{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# M-Estimators for Robust Linear Modeling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:53:57.857185Z",
     "iopub.status.busy": "2021-02-02T06:53:57.856568Z",
     "iopub.status.idle": "2021-02-02T06:53:58.256205Z",
     "shell.execute_reply": "2021-02-02T06:53:58.257510Z"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:53:58.262609Z",
     "iopub.status.busy": "2021-02-02T06:53:58.261229Z",
     "iopub.status.idle": "2021-02-02T06:53:59.205872Z",
     "shell.execute_reply": "2021-02-02T06:53:59.206244Z"
    }
   },
   "outputs": [],
   "source": [
    "from statsmodels.compat import lmap\n",
    "import numpy as np\n",
    "from scipy import stats\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import statsmodels.api as sm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* An M-estimator minimizes the function \n",
    "\n",
    "$$Q(e_i, \\rho) = \\sum_i~\\rho \\left (\\frac{e_i}{s}\\right )$$\n",
    "\n",
    "where $\\rho$ is a symmetric function of the residuals \n",
    "\n",
    "* The effect of $\\rho$ is to reduce the influence of outliers\n",
    "* $s$ is an estimate of scale. \n",
    "* The robust estimates $\\hat{\\beta}$ are computed by the iteratively re-weighted least squares algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* We have several choices available for the weighting functions to be used"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:53:59.210830Z",
     "iopub.status.busy": "2021-02-02T06:53:59.210406Z",
     "iopub.status.idle": "2021-02-02T06:53:59.213499Z",
     "shell.execute_reply": "2021-02-02T06:53:59.213857Z"
    }
   },
   "outputs": [],
   "source": [
    "norms = sm.robust.norms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:53:59.218766Z",
     "iopub.status.busy": "2021-02-02T06:53:59.216000Z",
     "iopub.status.idle": "2021-02-02T06:53:59.221402Z",
     "shell.execute_reply": "2021-02-02T06:53:59.221761Z"
    }
   },
   "outputs": [],
   "source": [
    "def plot_weights(support, weights_func, xlabels, xticks):\n",
    "    fig = plt.figure(figsize=(12,8))\n",
    "    ax = fig.add_subplot(111)\n",
    "    ax.plot(support, weights_func(support))\n",
    "    ax.set_xticks(xticks)\n",
    "    ax.set_xticklabels(xlabels, fontsize=16)\n",
    "    ax.set_ylim(-.1, 1.1)\n",
    "    return ax"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Andrew's Wave"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:53:59.226686Z",
     "iopub.status.busy": "2021-02-02T06:53:59.226269Z",
     "iopub.status.idle": "2021-02-02T06:53:59.229563Z",
     "shell.execute_reply": "2021-02-02T06:53:59.229938Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function weights in module statsmodels.robust.norms:\n",
      "\n",
      "weights(self, z)\n",
      "    Andrew's wave weighting function for the IRLS algorithm\n",
      "    \n",
      "    The psi function scaled by z\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    z : array_like\n",
      "        1d array\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    weights : ndarray\n",
      "        weights(z) = sin(z/a)/(z/a)     for \\|z\\| <= a*pi\n",
      "    \n",
      "        weights(z) = 0                  for \\|z\\| > a*pi\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(norms.AndrewWave.weights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:53:59.254935Z",
     "iopub.status.busy": "2021-02-02T06:53:59.232051Z",
     "iopub.status.idle": "2021-02-02T06:53:59.648319Z",
     "shell.execute_reply": "2021-02-02T06:53:59.648732Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 1,
     "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": [
    "a = 1.339\n",
    "support = np.linspace(-np.pi*a, np.pi*a, 100)\n",
    "andrew = norms.AndrewWave(a=a)\n",
    "plot_weights(support, andrew.weights, ['$-\\pi*a$', '0', '$\\pi*a$'], [-np.pi*a, 0, np.pi*a]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hampel's 17A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:53:59.651621Z",
     "iopub.status.busy": "2021-02-02T06:53:59.650961Z",
     "iopub.status.idle": "2021-02-02T06:53:59.655097Z",
     "shell.execute_reply": "2021-02-02T06:53:59.655524Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function weights in module statsmodels.robust.norms:\n",
      "\n",
      "weights(self, z)\n",
      "    Hampel weighting function for the IRLS algorithm\n",
      "    \n",
      "    The psi function scaled by z\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    z : array_like\n",
      "        1d array\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    weights : ndarray\n",
      "        weights(z) = 1                            for \\|z\\| <= a\n",
      "    \n",
      "        weights(z) = a/\\|z\\|                        for a < \\|z\\| <= b\n",
      "    \n",
      "        weights(z) = a*(c - \\|z\\|)/(\\|z\\|*(c-b))      for b < \\|z\\| <= c\n",
      "    \n",
      "        weights(z) = 0                            for \\|z\\| > c\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(norms.Hampel.weights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:53:59.658203Z",
     "iopub.status.busy": "2021-02-02T06:53:59.657553Z",
     "iopub.status.idle": "2021-02-02T06:53:59.804681Z",
     "shell.execute_reply": "2021-02-02T06:53:59.805085Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 1,
     "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": [
    "c = 8\n",
    "support = np.linspace(-3*c, 3*c, 1000)\n",
    "hampel = norms.Hampel(a=2., b=4., c=c)\n",
    "plot_weights(support, hampel.weights, ['3*c', '0', '3*c'], [-3*c, 0, 3*c]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Huber's t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:53:59.808030Z",
     "iopub.status.busy": "2021-02-02T06:53:59.807346Z",
     "iopub.status.idle": "2021-02-02T06:53:59.811536Z",
     "shell.execute_reply": "2021-02-02T06:53:59.812094Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function weights in module statsmodels.robust.norms:\n",
      "\n",
      "weights(self, z)\n",
      "    Huber's t weighting function for the IRLS algorithm\n",
      "    \n",
      "    The psi function scaled by z\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    z : array_like\n",
      "        1d array\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    weights : ndarray\n",
      "        weights(z) = 1          for \\|z\\| <= t\n",
      "    \n",
      "        weights(z) = t/\\|z\\|      for \\|z\\| > t\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(norms.HuberT.weights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:53:59.835203Z",
     "iopub.status.busy": "2021-02-02T06:53:59.817015Z",
     "iopub.status.idle": "2021-02-02T06:53:59.939989Z",
     "shell.execute_reply": "2021-02-02T06:53:59.939551Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 1,
     "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": [
    "t = 1.345\n",
    "support = np.linspace(-3*t, 3*t, 1000)\n",
    "huber = norms.HuberT(t=t)\n",
    "plot_weights(support, huber.weights, ['-3*t', '0', '3*t'], [-3*t, 0, 3*t]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Least Squares"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:53:59.944608Z",
