{ "cells": [ { "cell_type": "markdown", "id": "49205efd", "metadata": {}, "source": [ "(GLM-robust)=\n", "# GLM: Robust Linear Regression\n", "\n", ":::{post} January 10, 2023\n", ":tags: regression, linear model, robust\n", ":category: beginner\n", ":author: Thomas Wiecki, Chris Fonnesbeck, Abhipsha Das, Conor Hassan, Igor Kuvychko, Reshama Shaikh, Oriol Abril Pla\n", ":::" ] }, { "cell_type": "markdown", "id": "06c2678d", "metadata": {}, "source": [ "# GLM: Robust Linear Regression\n", "\n", "The tutorial is the second of a three-part series on Bayesian *generalized linear models (GLMs)*, that first appeared on [Thomas Wiecki's blog](https://twiecki.io/):\n", "\n", " 1. {ref}Linear Regression \n", " 2. {ref}Robust Linear Regression \n", " 3. {ref}Hierarchical Linear Regression \n", " \n", "In this blog post I will write about:\n", "\n", " - How a few outliers can largely affect the fit of linear regression models.\n", " - How replacing the normal likelihood with Student T distribution produces robust regression.\n", "\n", "In the {ref}linear regression tutorial  I described how minimizing the squared distance of the regression line is the same as maximizing the likelihood of a Normal distribution with the mean coming from the regression line. This latter probabilistic expression allows us to easily formulate a Bayesian linear regression model.\n", "\n", "This worked splendidly on simulated data. The problem with simulated data though is that it's, well, simulated. In the real world things tend to get more messy and assumptions like normality are easily violated by a few outliers. \n", "\n", "Lets see what happens if we add some outliers to our simulated data from the last post." ] }, { "cell_type": "markdown", "id": "8a7e7bd7", "metadata": {}, "source": [ "First, let's import our modules." ] }, { "cell_type": "code", "execution_count": 1, "id": "33d93af2", "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "import arviz as az\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import pandas as pd\n", "import pymc as pm\n", "import pytensor\n", "import pytensor.tensor as pt\n", "import xarray as xr" ] }, { "cell_type": "code", "execution_count": 2, "id": "c6efb067", "metadata": {}, "outputs": [], "source": [ "RANDOM_SEED = 8927\n", "rng = np.random.default_rng(RANDOM_SEED)\n", "%config InlineBackend.figure_format = 'retina'\n", "az.style.use(\"arviz-darkgrid\")" ] }, { "cell_type": "markdown", "id": "87df168f", "metadata": {}, "source": [ "Create some toy data but also add some outliers." ] }, { "cell_type": "code", "execution_count": 3, "id": "23188f24", "metadata": {}, "outputs": [], "source": [ "size = 100\n", "true_intercept = 1\n", "true_slope = 2\n", "\n", "x = np.linspace(0, 1, size)\n", "# y = a + b*x\n", "true_regression_line = true_intercept + true_slope * x\n", "# add noise\n", "y = true_regression_line + rng.normal(scale=0.5, size=size)\n", "\n", "# Add outliers\n", "x_out = np.append(x, [0.1, 0.15, 0.2])\n", "y_out = np.append(y, [8, 6, 9])\n", "\n", "data = pd.DataFrame(dict(x=x_out, y=y_out))" ] }, { "cell_type": "markdown", "id": "2ff56f93", "metadata": {}, "source": [ "Plot the data together with the true regression line (the three points in the upper left corner are the outliers we added)." ] }, { "cell_type": "code", "execution_count": 4, "id": "21e7220c", "metadata": {}, "outputs": [ { "data": { "image/png": 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1bt1ajRs3Vu3atQ01nXPLyZMnDe2MN3VzpHbt2ob2iRMnslzG19fXdEPFzKQfkS3JMNq9KChTpozT86Z/rpn9EJF+v7Zarbrrrrtc6k/64zqvzlGFDeFxNqxZs0YjR460e/LPKDQ0VO+8846WLFmiSZMmqWzZsvnQQwAAAADXm+SqbXWty3R57FnMDfOyKcW/ipIadLlu6h1LqfVlC4vo6GhZrVZb22q1GgJEV129ejU3umVi78Z19kRFRRnauf1c0o8A9fDwcKlGb3ZLlbiyv+T18w8ODtaoUaP0/vvv227oFhsbqzVr1mjNmjWSJD8/PzVt2lRt2rRRhw4dDKUwMvLy8tLHH3+sV155RRcvXrT1+Z9//rHdTK9YsWKqX7++WrZsqbvuukuVKlXK9nNKL/176ebmpsDAQKeXDQoKkpubmy2UdCaQdDY4tif9MVoUZPe5ZvY883q/vh4RHrto48aNevnll5WYmGib5uHhodatW6tWrVoqXry4IiMjtWPHDu3fv982z65du9SzZ08tXLiwUP1xBwAAAFB0JN/U5roKPpFzzo4izQ+5HaSkH+GXm5x9zXLz+dgLstICU0kuj4bN7uhZV/aX3Hz+mb2X9957r2rXrq1Zs2Zp/fr1htdESg1SN2zYoA0bNmj8+PF6/PHH9cILL2QaKNasWVNz587VnDlztGLFClNQGB8fr+3bt2v79u2aNm2a2rdvryFDhphKO7gqJibG9m9vb2+XbvRosVhUrFgx20jZojYyuKjJj/36elN4/soUAdeuXdNbb71lCI5btGihjz/+2FDLJ83ff/+t1157zfaL19GjR/XFF19o5MiR+dZnAAAAAADyQ8abvfXq1Uv9+/cvoN7kXPrn4+bmpg0bNsjT01MWi0UBAQGSUkcxZnckZ/qBZdeuXVNKSorTNaLTh5V5Jf3zb9SokaZPn54n26levbrGjh2rq1evatu2bQoJCdGePXu0f/9+W0kLKTX4nTdvnrZu3aopU6ZkOjDP399fL774ovr376+dO3dqx44d2rNnj3bv3m143axWq9avX69t27Zp0qRJLpWayKhEiRK2f1+7dk1Wq9XpANlqtSo+Pt7WdmUEOlyXfr8uU6aMli9fXoC9KRq4YZ4L1q1bpzNnztja1apV0/Tp0+0Gx5LUpk0bzZgxw/DL3qJFi0y/pAEAAAAAkB9cGRGZnjM3MksLVNMU9ZvIp38+KSkphjwgt9dvtVp1/vx5p5dNq+ubl9L3Lz/ey5IlS9pGAn/11Vdas2aNPvvsM91///2GkdahoaGaMGFCluvz8PBQ8+bN1adPH33++edavXq1ZsyYoe7duxue25UrV/TWW2/lqHxB+lIoKSkpioyMdHrZiIgIwwhWR6U5kHPp3/tLly4ZgnvYR3jsgr///tvQ7tWrV5a/CNWpU0cdO3a0tWNiYpy6cyZQFO3clb1f3LO7HAAAAADXpL+h1LVr15xe7tKlS1nO4+Pjo3LlytnaISEhLvWtsKlevbqhvWPHjlxdf8aRrvv27XN62fRlMvNK+ucfHh5uuilcXvP29lbbtm01evRozZw505C/rF692qX9V5Lc3d3VoEEDvfjii1q4cKHhpoMnTpzI0f560003GdoZb7boyMGDBw3twnQTzOtR+v3aarUW+fNUfiA8dkHGXwGbNGni1HLNmjUztC9cuJBbXQIKjZmzUjRosFVz57sWBM+db9WgwVbNnHVj1AoCAAAAMtadzc+6melHSEZHRztdX9XZ4PSWW26x/fvixYvatm2bax0sRFq0aGFor1q1KlfX36hRI0P7t99+c2q5uLg4bdq0KVf7Yk/691LK/efvilq1aunRRx+1tePj43MUZvv6+mrAgAGGaaGhodleX8b38o8//nB62fXr1xvaDRs2zHY/kLXCtF8XFYTHLsj4B93ZOz6m/2VXyv5lQkBhtXOXVbNmp/576nTnA+S5862aOj113lmzGYEMAACAG0PGK1ivXLmSb9vOzqi70NBQ7dq1y6n133333Yb21KlTc1QOoCCVL1/eEOTt2LHDdEVyTtSoUUO1a9e2tf/44w8dOHAgy+Vmz56dLzdVu+222wz76g8//KDw8PA8325mKlWqZGinvx9VQa+vfv36CgoKsrVXrVrl1Gt18eJFrVmzxtYuU6aM6tevn+1+IGuNGjVS+fLlbe1Vq1bpyJEjBdijwo/w2AWVK1c2tJ2tMZSxNhCXIOB607iRRf37/vejiDMBcvrgWJL697WocSN+WAEAAMD1r0KFCoa2K+UKcqpBgwaG9vfff+9w/mvXrmncuHFOr79Vq1aGwHX37t0aP368SzeVi4+P186dO52ePy/16dPH0H7nnXd09OhRl9Zx+PDhTGvgPvXUU7Z/p6SkaOTIkQ5rH69bt05z5sxxafvZ5e/vr65du9raV65c0YgRI3T16lWX1vPPP//Ynb5nzx6X1pPxh470AaAkHThwwKUfKjKuL+Nx6QpPT0917tzZ1o6JidFHH33ksD9JSUl6//33DT8EdOnSxXRlAnKXh4eHevXqZWsnJyfr9ddf18WLF11aT0hIyA1zTzPCYxfcfvvthvYvv/yS5TLJycmGIfCVKlUy/LIIXC+6d3M+QLYXHHfvRnAMAACAG0P16tVVsmRJW/ubb77RX3/95XIN1+yoWLGimjZtamtv2bJFEydOVFJSkmneo0ePauDAgTp48KDhhmVZGTlypGHE6qJFizR06NAsywIcOXJE06ZNU+fOnTVv3jynt5eXWrVqpYceesjWjoqKUu/evTV37lyHN9qKi4vTb7/9pqFDh6p79+6ZBlP33XefWrZsaWufOXNGPXr00Jw5cxQWFqakpCTFxsZq9+7deu+99/Tmm28qOTk530ob9OrVSzfffLOtvXv3bj333HPauHGjwx8ELl26pB9++EHdu3fXG2+8YXeePn366IUXXtDSpUsd3mAuISFBX3/9taGsR6NGjVSqVCnDfBMmTFDXrl31zTffZFnSYv369fryyy9t7WLFiqlNmzYOl8lKt27dDIH2H3/8oZEjRyoiIsI0b3h4uF5//XXDSPbKlSvrySefzFEf4JyHHnrIcNydOnVKPXv21K+//uow8L98+bKWL1+ufv36qX///jfMzfb4OcMFd9xxh2rXrm0rZv7jjz+qQ4cOuvPOO+3Ob7Va9fHHH+v48eO2aYMGDZKbG5k9rk9pAXBaMJz2//TBMMExAAAAbnQeHh568MEHtWDBAkmpl66/8sorklJDrPTfGcePH+/0/Xac1a9fPw0YMMAW/s2dO1dr165V69atFRQUpKtXr2r//v3as2ePUlJSVLp0aT322GOaNm2aU+uvXr263n33XY0cOdIWrmzevFmbN29WcHCw7RJ/Nzc3XblyRWfPntWhQ4dcHvmXX4YPH65z587ZRtDGxsbq3Xff1fjx49W4cWNVqVJFJUqU0LVr1xQVFaUjR47oyJEjTpdBGDNmjAYNGqRjx45JSg2oJk2apEmTJtmdv0GDBurTp4+GDBlim+bu7p7DZ2lf8eLF9fHHH2vAgAG2EdFhYWF69dVXVaZMGTVt2lRlypSRt7e3YmJidOnSJR06dEhhYWG2/Sv9DyUZ7d69W7t379bHH3+sqlWrqmbNmipdurR8fHwUHx+vM2fOaNu2bYqKijI815dfftnu+s6cOaOpU6dq6tSpKleunGrXrq0KFSqoZMmSSk5O1sWLF7Vz506dOnXKsNyAAQNUokSJHL1WJUqU0DvvvKPBgwfb9vsNGzZo8+bNatWqle0q9BMnTmjLli2G4NHHx0djx441lbRB3nB3d9e4ceM0cOBAHT58WJIUERGhMWPG6PPPP1fTpk1VoUIFFS9eXLGxsYqMjFRoaKiOHz9eZMvw5AThsQvc3d01fvx4devWTVFRUUpOTtbAgQP15JNP6tFHH1WtWrVUvHhxRUZGKiQkRN988422bNliW/6pp57SY489VoDPAMh7jgJkgmMAAAAgVb9+/bR//35TeYaMI9nyIqho0qSJBg0apIkTJ9qmnT17VkuWLDHNW6ZMGf3vf/+zBSzOuvXWWzVt2jSNHDlSZ86csU0/evSoU2UfXBnpnNc8PT01fvx4TZw4Ud9//70tFL169apTN66zWCwOSxEEBQVp0qRJeu+997JcX8eOHTVy5EjTfpPT4NORihUr6ptvvtHo0aMNJSguXryo1atXZ7m8M+9lSkqKjh07ZgvQM+Pj46Nx48apXr16Wa7z/PnzDkuASJKbm5uef/55Q/mQnGjcuLEmTpyo1157zRZ4x8fHO7yBXlBQkD799FPVrVs3V/oA5/j5+emrr77SBx98YNiPo6Ki9Pvvv2e5vLu7+w0zOJTw2EU1atTQwoUL9eabb2rr1q1KSUnRd999p++++y7TZUqXLq3Bgwfn6PKDG+Eme+mf443wfK9nPZ6xyGJJ0ZRp/wXI8xdYdfnyf/MM6GdR9243xon2esTxChQNHKtA0cHxeuPx8fHRlClTtG7dOq1fv16HDh3SpUuXdO3aNcPN2i0Wi8P9I+PjzurRo4eqVKmiL7/80jQKU0odAd2hQwe9/PLLCggIMN1Qypnt1q1bVz/88INWrFihRYsWZRlABwYGqkWLFurUqZNuvfXWXDsW7L1mrvL09NTQoUP1yCOP6Ntvv9Wff/7psPavu7u76tSpo1tvvVX33XefKlas6HD9pUqV0meffaYtW7Zo1apV2rlzpy5duiR3d3eVLVtW9erV04MPPqhmzZpJkqKjow3L+/r6Zvq8Mu4/2Xn+QUFBmjhxov7++2/NmzdPO3bssFvqJI23t7eaNGmiO+64Q3fddZfdbX766afauHGj/vnnH7v7YHr+/v6666679Pzzz5vKVaR55ZVXtHbtWm3evFmhoaEOf3jx8vJS27Zt9dxzz6lOnToOt52eM69fo0aNtHDhQs2ePVs//fSTLqf/IpxOQECAHn74YfXs2dPh6Oz023alH/aWc3XZ7KzbmXk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\n", 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