{ "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, "execution": { "iopub.execute_input": "2021-02-02T06:53:33.634339Z", "iopub.status.busy": "2021-02-02T06:53:33.626424Z", "iopub.status.idle": "2021-02-02T06:53:34.173620Z", "shell.execute_reply": "2021-02-02T06:53:34.175286Z" } }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2021-02-02T06:53:34.181862Z", "iopub.status.busy": "2021-02-02T06:53:34.180455Z", "iopub.status.idle": "2021-02-02T06:53:35.430342Z", "shell.execute_reply": "2021-02-02T06:53:35.431614Z" } }, "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": 1, "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": { "execution": { "iopub.execute_input": "2021-02-02T06:53:35.437473Z", "iopub.status.busy": "2021-02-02T06:53:35.435811Z", "iopub.status.idle": "2021-02-02T06:53:35.524669Z", "shell.execute_reply": "2021-02-02T06:53:35.526000Z" } }, "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, 02 Feb 2021 No. Observations: 235\n", "Time: 06:53:35 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": { "execution": { "iopub.execute_input": "2021-02-02T06:53:35.532188Z", "iopub.status.busy": "2021-02-02T06:53:35.530370Z", "iopub.status.idle": "2021-02-02T06:53:36.015320Z", "shell.execute_reply": "2021-02-02T06:53:36.016800Z" } }, "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 0.15 111.693659 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': 147.47538852370585, 'b': 0.4851784236769232, 'lb': 0.45687381301842295, 'ub': 0.5134830343354234}\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": { "execution": { "iopub.execute_input": "2021-02-02T06:53:36.023554Z", "iopub.status.busy": "2021-02-02T06:53:36.021504Z", "iopub.status.idle": "2021-02-02T06:53:36.482494Z", "shell.execute_reply": "2021-02-02T06:53:36.480876Z" } }, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Food expenditure')" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "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": { "execution": { "iopub.execute_input": "2021-02-02T06:53:36.489902Z", "iopub.status.busy": "2021-02-02T06:53:36.489013Z", "iopub.status.idle": "2021-02-02T06:53:36.989373Z", "shell.execute_reply": "2021-02-02T06:53:36.990872Z" } }, "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": "3.7.9" } }, "nbformat": 4, "nbformat_minor": 1 }