     "iopub.status.busy": "2021-02-02T06:53:59.943958Z",
     "iopub.status.idle": "2021-02-02T06:53:59.947665Z",
     "shell.execute_reply": "2021-02-02T06:53:59.947316Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function weights in module statsmodels.robust.norms:\n",
      "\n",
      "weights(self, z)\n",
      "    The least squares estimator weighting function for the IRLS algorithm.\n",
      "    \n",
      "    The psi function scaled by the input z\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    z : array_like\n",
      "        1d array\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    weights : ndarray\n",
      "        weights(z) = np.ones(z.shape)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(norms.LeastSquares.weights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:53:59.962806Z",
     "iopub.status.busy": "2021-02-02T06:53:59.958774Z",
     "iopub.status.idle": "2021-02-02T06:54:00.041068Z",
     "shell.execute_reply": "2021-02-02T06:54:00.041391Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 1,
     "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": [
    "support = np.linspace(-3, 3, 1000)\n",
    "lst_sq = norms.LeastSquares()\n",
    "plot_weights(support, lst_sq.weights, ['-3', '0', '3'], [-3, 0, 3]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Ramsay's Ea"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:00.046169Z",
     "iopub.status.busy": "2021-02-02T06:54:00.045171Z",
     "iopub.status.idle": "2021-02-02T06:54:00.048091Z",
     "shell.execute_reply": "2021-02-02T06:54:00.047665Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function weights in module statsmodels.robust.norms:\n",
      "\n",
      "weights(self, z)\n",
      "    Ramsay's Ea weighting function for the IRLS algorithm\n",
      "    \n",
      "    The psi function scaled by z\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    z : array_like\n",
      "        1d array\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    weights : ndarray\n",
      "        weights(z) = exp(-a*\\|z\\|)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(norms.RamsayE.weights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:00.063651Z",
     "iopub.status.busy": "2021-02-02T06:54:00.061722Z",
     "iopub.status.idle": "2021-02-02T06:54:00.142292Z",
     "shell.execute_reply": "2021-02-02T06:54:00.142658Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 1,
     "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": [
    "a = .3\n",
    "support = np.linspace(-3*a, 3*a, 1000)\n",
    "ramsay = norms.RamsayE(a=a)\n",
    "plot_weights(support, ramsay.weights, ['-3*a', '0', '3*a'], [-3*a, 0, 3*a]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Trimmed Mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:00.147471Z",
     "iopub.status.busy": "2021-02-02T06:54:00.146456Z",
     "iopub.status.idle": "2021-02-02T06:54:00.149257Z",
     "shell.execute_reply": "2021-02-02T06:54:00.148894Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function weights in module statsmodels.robust.norms:\n",
      "\n",
      "weights(self, z)\n",
      "    Least trimmed mean weighting function for the IRLS algorithm\n",
      "    \n",
      "    The psi function scaled by z\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    z : array_like\n",
      "        1d array\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    weights : ndarray\n",
      "        weights(z) = 1             for \\|z\\| <= c\n",
      "    \n",
      "        weights(z) = 0             for \\|z\\| > c\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(norms.TrimmedMean.weights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:00.165445Z",
     "iopub.status.busy": "2021-02-02T06:54:00.164659Z",
     "iopub.status.idle": "2021-02-02T06:54:00.248508Z",
     "shell.execute_reply": "2021-02-02T06:54:00.248861Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 1,
     "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": [
    "c = 2\n",
    "support = np.linspace(-3*c, 3*c, 1000)\n",
    "trimmed = norms.TrimmedMean(c=c)\n",
    "plot_weights(support, trimmed.weights, ['-3*c', '0', '3*c'], [-3*c, 0, 3*c]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Tukey's Biweight"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:00.253788Z",
     "iopub.status.busy": "2021-02-02T06:54:00.252697Z",
     "iopub.status.idle": "2021-02-02T06:54:00.255296Z",
     "shell.execute_reply": "2021-02-02T06:54:00.255624Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function weights in module statsmodels.robust.norms:\n",
      "\n",
      "weights(self, z)\n",
      "    Tukey's biweight weighting function for the IRLS algorithm\n",
      "    \n",
      "    The psi function scaled by z\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    z : array_like\n",
      "        1d array\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    weights : ndarray\n",
      "        psi(z) = (1 - (z/c)**2)**2          for \\|z\\| <= R\n",
      "    \n",
      "        psi(z) = 0                          for \\|z\\| > R\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(norms.TukeyBiweight.weights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:00.268263Z",
     "iopub.status.busy": "2021-02-02T06:54:00.267485Z",
     "iopub.status.idle": "2021-02-02T06:54:00.362673Z",
     "shell.execute_reply": "2021-02-02T06:54:00.363042Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 1,
     "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": [
    "c = 4.685\n",
    "support = np.linspace(-3*c, 3*c, 1000)\n",
    "tukey = norms.TukeyBiweight(c=c)\n",
    "plot_weights(support, tukey.weights, ['-3*c', '0', '3*c'], [-3*c, 0, 3*c]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Scale Estimators"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Robust estimates of the location"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:00.367946Z",
     "iopub.status.busy": "2021-02-02T06:54:00.366781Z",
     "iopub.status.idle": "2021-02-02T06:54:00.368901Z",
     "shell.execute_reply": "2021-02-02T06:54:00.369259Z"
    }
   },
   "outputs": [],
   "source": [
    "x = np.array([1, 2, 3, 4, 500])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* The mean is not a robust estimator of location"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:00.373909Z",
     "iopub.status.busy": "2021-02-02T06:54:00.373384Z",
     "iopub.status.idle": "2021-02-02T06:54:00.376129Z",
     "shell.execute_reply": "2021-02-02T06:54:00.376489Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "102.0"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* The median, on the other hand, is a robust estimator with a breakdown point of 50%"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:00.381079Z",
     "iopub.status.busy": "2021-02-02T06:54:00.380581Z",
     "iopub.status.idle": "2021-02-02T06:54:00.383232Z",
     "shell.execute_reply": "2021-02-02T06:54:00.383587Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.0"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.median(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Analogously for the scale\n",
    "* The standard deviation is not robust"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:00.388174Z",
     "iopub.status.busy": "2021-02-02T06:54:00.387572Z",
