{
 "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, 09 Aug 2020                                         \n",
      "Time:                        21:12:11                                         \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": [
      "[ 5.13175978  0.50425606 -0.01197198]\n",
      "[0.44407238 0.06855878 0.00606639]\n",
      "[ 4.83246022  5.08514976  5.33385029  5.57856183  5.81928437  6.05601792\n",
      "  6.28876246  6.517518    6.74228455  6.96306209  7.17985064  7.39265019\n",
      "  7.60146074  7.80628229  8.00711485  8.2039584   8.39681296  8.58567851\n",
      "  8.77055507  8.95144263  9.12834119  9.30125075  9.47017131  9.63510288\n",
      "  9.79604544  9.95299901 10.10596358 10.25493915 10.39992572 10.54092329\n",
      " 10.67793186 10.81095143 10.93998201 11.06502359 11.18607616 11.30313974\n",
      " 11.41621432 11.5252999  11.63039649 11.73150407 11.82862266 11.92175224\n",
      " 12.01089283 12.09604442 12.17720701 12.2543806  12.32756519 12.39676079\n",
      " 12.46196738 12.52318498]\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": [
      "[ 5.07325243e+00  4.86420020e-01 -1.18272005e-03]\n",
      "[0.11908714 0.01838545 0.00162683]\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 0x7fe56e2196d0>"
      ]
     },
     "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": [
      "[5.61430398 0.38453624]\n",
      "[0.38170747 0.03288946]\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": [
      "[5.11807284 0.47638127]\n",
      "[0.09392871 0.00809328]\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
}
