{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Robust Linear Models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "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": {},
   "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": {},
   "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, 08 Sep 2020                                         \n",
      "Time:                        17:35:08                                         \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": {},
   "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": {},
   "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": {},
   "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": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 5.20358527  0.50200262 -0.01159169]\n",
      "[0.44949335 0.06939571 0.00614045]\n",
      "[ 4.91379301  5.16407392  5.41049254  5.65304887  5.89174291  6.12657467\n",
      "  6.35754413  6.58465131  6.80789621  7.02727881  7.24279913  7.45445716\n",
      "  7.66225291  7.86618636  8.06625753  8.26246641  8.45481301  8.64329731\n",
      "  8.82791933  9.00867907  9.18557651  9.35861167  9.52778454  9.69309512\n",
      "  9.85454341 10.01212942 10.16585314 10.31571457 10.46171372 10.60385057\n",
      " 10.74212515 10.87653743 11.00708742 11.13377513 11.25660055 11.37556368\n",
      " 11.49066453 11.60190309 11.70927936 11.81279334 11.91244504 12.00823445\n",
      " 12.10016157 12.1882264  12.27242895 12.35276921 12.42924718 12.50186286\n",
      " 12.57061626 12.63550737]\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": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 5.14974914e+00  4.83451976e-01 -8.33371055e-04]\n",
      "[0.13860326 0.02139847 0.00189343]\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": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fb6f88e8310>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "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": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[5.67080135 0.38608572]\n",
      "[0.38510854 0.03318251]\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": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[5.18104336 0.47549722]\n",
      "[0.11380098 0.00980555]\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": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "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": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