     "iopub.status.idle": "2021-02-02T06:54:00.390256Z",
     "shell.execute_reply": "2021-02-02T06:54:00.390611Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "199.00251254695254"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.std()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Median Absolute Deviation\n",
    "\n",
    "$$ median_i |X_i - median_j(X_j)|) $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Standardized Median Absolute Deviation is a consistent estimator for $\\hat{\\sigma}$\n",
    "\n",
    "$$\\hat{\\sigma}=K \\cdot MAD$$\n",
    "\n",
    "where $K$ depends on the distribution. For the normal distribution for example,\n",
    "\n",
    "$$K = \\Phi^{-1}(.75)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:00.395376Z",
     "iopub.status.busy": "2021-02-02T06:54:00.394877Z",
     "iopub.status.idle": "2021-02-02T06:54:00.397558Z",
     "shell.execute_reply": "2021-02-02T06:54:00.397903Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6744897501960817"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.norm.ppf(.75)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:00.402623Z",
     "iopub.status.busy": "2021-02-02T06:54:00.401569Z",
     "iopub.status.idle": "2021-02-02T06:54:00.404165Z",
     "shell.execute_reply": "2021-02-02T06:54:00.404516Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  1   2   3   4 500]\n"
     ]
    }
   ],
   "source": [
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:00.409273Z",
     "iopub.status.busy": "2021-02-02T06:54:00.408779Z",
     "iopub.status.idle": "2021-02-02T06:54:00.411757Z",
     "shell.execute_reply": "2021-02-02T06:54:00.412107Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.482602218505602"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sm.robust.scale.mad(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:00.416975Z",
     "iopub.status.busy": "2021-02-02T06:54:00.416442Z",
     "iopub.status.idle": "2021-02-02T06:54:00.419049Z",
     "shell.execute_reply": "2021-02-02T06:54:00.419391Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.4142135623730951"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array([1,2,3,4,5.]).std()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another robust estimator of scale is the Interquartile Range (IQR)\n",
    "\n",
    "$$\\left(\\hat{X}_{0.75} - \\hat{X}_{0.25}\\right),$$\n",
    "\n",
    "where $\\hat{X}_{p}$ is the sample p-th quantile and $K$ depends on the distribution. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The standardized IQR, given by $K \\cdot \\text{IQR}$ for\n",
    "$$K = \\frac{1}{\\Phi^{-1}(.75) - \\Phi^{-1}(.25)} \\approx 0.74,$$\n",
    "is a consistent estimator of the standard deviation for normal data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:00.424770Z",
     "iopub.status.busy": "2021-02-02T06:54:00.423848Z",
     "iopub.status.idle": "2021-02-02T06:54:00.426547Z",
     "shell.execute_reply": "2021-02-02T06:54:00.426908Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(1.48260222)"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sm.robust.scale.iqr(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The IQR is less robust than the MAD in the sense that it has a lower breakdown point: it can withstand 25\\% outlying observations before being completely ruined, whereas the MAD can withstand 50\\% outlying observations. However, the IQR is better suited for asymmetric distributions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Yet another robust estimator of scale is the $Q_n$ estimator, introduced in Rousseeuw & Croux (1993), 'Alternatives to the Median Absolute Deviation'. Then $Q_n$ estimator is given by\n",
    "$$\n",
    "Q_n = K \\left\\lbrace \\vert X_{i} - X_{j}\\vert : i<j\\right\\rbrace_{(h)}\n",
    "$$\n",
    "where $h\\approx (1/4){{n}\\choose{2}}$ and $K$ is a given constant. In words, the $Q_n$ estimator is the normalized $h$-th order statistic of the absolute differences of the data. The normalizing constant $K$ is usually chosen as 2.219144, to make the estimator consistent for the standard deviation in the case of normal data. The $Q_n$ estimator has a 50\\% breakdown point and a 82\\% asymptotic efficiency at the normal distribution, much higher than the 37\\% efficiency of the MAD."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:00.431783Z",
     "iopub.status.busy": "2021-02-02T06:54:00.431239Z",
     "iopub.status.idle": "2021-02-02T06:54:00.433920Z",
     "shell.execute_reply": "2021-02-02T06:54:00.434263Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.219144465985076"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sm.robust.scale.qn_scale(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* The default for Robust Linear Models is MAD\n",
    "* another popular choice is Huber's proposal 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:00.439442Z",
     "iopub.status.busy": "2021-02-02T06:54:00.438357Z",
     "iopub.status.idle": "2021-02-02T06:54:00.440506Z",
     "shell.execute_reply": "2021-02-02T06:54:00.440930Z"
    }
   },
   "outputs": [],
   "source": [
    "np.random.seed(12345)\n",
    "fat_tails = stats.t(6).rvs(40)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:00.458612Z",
     "iopub.status.busy": "2021-02-02T06:54:00.457762Z",
     "iopub.status.idle": "2021-02-02T06:54:00.577411Z",
     "shell.execute_reply": "2021-02-02T06:54:00.577780Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f0974a36550>]"
      ]
     },
     "execution_count": 1,
     "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": [
    "kde = sm.nonparametric.KDEUnivariate(fat_tails)\n",
    "kde.fit()\n",
    "fig = plt.figure(figsize=(12,8))\n",
    "ax = fig.add_subplot(111)\n",
    "ax.plot(kde.support, kde.density);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:00.582915Z",
     "iopub.status.busy": "2021-02-02T06:54:00.582064Z",
     "iopub.status.idle": "2021-02-02T06:54:00.584726Z",
     "shell.execute_reply": "2021-02-02T06:54:00.585074Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0688231044810875 1.3471633229698652\n"
     ]
    }
   ],
   "source": [
    "print(fat_tails.mean(), fat_tails.std())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:00.590417Z",
     "iopub.status.busy": "2021-02-02T06:54:00.589019Z",
     "iopub.status.idle": "2021-02-02T06:54:00.591958Z",
     "shell.execute_reply": "2021-02-02T06:54:00.591565Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(0.0688231044810875, 1.3471633229698652)\n"
     ]
    }
   ],
   "source": [
    "print(stats.norm.fit(fat_tails))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:00.607718Z",
     "iopub.status.busy": "2021-02-02T06:54:00.605781Z",
     "iopub.status.idle": "2021-02-02T06:54:00.609856Z",
     "shell.execute_reply": "2021-02-02T06:54:00.610201Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(6, 0.03900835312789366, 1.0563837144431252)\n"
     ]
    }
   ],
   "source": [
    "print(stats.t.fit(fat_tails, f0=6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:00.617357Z",
     "iopub.status.busy": "2021-02-02T06:54:00.616263Z",
     "iopub.status.idle": "2021-02-02T06:54:00.618855Z",
     "shell.execute_reply": "2021-02-02T06:54:00.619195Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.04048984333271795 1.1557140047569665\n"
     ]
