{
 "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, 07 Dec 2020                                         \n",
      "Time:                        17:22:22                                         \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": [
      "[ 5.08848746  0.50332037 -0.01093516]\n",
      "[0.45108906 0.06964206 0.00616225]\n",
      "[ 4.81510835  5.06335679  5.3079617   5.54892307  5.7862409   6.01991519\n",
      "  6.24994595  6.47633317  6.69907686  6.91817701  7.13363362  7.34544669\n",
      "  7.55361623  7.75814223  7.9590247   8.15626363  8.34985902  8.53981087\n",
      "  8.72611919  8.90878397  9.08780522  9.26318293  9.4349171   9.60300773\n",
      "  9.76745483  9.92825839 10.08541842 10.23893491 10.38880786 10.53503727\n",
      " 10.67762315 10.81656549 10.9518643  11.08351957 11.2115313  11.33589949\n",
      " 11.45662415 11.57370527 11.68714286 11.79693691 11.90308742 12.00559439\n",
      " 12.10445783 12.19967773 12.2912541  12.37918693 12.46347622 12.54412197\n",
      " 12.62112419 12.69448287]\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": [
      "[5.03485048e+00 4.85444929e-01 1.38311473e-05]\n",
      "[0.12492754 0.01928713 0.00170661]\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 0x7f09cf1d8910>"
      ]
     },
     "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": [
      "[5.52924154 0.39396873]\n",
      "[0.38488781 0.03316349]\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": [
      "[5.03443065 0.48557438]\n",
      "[0.102518   0.00883337]\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": "3.9.1rc1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
