5.92020349\n", " 6.17470812 6.4243435 6.66910964 6.90900652 7.14403415 7.37419253\n", " 7.59948167 7.81990155 8.03545218 8.24613356 8.45194569 8.65288857\n", " 8.84896221 9.04016659 9.22650172 9.4079676 9.58456423 9.75629162\n", " 9.92314975 10.08513863 10.24225826 10.39450864 10.54188977 10.68440166\n", " 10.82204429 10.95481767 11.0827218 11.20575668 11.32392231 11.4372187\n", " 11.54564583 11.64920371 11.74789234 11.84171172 11.93066185 12.01474273\n", " 12.09395437 12.16829675 12.23776988 12.30237376 12.36210839 12.41697377\n", " 12.4669699 12.51209678]\n" ] } ], "source": [ "res = sm.OLS(y2, X).fit()\n", "print(res.params)\n", "print(res.bse)\n", "print(res.predict())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Estimate RLM:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "execution": { "iopub.execute_input": "2021-02-02T06:52:45.578530Z", "iopub.status.busy": "2021-02-02T06:52:45.576844Z", "iopub.status.idle": "2021-02-02T06:52:45.613302Z", "shell.execute_reply": "2021-02-02T06:52:45.614359Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 4.84780243e+00 5.33332553e-01 -4.59650485e-03]\n", "[0.15278692 0.02358824 0.00208719]\n" ] } ], "source": [ "resrlm = sm.RLM(y2, X).fit()\n", "print(resrlm.params)\n", "print(resrlm.bse)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Draw a plot to compare OLS estimates to the robust estimates:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "execution": { "iopub.execute_input": "2021-02-02T06:52:45.619985Z", "iopub.status.busy": "2021-02-02T06:52:45.618184Z", "iopub.status.idle": "2021-02-02T06:52:46.082393Z", "shell.execute_reply": "2021-02-02T06:52:46.083628Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(12,8))\n", "ax = fig.add_subplot(111)\n", "ax.plot(x1, y2, 'o',label=\"data\")\n", "ax.plot(x1, y_true2, 'b-', label=\"True\")\n", "prstd, iv_l, iv_u = wls_prediction_std(res)\n", "ax.plot(x1, res.fittedvalues, 'r-', label=\"OLS\")\n", "ax.plot(x1, iv_u, 'r--')\n", "ax.plot(x1, iv_l, 'r--')\n", "ax.plot(x1, resrlm.fittedvalues, 'g.-', label=\"RLM\")\n", "ax.legend(loc=\"best\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example 2: linear function with linear truth\n", "\n", "Fit a new OLS model using only the linear term and the constant:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "execution": { "iopub.execute_input": "2021-02-02T06:52:46.088935Z", "iopub.status.busy": "2021-02-02T06:52:46.087219Z", "iopub.status.idle": "2021-02-02T06:52:46.098733Z", "shell.execute_reply": "2021-02-02T06:52:46.099778Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[5.52901458 0.39687276]\n", "[0.3933935 0.03389637]\n" ] } ], "source": [ "X2 = X[:,[0,1]]\n", "res2 = sm.OLS(y2, X2).fit()\n", "print(res2.params)\n", "print(res2.bse)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Estimate RLM:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "execution": { "iopub.execute_input": "2021-02-02T06:52:46.105260Z", "iopub.status.busy": "2021-02-02T06:52:46.103393Z", "iopub.status.idle": "2021-02-02T06:52:46.128731Z", "shell.execute_reply": "2021-02-02T06:52:46.129623Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[5.01652461 0.48945402]\n", "[0.12230441 0.01053824]\n" ] } ], "source": [ "resrlm2 = sm.RLM(y2, X2).fit()\n", "print(resrlm2.params)\n", "print(resrlm2.bse)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Draw a plot to compare OLS estimates to the robust estimates:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "execution": { "iopub.execute_input": "2021-02-02T06:52:46.134554Z", "iopub.status.busy": "2021-02-02T06:52:46.133048Z", "iopub.status.idle": "2021-02-02T06:52:46.445220Z", "shell.execute_reply": "2021-02-02T06:52:46.446204Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "prstd, iv_l, iv_u = wls_prediction_std(res2)\n", "\n", "fig, ax = plt.subplots(figsize=(8,6))\n", "ax.plot(x1, y2, 'o', label=\"data\")\n", "ax.plot(x1, y_true2, 'b-', label=\"True\")\n", "ax.plot(x1, res2.fittedvalues, 'r-', label=\"OLS\")\n", "ax.plot(x1, iv_u, 'r--')\n", "ax.plot(x1, iv_l, 'r--')\n", "ax.plot(x1, resrlm2.fittedvalues, 'g.-', label=\"RLM\")\n", "legend = ax.legend(loc=\"best\")" ] } ], "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": "3.7.9" } }, "nbformat": 4, "nbformat_minor": 1 }