    }
   ],
   "source": [
    "huber = sm.robust.scale.Huber()\n",
    "loc, scale = huber(fat_tails)\n",
    "print(loc, scale)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:00.623391Z",
     "iopub.status.busy": "2021-02-02T06:54:00.622689Z",
     "iopub.status.idle": "2021-02-02T06:54:00.625618Z",
     "shell.execute_reply": "2021-02-02T06:54:00.625949Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.115335001165415"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sm.robust.mad(fat_tails)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:00.636951Z",
     "iopub.status.busy": "2021-02-02T06:54:00.636205Z",
     "iopub.status.idle": "2021-02-02T06:54:00.641557Z",
     "shell.execute_reply": "2021-02-02T06:54:00.642129Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0483916565928972"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sm.robust.mad(fat_tails, c=stats.t(6).ppf(.75))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:00.648606Z",
     "iopub.status.busy": "2021-02-02T06:54:00.647507Z",
     "iopub.status.idle": "2021-02-02T06:54:00.651846Z",
     "shell.execute_reply": "2021-02-02T06:54:00.652403Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.115335001165415"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sm.robust.scale.mad(fat_tails)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Duncan's Occupational Prestige data - M-estimation for outliers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:00.662475Z",
     "iopub.status.busy": "2021-02-02T06:54:00.661110Z",
     "iopub.status.idle": "2021-02-02T06:54:00.663182Z",
     "shell.execute_reply": "2021-02-02T06:54:00.661756Z"
    }
   },
   "outputs": [],
   "source": [
    "from statsmodels.graphics.api import abline_plot\n",
    "from statsmodels.formula.api import ols, rlm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:00.673328Z",
     "iopub.status.busy": "2021-02-02T06:54:00.672614Z",
     "iopub.status.idle": "2021-02-02T06:54:00.691714Z",
     "shell.execute_reply": "2021-02-02T06:54:00.692681Z"
    }
   },
   "outputs": [],
   "source": [
    "prestige = sm.datasets.get_rdataset(\"Duncan\", \"carData\", cache=True).data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:00.696805Z",
     "iopub.status.busy": "2021-02-02T06:54:00.696397Z",
     "iopub.status.idle": "2021-02-02T06:54:00.704158Z",
     "shell.execute_reply": "2021-02-02T06:54:00.705003Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "            type  income  education  prestige\n",
      "accountant  prof      62         86        82\n",
      "pilot       prof      72         76        83\n",
      "architect   prof      75         92        90\n",
      "author      prof      55         90        76\n",
      "chemist     prof      64         86        90\n",
      "minister    prof      21         84        87\n",
      "professor   prof      64         93        93\n",
      "dentist     prof      80        100        90\n",
      "reporter      wc      67         87        52\n",
      "engineer    prof      72         86        88\n"
     ]
    }
   ],
   "source": [
    "print(prestige.head(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:00.708988Z",
     "iopub.status.busy": "2021-02-02T06:54:00.707639Z",
     "iopub.status.idle": "2021-02-02T06:54:01.141983Z",
     "shell.execute_reply": "2021-02-02T06:54:01.142930Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f09749bd190>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x864 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12,12))\n",
    "ax1 = fig.add_subplot(211, xlabel='Income', ylabel='Prestige')\n",
    "ax1.scatter(prestige.income, prestige.prestige)\n",
    "xy_outlier = prestige.loc['minister', ['income','prestige']]\n",
    "ax1.annotate('Minister', xy_outlier, xy_outlier+1, fontsize=16)\n",
    "ax2 = fig.add_subplot(212, xlabel='Education',\n",
    "                           ylabel='Prestige')\n",
    "ax2.scatter(prestige.education, prestige.prestige);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:01.147441Z",
     "iopub.status.busy": "2021-02-02T06:54:01.146006Z",
     "iopub.status.idle": "2021-02-02T06:54:01.173830Z",
     "shell.execute_reply": "2021-02-02T06:54:01.174838Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:               prestige   R-squared:                       0.828\n",
      "Model:                            OLS   Adj. R-squared:                  0.820\n",
      "Method:                 Least Squares   F-statistic:                     101.2\n",
      "Date:                Tue, 02 Feb 2021   Prob (F-statistic):           8.65e-17\n",
      "Time:                        06:54:01   Log-Likelihood:                -178.98\n",
      "No. Observations:                  45   AIC:                             364.0\n",
      "Df Residuals:                      42   BIC:                             369.4\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     -6.0647      4.272     -1.420      0.163     -14.686       2.556\n",
      "income         0.5987      0.120      5.003      0.000       0.357       0.840\n",
      "education      0.5458      0.098      5.555      0.000       0.348       0.744\n",
      "==============================================================================\n",
      "Omnibus:                        1.279   Durbin-Watson:                   1.458\n",
      "Prob(Omnibus):                  0.528   Jarque-Bera (JB):                0.520\n",
      "Skew:                           0.155   Prob(JB):                        0.771\n",
      "Kurtosis:                       3.426   Cond. No.                         163.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "ols_model = ols('prestige ~ income + education', prestige).fit()\n",
    "print(ols_model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:01.179067Z",
     "iopub.status.busy": "2021-02-02T06:54:01.177747Z",
     "iopub.status.idle": "2021-02-02T06:54:01.220551Z",
     "shell.execute_reply": "2021-02-02T06:54:01.221150Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "accountant            0.303900\n",
      "pilot                 0.340920\n",
      "architect             0.072256\n",
      "author                0.000711\n",
      "chemist               0.826578\n",
      "minister              3.134519\n",
      "professor             0.768277\n",
      "dentist              -0.498082\n",
      "reporter             -2.397022\n",
      "engineer              0.306225\n",
      "undertaker           -0.187339\n",
      "lawyer               -0.303082\n",
      "physician             0.355687\n",
      "welfare.worker       -0.411406\n",
      "teacher               0.050510\n",
      "conductor            -1.704032\n",
      "contractor            2.043805\n",
      "factory.owner         1.602429\n",
      "store.manager         0.142425\n",
      "banker                0.508388\n",
      "bookkeeper           -0.902388\n",
      "mail.carrier         -1.433249\n",
      "insurance.agent      -1.930919\n",
      "store.clerk          -1.760491\n",
      "carpenter             1.068858\n",
      "electrician           0.731949\n",
      "RR.engineer           0.808922\n",
      "machinist             1.887047\n",
      "auto.repairman        0.522735\n",
      "plumber              -0.377954\n",
