{
 "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": [
      "[ 5.05786081  0.52276632 -0.01349978]\n",
      "[0.446898   0.06899502 0.00610499]\n",
      "[ 4.72036633  4.98659245  5.24832052  5.50555054  5.75828251  6.00651642\n",
      "  6.25025228  6.48949009  6.72422985  6.95447155  7.18021521  7.40146081\n",
      "  7.61820835  7.83045785  8.03820929  8.24146268  8.44021802  8.63447531\n",
      "  8.82423454  9.00949573  9.19025886  9.36652393  9.53829096  9.70555993\n",
      "  9.86833085 10.02660372 10.18037853 10.3296553  10.47443401 10.61471467\n",
      " 10.75049727 10.88178183 11.00856833 11.13085678 11.24864718 11.36193952\n",
      " 11.47073381 11.57503005 11.67482824 11.77012838 11.86093046 11.94723449\n",
      " 12.02904047 12.1063484  12.17915827 12.24747009 12.31128386 12.37059958\n",
      " 12.42541724 12.47573686]\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": [
      "[ 5.01137556e+00  5.01734958e-01 -2.56066234e-03]\n",
      "[0.1483856  0.02290873 0.00202707]\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 0x7f6444e05520>"
      ]
     },
     "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": [
      "[5.60198458 0.38776853]\n",
      "[0.38787318 0.03342072]\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": [
      "[5.09293105 0.47943924]\n",
      "[0.109413   0.00942747]\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
}
