{
 "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:                Mon, 24 Feb 2020                                         \n",
      "Time:                        22:49:06                                         \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": [
      "[ 5.10884646  0.53153982 -0.01493959]\n",
      "[0.43932799 0.06782631 0.00600158]\n",
      "[ 4.73535665  5.01080071  5.28126698  5.54675546  5.80726615  6.06279905\n",
      "  6.31335416  6.55893148  6.79953101  7.03515275  7.2657967   7.49146286\n",
      "  7.71215123  7.92786181  8.1385946   8.3443496   8.54512681  8.74092623\n",
      "  8.93174786  9.1175917   9.29845775  9.474346    9.64525647  9.81118915\n",
      "  9.97214404 10.12812114 10.27912045 10.42514197 10.56618569 10.70225163\n",
      " 10.83333978 10.95945014 11.08058271 11.19673748 11.30791447 11.41411367\n",
      " 11.51533508 11.6115787  11.70284452 11.78913256 11.87044281 11.94677526\n",
      " 12.01812993 12.08450681 12.14590589 12.20232719 12.2537707  12.30023641\n",
      " 12.34172434 12.37823448]\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": [
      "[ 4.99505385  0.52677011 -0.00604195]\n",
      "[0.15225709 0.02350644 0.00207996]\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 0x7fdea84ea550>"
      ]
     },
     "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": [
      "[5.71100351 0.38214389]\n",
      "[0.3860745  0.03326574]\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": [
      "[5.25790817 0.46873405]\n",
      "[0.12445114 0.01072321]\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": "3.8.2rc2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