      "gas.stn.attendant    -0.666596\n",
      "coal.miner            1.018527\n",
      "streetcar.motorman   -1.104485\n",
      "taxi.driver           0.023322\n",
      "truck.driver         -0.129227\n",
      "machine.operator      0.499922\n",
      "barber                0.173805\n",
      "bartender            -0.902422\n",
      "shoe.shiner          -0.429357\n",
      "cook                  0.127207\n",
      "soda.clerk           -0.883095\n",
      "watchman             -0.513502\n",
      "janitor              -0.079890\n",
      "policeman             0.078847\n",
      "waiter               -0.475972\n",
      "Name: student_resid, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "infl = ols_model.get_influence()\n",
    "student = infl.summary_frame()['student_resid']\n",
    "print(student)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:01.226661Z",
     "iopub.status.busy": "2021-02-02T06:54:01.226234Z",
     "iopub.status.idle": "2021-02-02T06:54:01.234213Z",
     "shell.execute_reply": "2021-02-02T06:54:01.233464Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "minister      3.134519\n",
      "reporter     -2.397022\n",
      "contractor    2.043805\n",
      "Name: student_resid, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "print(student.loc[np.abs(student) > 2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:01.241540Z",
     "iopub.status.busy": "2021-02-02T06:54:01.240841Z",
     "iopub.status.idle": "2021-02-02T06:54:01.243484Z",
     "shell.execute_reply": "2021-02-02T06:54:01.243960Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dfb_Intercept      0.144937\n",
      "dfb_income        -1.220939\n",
      "dfb_education      1.263019\n",
      "cooks_d            0.566380\n",
      "standard_resid     2.849416\n",
      "hat_diag           0.173058\n",
      "dffits_internal    1.303510\n",
      "student_resid      3.134519\n",
      "dffits             1.433935\n",
      "Name: minister, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "print(infl.summary_frame().loc['minister'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:01.256542Z",
     "iopub.status.busy": "2021-02-02T06:54:01.246424Z",
     "iopub.status.idle": "2021-02-02T06:54:01.287199Z",
     "shell.execute_reply": "2021-02-02T06:54:01.287530Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                    student_resid   unadj_p  sidak(p)\n",
      "minister                 3.134519  0.003177  0.133421\n",
      "reporter                -2.397022  0.021170  0.618213\n",
      "contractor               2.043805  0.047433  0.887721\n",
      "insurance.agent         -1.930919  0.060428  0.939485\n",
      "machinist                1.887047  0.066248  0.954247\n",
      "store.clerk             -1.760491  0.085783  0.982331\n",
      "conductor               -1.704032  0.095944  0.989315\n",
      "factory.owner            1.602429  0.116738  0.996250\n",
      "mail.carrier            -1.433249  0.159369  0.999595\n",
      "streetcar.motorman      -1.104485  0.275823  1.000000\n",
      "carpenter                1.068858  0.291386  1.000000\n",
      "coal.miner               1.018527  0.314400  1.000000\n",
      "bartender               -0.902422  0.372104  1.000000\n",
      "bookkeeper              -0.902388  0.372122  1.000000\n",
      "soda.clerk              -0.883095  0.382334  1.000000\n",
      "chemist                  0.826578  0.413261  1.000000\n",
      "RR.engineer              0.808922  0.423229  1.000000\n",
      "professor                0.768277  0.446725  1.000000\n",
      "electrician              0.731949  0.468363  1.000000\n",
      "gas.stn.attendant       -0.666596  0.508764  1.000000\n",
      "auto.repairman           0.522735  0.603972  1.000000\n",
      "watchman                -0.513502  0.610357  1.000000\n",
      "banker                   0.508388  0.613906  1.000000\n",
      "machine.operator         0.499922  0.619802  1.000000\n",
      "dentist                 -0.498082  0.621088  1.000000\n",
      "waiter                  -0.475972  0.636621  1.000000\n",
      "shoe.shiner             -0.429357  0.669912  1.000000\n",
      "welfare.worker          -0.411406  0.682918  1.000000\n",
      "plumber                 -0.377954  0.707414  1.000000\n",
      "physician                0.355687  0.723898  1.000000\n",
      "pilot                    0.340920  0.734905  1.000000\n",
      "engineer                 0.306225  0.760983  1.000000\n",
      "accountant               0.303900  0.762741  1.000000\n",
      "lawyer                  -0.303082  0.763360  1.000000\n",
      "undertaker              -0.187339  0.852319  1.000000\n",
      "barber                   0.173805  0.862874  1.000000\n",
      "store.manager            0.142425  0.887442  1.000000\n",
      "truck.driver            -0.129227  0.897810  1.000000\n",
      "cook                     0.127207  0.899399  1.000000\n",
      "janitor                 -0.079890  0.936713  1.000000\n",
      "policeman                0.078847  0.937538  1.000000\n",
      "architect                0.072256  0.942750  1.000000\n",
      "teacher                  0.050510  0.959961  1.000000\n",
      "taxi.driver              0.023322  0.981507  1.000000\n",
      "author                   0.000711  0.999436  1.000000\n"
     ]
    }
   ],
   "source": [
    "sidak = ols_model.outlier_test('sidak')\n",
    "sidak.sort_values('unadj_p', inplace=True)\n",
    "print(sidak)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:01.292983Z",
     "iopub.status.busy": "2021-02-02T06:54:01.292248Z",
     "iopub.status.idle": "2021-02-02T06:54:01.316396Z",
     "shell.execute_reply": "2021-02-02T06:54:01.316747Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                    student_resid   unadj_p  fdr_bh(p)\n",
      "minister                 3.134519  0.003177   0.142974\n",
      "reporter                -2.397022  0.021170   0.476332\n",
      "contractor               2.043805  0.047433   0.596233\n",
      "insurance.agent         -1.930919  0.060428   0.596233\n",
      "machinist                1.887047  0.066248   0.596233\n",
      "store.clerk             -1.760491  0.085783   0.616782\n",
      "conductor               -1.704032  0.095944   0.616782\n",
      "factory.owner            1.602429  0.116738   0.656653\n",
      "mail.carrier            -1.433249  0.159369   0.796844\n",
      "streetcar.motorman      -1.104485  0.275823   0.999436\n",
      "carpenter                1.068858  0.291386   0.999436\n",
      "coal.miner               1.018527  0.314400   0.999436\n",
      "bartender               -0.902422  0.372104   0.999436\n",
      "bookkeeper              -0.902388  0.372122   0.999436\n",
      "soda.clerk              -0.883095  0.382334   0.999436\n",
      "chemist                  0.826578  0.413261   0.999436\n",
      "RR.engineer              0.808922  0.423229   0.999436\n",
      "professor                0.768277  0.446725   0.999436\n",
      "electrician              0.731949  0.468363   0.999436\n",
      "gas.stn.attendant       -0.666596  0.508764   0.999436\n",
      "auto.repairman           0.522735  0.603972   0.999436\n",
      "watchman                -0.513502  0.610357   0.999436\n",
      "banker                   0.508388  0.613906   0.999436\n",
