{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Quantile regression" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "This example page shows how to use ``statsmodels``' ``QuantReg`` class to replicate parts of the analysis published in \n", "\n", "* Koenker, Roger and Kevin F. Hallock. \"Quantile Regression\". Journal of Economic Perspectives, Volume 15, Number 4, Fall 2001, Pages 143–156\n", "\n", "We are interested in the relationship between income and expenditures on food for a sample of working class Belgian households in 1857 (the Engel data). \n", "\n", "## Setup\n", "\n", "We first need to load some modules and to retrieve the data. Conveniently, the Engel dataset is shipped with ``statsmodels``." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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incomefoodexp
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" ], "text/plain": [ " income foodexp\n", "0 420.157651 255.839425\n", "1 541.411707 310.958667\n", "2 901.157457 485.680014\n", "3 639.080229 402.997356\n", "4 750.875606 495.560775" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import numpy as np\n", "import pandas as pd\n", "import statsmodels.api as sm\n", "import statsmodels.formula.api as smf\n", "import matplotlib.pyplot as plt\n", "\n", "data = sm.datasets.engel.load_pandas().data\n", "data.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Least Absolute Deviation\n", "\n", "The LAD model is a special case of quantile regression where q=0.5" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " QuantReg Regression Results \n", "==============================================================================\n", "Dep. Variable: foodexp Pseudo R-squared: 0.6206\n", "Model: QuantReg Bandwidth: 64.51\n", "Method: Least Squares Sparsity: 209.3\n", "Date: Tue, 17 Dec 2019 No. Observations: 235\n", "Time: 23:41:57 Df Residuals: 233\n", " Df Model: 1\n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "Intercept 81.4823 14.634 5.568 0.000 52.649 110.315\n", "income 0.5602 0.013 42.516 0.000 0.534 0.586\n", "==============================================================================\n", "\n", "The condition number is large, 2.38e+03. This might indicate that there are\n", "strong multicollinearity or other numerical problems.\n" ] } ], "source": [ "mod = smf.quantreg('foodexp ~ income', data)\n", "res = mod.fit(q=.5)\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Visualizing the results\n", "\n", "We estimate the quantile regression model for many quantiles between .05 and .95, and compare best fit line from each of these models to Ordinary Least Squares results. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Prepare data for plotting\n", "\n", "For convenience, we place the quantile regression results in a Pandas DataFrame, and the OLS results in a dictionary." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " q a b lb ub\n", "0 0.05 124.880097 0.343361 0.268632 0.418090\n", "1 0.15 111.693660 0.423708 0.382780 0.464636\n", "2 0.25 95.483539 0.474103 0.439900 0.508306\n", "3 0.35 105.841294 0.488901 0.457759 0.520043\n", "4 0.45 81.083647 0.552428 0.525021 0.579835\n", "5 0.55 89.661370 0.565601 0.540955 0.590247\n", "6 0.65 74.033435 0.604576 0.582169 0.626982\n", "7 0.75 62.396584 0.644014 0.622411 0.665617\n", "8 0.85 52.272216 0.677603 0.657383 0.697823\n", "9 0.95 64.103964 0.709069 0.687831 0.730306\n", "{'a': 147.47538852370562, 'b': 0.48517842367692354, 'lb': 0.4568738130184233, 'ub': 0.5134830343354237}\n" ] } ], "source": [ "quantiles = np.arange(.05, .96, .1)\n", "def fit_model(q):\n", " res = mod.fit(q=q)\n", " return [q, res.params['Intercept'], res.params['income']] + \\\n", " res.conf_int().loc['income'].tolist()\n", " \n", "models = [fit_model(x) for x in quantiles]\n", "models = pd.DataFrame(models, columns=['q', 'a', 'b', 'lb', 'ub'])\n", "\n", "ols = smf.ols('foodexp ~ income', data).fit()\n", "ols_ci = ols.conf_int().loc['income'].tolist()\n", "ols = dict(a = ols.params['Intercept'],\n", " b = ols.params['income'],\n", " lb = ols_ci[0],\n", " ub = ols_ci[1])\n", "\n", "print(models)\n", "print(ols)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### First plot\n", "\n", "This plot compares best fit lines for 10 quantile regression models to the least squares fit. As Koenker and Hallock (2001) point out, we see that:\n", "\n", "1. Food expenditure increases with income\n", "2. The *dispersion* of food expenditure increases with income\n", "3. The least squares estimates fit low income observations quite poorly (i.e. the OLS line passes over most low income households)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x = np.arange(data.income.min(), data.income.max(), 50)\n", "get_y = lambda a, b: a + b * x\n", "\n", "fig, ax = plt.subplots(figsize=(8, 6))\n", "\n", "for i in range(models.shape[0]):\n", " y = get_y(models.a[i], models.b[i])\n", " ax.plot(x, y, linestyle='dotted', color='grey')\n", " \n", "y = get_y(ols['a'], ols['b'])\n", "\n", "ax.plot(x, y, color='red', label='OLS')\n", "ax.scatter(data.income, data.foodexp, alpha=.2)\n", "ax.set_xlim((240, 3000))\n", "ax.set_ylim((240, 2000))\n", "legend = ax.legend()\n", "ax.set_xlabel('Income', fontsize=16)\n", "ax.set_ylabel('Food expenditure', fontsize=16);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Second plot\n", "\n", "The dotted black lines form 95% point-wise confidence band around 10 quantile regression estimates (solid black line). The red lines represent OLS regression results along with their 95% confidence interval.\n", "\n", "In most cases, the quantile regression point estimates lie outside the OLS confidence interval, which suggests that the effect of income on food expenditure may not be constant across the distribution." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "n = models.shape[0]\n", "p1 = plt.plot(models.q, models.b, color='black', label='Quantile Reg.')\n", "p2 = plt.plot(models.q, models.ub, linestyle='dotted', color='black')\n", "p3 = plt.plot(models.q, models.lb, linestyle='dotted', color='black')\n", "p4 = plt.plot(models.q, [ols['b']] * n, color='red', label='OLS')\n", "p5 = plt.plot(models.q, [ols['lb']] * n, linestyle='dotted', color='red')\n", "p6 = plt.plot(models.q, [ols['ub']] * n, linestyle='dotted', color='red')\n", "plt.ylabel(r'$\\beta_{income}$')\n", "plt.xlabel('Quantiles of the conditional food expenditure distribution')\n", "plt.legend()\n", "plt.show()" ] } ], "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": "3.7.5" } }, "nbformat": 4, "nbformat_minor": 1 }