{
 "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:                Thu, 05 Nov 2020                                         \n",
      "Time:                        07:28:38                                         \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": [
      "[ 5.1409435   0.51155665 -0.01167533]\n",
      "[0.44050267 0.06800767 0.00601763]\n",
      "[ 4.8490602   5.10356818  5.35418599  5.60091365  5.84375115  6.0826985\n",
      "  6.31775569  6.54892272  6.7761996   6.99958632  7.21908288  7.43468929\n",
      "  7.64640554  7.85423163  8.05816757  8.25821335  8.45436898  8.64663445\n",
      "  8.83500976  9.01949491  9.20008991  9.37679476  9.54960944  9.71853397\n",
      "  9.88356835 10.04471256 10.20196663 10.35533053 10.50480428 10.65038787\n",
      " 10.79208131 10.92988459 11.06379771 11.19382067 11.31995348 11.44219614\n",
      " 11.56054863 11.67501098 11.78558316 11.89226519 11.99505706 12.09395877\n",
      " 12.18897033 12.28009173 12.36732298 12.45066407 12.530115   12.60567578\n",
      " 12.6773464  12.74512686]\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": [
      "[ 5.10410129e+00  4.91683010e-01 -1.04482612e-03]\n",
      "[0.15423383 0.02381162 0.00210696]\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 0x7f7b49051460>"
      ]
     },
     "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": [
      "[5.61153086 0.39480333]\n",
      "[0.37815392 0.03258327]\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": [
      "[5.13611868 0.4824832 ]\n",
      "[0.12046995 0.01038018]\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": "3.8.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