      "machine.operator         0.499922  0.619802   0.999436\n",
      "dentist                 -0.498082  0.621088   0.999436\n",
      "waiter                  -0.475972  0.636621   0.999436\n",
      "shoe.shiner             -0.429357  0.669912   0.999436\n",
      "welfare.worker          -0.411406  0.682918   0.999436\n",
      "plumber                 -0.377954  0.707414   0.999436\n",
      "physician                0.355687  0.723898   0.999436\n",
      "pilot                    0.340920  0.734905   0.999436\n",
      "engineer                 0.306225  0.760983   0.999436\n",
      "accountant               0.303900  0.762741   0.999436\n",
      "lawyer                  -0.303082  0.763360   0.999436\n",
      "undertaker              -0.187339  0.852319   0.999436\n",
      "barber                   0.173805  0.862874   0.999436\n",
      "store.manager            0.142425  0.887442   0.999436\n",
      "truck.driver            -0.129227  0.897810   0.999436\n",
      "cook                     0.127207  0.899399   0.999436\n",
      "janitor                 -0.079890  0.936713   0.999436\n",
      "policeman                0.078847  0.937538   0.999436\n",
      "architect                0.072256  0.942750   0.999436\n",
      "teacher                  0.050510  0.959961   0.999436\n",
      "taxi.driver              0.023322  0.981507   0.999436\n",
      "author                   0.000711  0.999436   0.999436\n"
     ]
    }
   ],
   "source": [
    "fdr = ols_model.outlier_test('fdr_bh')\n",
    "fdr.sort_values('unadj_p', inplace=True)\n",
    "print(fdr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:01.326010Z",
     "iopub.status.busy": "2021-02-02T06:54:01.324486Z",
     "iopub.status.idle": "2021-02-02T06:54:01.337936Z",
     "shell.execute_reply": "2021-02-02T06:54:01.338277Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                    Robust linear Model Regression Results                    \n",
      "==============================================================================\n",
      "Dep. Variable:               prestige   No. Observations:                   45\n",
      "Model:                            RLM   Df Residuals:                       42\n",
      "Method:                          IRLS   Df Model:                            2\n",
      "Norm:                          HuberT                                         \n",
      "Scale Est.:                       mad                                         \n",
      "Cov Type:                          H1                                         \n",
      "Date:                Tue, 02 Feb 2021                                         \n",
      "Time:                        06:54:01                                         \n",
      "No. Iterations:                    18                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     -7.1107      3.879     -1.833      0.067     -14.713       0.492\n",
      "income         0.7015      0.109      6.456      0.000       0.489       0.914\n",
      "education      0.4854      0.089      5.441      0.000       0.311       0.660\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": [
    "rlm_model = rlm('prestige ~ income + education', prestige).fit()\n",
    "print(rlm_model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:01.342857Z",
     "iopub.status.busy": "2021-02-02T06:54:01.342461Z",
     "iopub.status.idle": "2021-02-02T06:54:01.345623Z",
     "shell.execute_reply": "2021-02-02T06:54:01.345967Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "accountant            1.000000\n",
      "pilot                 1.000000\n",
      "architect             1.000000\n",
      "author                1.000000\n",
      "chemist               1.000000\n",
      "minister              0.344596\n",
      "professor             1.000000\n",
      "dentist               1.000000\n",
      "reporter              0.441669\n",
      "engineer              1.000000\n",
      "undertaker            1.000000\n",
      "lawyer                1.000000\n",
      "physician             1.000000\n",
      "welfare.worker        1.000000\n",
      "teacher               1.000000\n",
      "conductor             0.538445\n",
      "contractor            0.552262\n",
      "factory.owner         0.706169\n",
      "store.manager         1.000000\n",
      "banker                1.000000\n",
      "bookkeeper            1.000000\n",
      "mail.carrier          0.690764\n",
      "insurance.agent       0.533499\n",
      "store.clerk           0.618656\n",
      "carpenter             0.935848\n",
      "electrician           1.000000\n",
      "RR.engineer           1.000000\n",
      "machinist             0.570360\n",
      "auto.repairman        1.000000\n",
      "plumber               1.000000\n",
      "gas.stn.attendant     1.000000\n",
      "coal.miner            0.963821\n",
      "streetcar.motorman    0.832870\n",
      "taxi.driver           1.000000\n",
      "truck.driver          1.000000\n",
      "machine.operator      1.000000\n",
      "barber                1.000000\n",
      "bartender             1.000000\n",
      "shoe.shiner           1.000000\n",
      "cook                  1.000000\n",
      "soda.clerk            1.000000\n",
      "watchman              1.000000\n",
      "janitor               1.000000\n",
      "policeman             1.000000\n",
      "waiter                1.000000\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "print(rlm_model.weights)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hertzprung Russell data for Star Cluster CYG 0B1 - Leverage Points"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Data is on the luminosity and temperature of 47 stars in the direction of Cygnus."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:01.351008Z",
     "iopub.status.busy": "2021-02-02T06:54:01.350392Z",
     "iopub.status.idle": "2021-02-02T06:54:01.863927Z",
     "shell.execute_reply": "2021-02-02T06:54:01.864612Z"
    }
   },
   "outputs": [],
   "source": [
    "dta = sm.datasets.get_rdataset(\"starsCYG\", \"robustbase\", cache=True).data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:01.872462Z",
     "iopub.status.busy": "2021-02-02T06:54:01.867392Z",
     "iopub.status.idle": "2021-02-02T06:54:02.169765Z",
     "shell.execute_reply": "2021-02-02T06:54:02.170685Z"
    }
   },
   "outputs": [
    {
     "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": [
    "from matplotlib.patches import Ellipse\n",
    "fig = plt.figure(figsize=(12,8))\n",
    "ax = fig.add_subplot(111, xlabel='log(Temp)', ylabel='log(Light)', title='Hertzsprung-Russell Diagram of Star Cluster CYG OB1')\n",
    "ax.scatter(*dta.values.T)\n",
    "# highlight outliers\n",
    "e = Ellipse((3.5, 6), .2, 1, alpha=.25, color='r')\n",
    "ax.add_patch(e);\n",
    "ax.annotate('Red giants', xy=(3.6, 6), xytext=(3.8, 6),\n",
    "            arrowprops=dict(facecolor='black', shrink=0.05, width=2),\n",
    "            horizontalalignment='left', verticalalignment='bottom',\n",
    "            clip_on=True, # clip to the axes bounding box\n",
    "            fontsize=16,\n",
    "     )\n",
    "# annotate these with their index\n",
    "for i,row in dta.loc[dta['log.Te'] < 3.8].iterrows():\n",
