{
 "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:                Sat, 07 Nov 2020                                         \n",
      "Time:                        11:34:25                                         \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": [
      "[ 5.12256819  0.51367659 -0.01337823]\n",
      "[0.45328178 0.06998059 0.0061922 ]\n",
      "[ 4.78811249  5.05015264  5.30773524  5.56086029  5.80952778  6.05373772\n",
      "  6.29349012  6.52878495  6.75962224  6.98600198  7.20792416  7.42538879\n",
      "  7.63839587  7.84694539  8.05103737  8.25067179  8.44584866  8.63656798\n",
      "  8.82282975  9.00463396  9.18198062  9.35486973  9.52330129  9.6872753\n",
      "  9.84679175 10.00185066 10.15245201 10.2985958  10.44028205 10.57751075\n",
      " 10.71028189 10.83859548 10.96245152 11.08185    11.19679094 11.30727432\n",
      " 11.41330015 11.51486843 11.61197915 11.70463233 11.79282795 11.87656602\n",
      " 11.95584654 12.0306695  12.10103492 12.16694278 12.22839309 12.28538585\n",
      " 12.33792105 12.38599871]\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": [
      "[ 5.06148029e+00  4.95910060e-01 -2.86498753e-03]\n",
      "[0.14350695 0.02215554 0.00196042]\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 0x7eff8dc73490>"
      ]
     },
     "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": [
      "[5.66179269 0.37989431]\n",
      "[0.39257147 0.03382555]\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": [
      "[5.13865903 0.4721903 ]\n",
      "[0.11128945 0.00958915]\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
}
