{
 "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:                Sun, 16 Aug 2020                                         \n",
      "Time:                        18:00:44                                         \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": [
      "[ 5.04981638  0.51972582 -0.01238861]\n",
      "[0.46798118 0.07224998 0.00639301]\n",
      "[ 4.74010123  5.00073605  5.25724305  5.50962224  5.75787361  6.00199716\n",
      "  6.2419929   6.47786083  6.70960094  6.93721323  7.16069771  7.38005437\n",
      "  7.59528322  7.80638425  8.01335747  8.21620287  8.41492046  8.60951023\n",
      "  8.79997218  8.98630632  9.16851265  9.34659116  9.52054185  9.69036473\n",
      "  9.8560598  10.01762704 10.17506648 10.32837809 10.4775619  10.62261788\n",
      " 10.76354605 10.90034641 11.03301895 11.16156367 11.28598058 11.40626968\n",
      " 11.52243096 11.63446442 11.74237007 11.8461479  11.94579792 12.04132012\n",
      " 12.13271451 12.21998108 12.30311984 12.38213078 12.4570139  12.52776921\n",
      " 12.59439671 12.65689639]\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": [
      "[ 4.99079013e+00  5.02783428e-01 -1.98859653e-03]\n",
      "[0.15635307 0.0241388  0.00213591]\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 0x7f62eacabd00>"
      ]
     },
     "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": [
      "[5.54915304 0.39583976]\n",
      "[0.40170704 0.0346127 ]\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": [
      "[5.04652831 0.48644999]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "[0.12078914 0.01040768]\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
}