    "    ax.annotate(i, row, row + .01, fontsize=14)\n",
    "xlim, ylim = ax.get_xlim(), ax.get_ylim()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:02.174894Z",
     "iopub.status.busy": "2021-02-02T06:54:02.173701Z",
     "iopub.status.idle": "2021-02-02T06:54:02.189180Z",
     "shell.execute_reply": "2021-02-02T06:54:02.188568Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import Image\n",
    "Image(filename='star_diagram.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:02.194191Z",
     "iopub.status.busy": "2021-02-02T06:54:02.193547Z",
     "iopub.status.idle": "2021-02-02T06:54:02.435477Z",
     "shell.execute_reply": "2021-02-02T06:54:02.436111Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = dta['log.light']\n",
    "X = sm.add_constant(dta['log.Te'], prepend=True)\n",
    "ols_model = sm.OLS(y, X).fit()\n",
    "abline_plot(model_results=ols_model, ax=ax)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:02.439016Z",
     "iopub.status.busy": "2021-02-02T06:54:02.438366Z",
     "iopub.status.idle": "2021-02-02T06:54:02.726101Z",
     "shell.execute_reply": "2021-02-02T06:54:02.726500Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rlm_mod = sm.RLM(y, X, sm.robust.norms.TrimmedMean(.5)).fit()\n",
    "abline_plot(model_results=rlm_mod, ax=ax, color='red')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Why? Because M-estimators are not robust to leverage points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:02.729677Z",
     "iopub.status.busy": "2021-02-02T06:54:02.729022Z",
     "iopub.status.idle": "2021-02-02T06:54:02.733278Z",
     "shell.execute_reply": "2021-02-02T06:54:02.734177Z"
    }
   },
   "outputs": [],
   "source": [
    "infl = ols_model.get_influence()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:02.739492Z",
     "iopub.status.busy": "2021-02-02T06:54:02.738594Z",
     "iopub.status.idle": "2021-02-02T06:54:02.780600Z",
     "shell.execute_reply": "2021-02-02T06:54:02.781613Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10    0.194103\n",
       "19    0.194103\n",
       "29    0.198344\n",
       "33    0.194103\n",
       "Name: hat_diag, dtype: float64"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h_bar = 2*(ols_model.df_model + 1 )/ols_model.nobs\n",
    "hat_diag = infl.summary_frame()['hat_diag']\n",
    "hat_diag.loc[hat_diag > h_bar]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:02.784760Z",
     "iopub.status.busy": "2021-02-02T06:54:02.784091Z",
     "iopub.status.idle": "2021-02-02T06:54:02.824386Z",
     "shell.execute_reply": "2021-02-02T06:54:02.824711Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    student_resid   unadj_p  sidak(p)\n",
      "16      -2.049393  0.046415  0.892872\n",
      "13      -2.035329  0.047868  0.900286\n",
      "33       1.905847  0.063216  0.953543\n",
      "18      -1.575505  0.122304  0.997826\n",
      "3        1.522185  0.135118  0.998911\n",
      "1        1.522185  0.135118  0.998911\n",
      "21      -1.450418  0.154034  0.999615\n",
      "17      -1.426675  0.160731  0.999735\n",
      "29       1.388520  0.171969  0.999859\n",
      "14      -1.374733  0.176175  0.999889\n",
      "35       1.346543  0.185023  0.999933\n",
      "34      -1.272159  0.209999  0.999985\n",
      "28      -1.186946  0.241618  0.999998\n",
      "20      -1.150621  0.256103  0.999999\n",
      "44       1.134779  0.262612  0.999999\n",
      "39       1.091886  0.280826  1.000000\n",
      "19       1.064878  0.292740  1.000000\n",
      "6       -1.026873  0.310093  1.000000\n",
      "30      -1.009096  0.318446  1.000000\n",
      "22      -0.979768  0.332557  1.000000\n",
      "8        0.961218  0.341695  1.000000\n",
      "5        0.913802  0.365801  1.000000\n",
      "11       0.871997  0.387943  1.000000\n",
      "12       0.856685  0.396261  1.000000\n",
      "46      -0.833923  0.408829  1.000000\n",
      "10       0.743920  0.460879  1.000000\n",
      "42       0.727179  0.470968  1.000000\n",
      "15      -0.689258  0.494280  1.000000\n",
      "43       0.688272  0.494895  1.000000\n",
      "7        0.655712  0.515424  1.000000\n",
      "40      -0.646396  0.521381  1.000000\n",
      "26      -0.640978  0.524862  1.000000\n",
      "25      -0.545561  0.588123  1.000000\n",
      "37       0.472819  0.638680  1.000000\n",
      "32       0.472819  0.638680  1.000000\n",
      "38       0.462187  0.646225  1.000000\n",
      "0        0.430686  0.668799  1.000000\n",
      "31       0.341726  0.734184  1.000000\n",
      "36       0.318911  0.751303  1.000000\n",
      "4        0.307890  0.759619  1.000000\n",
      "9        0.235114  0.815211  1.000000\n",
      "41       0.187732  0.851950  1.000000\n",
      "2       -0.182093  0.856346  1.000000\n",
      "23      -0.156014  0.876736  1.000000\n",
      "27      -0.147406  0.883485  1.000000\n",
      "24       0.065195  0.948314  1.000000\n",
      "45       0.045675  0.963776  1.000000\n"
     ]
    }
   ],
   "source": [
    "sidak2 = ols_model.outlier_test('sidak')\n",
    "sidak2.sort_values('unadj_p', inplace=True)\n",
    "print(sidak2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:02.827565Z",
     "iopub.status.busy": "2021-02-02T06:54:02.826879Z",
     "iopub.status.idle": "2021-02-02T06:54:02.867660Z",
     "shell.execute_reply": "2021-02-02T06:54:02.868107Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    student_resid   unadj_p  fdr_bh(p)\n",
      "16      -2.049393  0.046415   0.764747\n",
      "13      -2.035329  0.047868   0.764747\n",
      "33       1.905847  0.063216   0.764747\n",
      "18      -1.575505  0.122304   0.764747\n",
      "3        1.522185  0.135118   0.764747\n",
      "1        1.522185  0.135118   0.764747\n",
      "21      -1.450418  0.154034   0.764747\n",
      "17      -1.426675  0.160731   0.764747\n",
      "29       1.388520  0.171969   0.764747\n",
      "14      -1.374733  0.176175   0.764747\n",
      "35       1.346543  0.185023   0.764747\n",
      "34      -1.272159  0.209999   0.764747\n",
      "28      -1.186946  0.241618   0.764747\n",
      "20      -1.150621  0.256103   0.764747\n",
      "44       1.134779  0.262612   0.764747\n",
      "39       1.091886  0.280826   0.764747\n",
      "19       1.064878  0.292740   0.764747\n",
      "6       -1.026873  0.310093   0.764747\n",
      "30      -1.009096  0.318446   0.764747\n",
      "22      -0.979768  0.332557   0.764747\n",
      "8        0.961218  0.341695   0.764747\n",
      "5        0.913802  0.365801   0.768599\n",
      "11       0.871997  0.387943   0.768599\n",
      "12       0.856685  0.396261   0.768599\n",
      "46      -0.833923  0.408829   0.768599\n",
      "10       0.743920  0.460879   0.770890\n",
      "42       0.727179  0.470968   0.770890\n",
      "15      -0.689258  0.494280   0.770890\n",
      "43       0.688272  0.494895   0.770890\n",
      "7        0.655712  0.515424   0.770890\n",
      "40      -0.646396  0.521381   0.770890\n",
      "26      -0.640978  0.524862   0.770890\n",
      "25      -0.545561  0.588123   0.837630\n",
      "37       0.472819  0.638680   0.843682\n",
      "32       0.472819  0.638680   0.843682\n",
      "38       0.462187  0.646225   0.843682\n",
      "0        0.430686  0.668799   0.849556\n",
      "31       0.341726  0.734184   0.892552\n",
