{
 "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, 26 Oct 2020                                         \n",
      "Time:                        07:28:11                                         \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": [
      "[ 5.04405132  0.52905623 -0.01433115]\n",
      "[0.43041959 0.06645098 0.00587989]\n",
      "[ 4.68577262  4.95782089  5.2250941   5.48759225  5.74531534  5.99826337\n",
      "  6.24643633  6.48983425  6.7284571   6.96230489  7.19137762  7.41567529\n",
      "  7.6351979   7.84994545  8.05991795  8.26511538  8.46553775  8.66118506\n",
      "  8.85205732  9.03815451  9.21947665  9.39602372  9.56779574  9.73479269\n",
      "  9.89701459 10.05446142 10.2071332  10.35502992 10.49815157 10.63649817\n",
      " 10.77006971 10.89886619 11.0228876  11.14213396 11.25660526 11.3663015\n",
      " 11.47122268 11.5713688  11.66673986 11.75733586 11.8431568  11.92420268\n",
      " 12.00047351 12.07196927 12.13868997 12.20063561 12.25780619 12.31020172\n",
      " 12.35782218 12.40066759]\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": [
      "[ 4.97600307e+00  5.13004495e-01 -4.16324225e-03]\n",
      "[0.1540141  0.0237777  0.00210396]\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 0x7f71da93cbb0>"
      ]
     },
     "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": [
      "[5.62168432 0.38574475]\n",
      "[0.37733479 0.03251269]\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": [
      "[5.12901757 0.47576438]\n",
      "[0.11089801 0.00955542]\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
}