      "36       0.318911  0.751303   0.892552\n",
      "4        0.307890  0.759619   0.892552\n",
      "9        0.235114  0.815211   0.922751\n",
      "41       0.187732  0.851950   0.922751\n",
      "2       -0.182093  0.856346   0.922751\n",
      "23      -0.156014  0.876736   0.922751\n",
      "27      -0.147406  0.883485   0.922751\n",
      "24       0.065195  0.948314   0.963776\n",
      "45       0.045675  0.963776   0.963776\n"
     ]
    }
   ],
   "source": [
    "fdr2 = ols_model.outlier_test('fdr_bh')\n",
    "fdr2.sort_values('unadj_p', inplace=True)\n",
    "print(fdr2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Let's delete that line"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:02.871014Z",
     "iopub.status.busy": "2021-02-02T06:54:02.870353Z",
     "iopub.status.idle": "2021-02-02T06:54:02.875295Z",
     "shell.execute_reply": "2021-02-02T06:54:02.875703Z"
    }
   },
   "outputs": [],
   "source": [
    "l =  ax.lines[-1]\n",
    "l.remove()\n",
    "del l"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:02.878684Z",
     "iopub.status.busy": "2021-02-02T06:54:02.878009Z",
     "iopub.status.idle": "2021-02-02T06:54:03.208802Z",
     "shell.execute_reply": "2021-02-02T06:54:03.209710Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weights = np.ones(len(X))\n",
    "weights[X[X['log.Te'] < 3.8].index.values - 1] = 0\n",
    "wls_model = sm.WLS(y, X, weights=weights).fit()\n",
    "abline_plot(model_results=wls_model, ax=ax, color='green')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* MM estimators are good for this type of problem, unfortunately, we do not yet have these yet. \n",
    "* It's being worked on, but it gives a good excuse to look at the R cell magics in the notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:03.213844Z",
     "iopub.status.busy": "2021-02-02T06:54:03.212602Z",
     "iopub.status.idle": "2021-02-02T06:54:03.217895Z",
     "shell.execute_reply": "2021-02-02T06:54:03.218775Z"
    }
   },
   "outputs": [],
   "source": [
    "yy = y.values[:,None]\n",
    "xx = X['log.Te'].values[:,None]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note**: The R code and the results in this notebook has been converted to markdown so that R is not required to build the documents. The R results in the notebook were computed using R 3.5.1 and robustbase 0.93."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "```ipython\n",
    "%load_ext rpy2.ipython\n",
    "\n",
    "%R library(robustbase)\n",
    "%Rpush yy xx\n",
    "%R mod <- lmrob(yy ~ xx);\n",
    "%R params <- mod$coefficients;\n",
    "%Rpull params\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "```ipython\n",
    "%R print(mod)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```\n",
    "Call:\n",
    "lmrob(formula = yy ~ xx)\n",
    " \\--> method = \"MM\"\n",
    "Coefficients:\n",
    "(Intercept)           xx  \n",
    "     -4.969        2.253  \n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:03.223474Z",
     "iopub.status.busy": "2021-02-02T06:54:03.222243Z",
     "iopub.status.idle": "2021-02-02T06:54:03.229627Z",
     "shell.execute_reply": "2021-02-02T06:54:03.230653Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-4.969387980288108 2.2531613477892365\n"
     ]
    }
   ],
   "source": [
    "params = [-4.969387980288108, 2.2531613477892365]  # Computed using R\n",
    "print(params[0], params[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:03.240507Z",
     "iopub.status.busy": "2021-02-02T06:54:03.233257Z",
     "iopub.status.idle": "2021-02-02T06:54:03.582892Z",
     "shell.execute_reply": "2021-02-02T06:54:03.584012Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abline_plot(intercept=params[0], slope=params[1], ax=ax, color='red')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise: Breakdown points of M-estimator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:03.588987Z",
     "iopub.status.busy": "2021-02-02T06:54:03.587478Z",
     "iopub.status.idle": "2021-02-02T06:54:03.595611Z",
     "shell.execute_reply": "2021-02-02T06:54:03.596658Z"
    }
   },
   "outputs": [],
   "source": [
    "np.random.seed(12345)\n",
    "nobs = 200\n",
    "beta_true = np.array([3, 1, 2.5, 3, -4])\n",
    "X = np.random.uniform(-20,20, size=(nobs, len(beta_true)-1))\n",
    "# stack a constant in front\n",
    "X = sm.add_constant(X, prepend=True) # np.c_[np.ones(nobs), X]\n",
    "mc_iter = 500\n",
    "contaminate = .25 # percentage of response variables to contaminate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:03.601091Z",
     "iopub.status.busy": "2021-02-02T06:54:03.599636Z",
     "iopub.status.idle": "2021-02-02T06:54:13.888609Z",
     "shell.execute_reply": "2021-02-02T06:54:13.889015Z"
    }
   },
   "outputs": [],
   "source": [
    "all_betas = []\n",
    "for i in range(mc_iter):\n",
    "    y = np.dot(X, beta_true) + np.random.normal(size=200)\n",
    "    random_idx = np.random.randint(0, nobs, size=int(contaminate * nobs))\n",
    "    y[random_idx] = np.random.uniform(-750, 750)\n",
    "    beta_hat = sm.RLM(y, X).fit().params\n",
    "    all_betas.append(beta_hat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:13.892168Z",
     "iopub.status.busy": "2021-02-02T06:54:13.891470Z",
     "iopub.status.idle": "2021-02-02T06:54:13.901527Z",
     "shell.execute_reply": "2021-02-02T06:54:13.901917Z"
    }
   },
   "outputs": [],
   "source": [
    "all_betas = np.asarray(all_betas)\n",
    "se_loss = lambda x : np.linalg.norm(x, ord=2)**2\n",
    "se_beta = lmap(se_loss, all_betas - beta_true)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Squared error loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:13.904925Z",
     "iopub.status.busy": "2021-02-02T06:54:13.904253Z",
     "iopub.status.idle": "2021-02-02T06:54:13.909883Z",
     "shell.execute_reply": "2021-02-02T06:54:13.910556Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.44502948730683367"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array(se_beta).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:13.916579Z",
     "iopub.status.busy": "2021-02-02T06:54:13.915665Z",
     "iopub.status.idle": "2021-02-02T06:54:13.922717Z",
     "shell.execute_reply": "2021-02-02T06:54:13.922007Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2.99711706,  0.99898147,  2.49909344,  2.99712918, -3.99626521])"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "all_betas.mean(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:13.928098Z",
     "iopub.status.busy": "2021-02-02T06:54:13.927299Z",
     "iopub.status.idle": "2021-02-02T06:54:13.934787Z",
     "shell.execute_reply": "2021-02-02T06:54:13.934095Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 3. ,  1. ,  2.5,  3. , -4. ])"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "beta_true"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:54:13.940653Z",
     "iopub.status.busy": "2021-02-02T06:54:13.938846Z",
     "iopub.status.idle": "2021-02-02T06:54:13.945728Z",
     "shell.execute_reply": "2021-02-02T06:54:13.946778Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.236091328688982e-05"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "se_loss(all_betas.mean(0) - beta_true)"
   ]
  }
 ],
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