{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Ordinary Least Squares" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2022-11-02T17:11:17.966783Z", "iopub.status.busy": "2022-11-02T17:11:17.966060Z", "iopub.status.idle": "2022-11-02T17:11:18.453001Z", "shell.execute_reply": "2022-11-02T17:11:18.452221Z" } }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2022-11-02T17:11:18.457293Z", "iopub.status.busy": "2022-11-02T17:11:18.456968Z", "iopub.status.idle": "2022-11-02T17:11:19.311655Z", "shell.execute_reply": "2022-11-02T17:11:19.310766Z" } }, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import pandas as pd\n", "import statsmodels.api as sm\n", "\n", "np.random.seed(9876789)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## OLS estimation\n", "\n", "Artificial data:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "execution": { "iopub.execute_input": "2022-11-02T17:11:19.317173Z", "iopub.status.busy": "2022-11-02T17:11:19.315860Z", "iopub.status.idle": "2022-11-02T17:11:19.321545Z", "shell.execute_reply": "2022-11-02T17:11:19.320993Z" } }, "outputs": [], "source": [ "nsample = 100\n", "x = np.linspace(0, 10, 100)\n", "X = np.column_stack((x, x ** 2))\n", "beta = np.array([1, 0.1, 10])\n", "e = np.random.normal(size=nsample)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Our model needs an intercept so we add a column of 1s:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "execution": { "iopub.execute_input": "2022-11-02T17:11:19.326136Z", "iopub.status.busy": "2022-11-02T17:11:19.325015Z", "iopub.status.idle": "2022-11-02T17:11:19.329700Z", "shell.execute_reply": "2022-11-02T17:11:19.329170Z" } }, "outputs": [], "source": [ "X = sm.add_constant(X)\n", "y = np.dot(X, beta) + e" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Fit and summary:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "execution": { "iopub.execute_input": "2022-11-02T17:11:19.334197Z", "iopub.status.busy": "2022-11-02T17:11:19.333073Z", "iopub.status.idle": "2022-11-02T17:11:19.346287Z", "shell.execute_reply": "2022-11-02T17:11:19.345653Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: y R-squared: 1.000\n", "Model: OLS Adj. R-squared: 1.000\n", "Method: Least Squares F-statistic: 4.020e+06\n", "Date: Wed, 02 Nov 2022 Prob (F-statistic): 2.83e-239\n", "Time: 17:11:19 Log-Likelihood: -146.51\n", "No. Observations: 100 AIC: 299.0\n", "Df Residuals: 97 BIC: 306.8\n", "Df Model: 2 \n", "Covariance Type: nonrobust \n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "const 1.3423 0.313 4.292 0.000 0.722 1.963\n", "x1 -0.0402 0.145 -0.278 0.781 -0.327 0.247\n", "x2 10.0103 0.014 715.745 0.000 9.982 10.038\n", "==============================================================================\n", "Omnibus: 2.042 Durbin-Watson: 2.274\n", "Prob(Omnibus): 0.360 Jarque-Bera (JB): 1.875\n", "Skew: 0.234 Prob(JB): 0.392\n", "Kurtosis: 2.519 Cond. No. 144.\n", "==============================================================================\n", "\n", "Notes:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n" ] } ], "source": [ "model = sm.OLS(y, X)\n", "results = model.fit()\n", "print(results.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Quantities of interest can be extracted directly from the fitted model. Type ``dir(results)`` for a full list. Here are some examples: " ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "execution": { "iopub.execute_input": "2022-11-02T17:11:19.351156Z", "iopub.status.busy": "2022-11-02T17:11:19.349987Z", "iopub.status.idle": "2022-11-02T17:11:19.356559Z", "shell.execute_reply": "2022-11-02T17:11:19.355979Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Parameters: [ 1.34233516 -0.04024948 10.01025357]\n", "R2: 0.9999879365025871\n" ] } ], "source": [ "print(\"Parameters: \", results.params)\n", "print(\"R2: \", results.rsquared)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## OLS non-linear curve but linear in parameters\n", "\n", "We simulate artificial data with a non-linear relationship between x and y:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "execution": { "iopub.execute_input": "2022-11-02T17:11:19.361310Z", "iopub.status.busy": "2022-11-02T17:11:19.360186Z", "iopub.status.idle": "2022-11-02T17:11:19.366159Z", "shell.execute_reply": "2022-11-02T17:11:19.365571Z" } }, "outputs": [], "source": [ "nsample = 50\n", "sig = 0.5\n", "x = np.linspace(0, 20, nsample)\n", "X = np.column_stack((x, np.sin(x), (x - 5) ** 2, np.ones(nsample)))\n", "beta = [0.5, 0.5, -0.02, 5.0]\n", "\n", "y_true = np.dot(X, beta)\n", "y = y_true + sig * np.random.normal(size=nsample)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Fit and summary:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "execution": { "iopub.execute_input": "2022-11-02T17:11:19.371473Z", "iopub.status.busy": "2022-11-02T17:11:19.370359Z", "iopub.status.idle": "2022-11-02T17:11:19.382661Z", "shell.execute_reply": "2022-11-02T17:11:19.382099Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: y R-squared: 0.933\n", "Model: OLS Adj. R-squared: 0.928\n", "Method: Least Squares F-statistic: 211.8\n", "Date: Wed, 02 Nov 2022 Prob (F-statistic): 6.30e-27\n", "Time: 17:11:19 Log-Likelihood: -34.438\n", "No. Observations: 50 AIC: 76.88\n", "Df Residuals: 46 BIC: 84.52\n", "Df Model: 3 \n", "Covariance Type: nonrobust \n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "x1 0.4687 0.026 17.751 0.000 0.416 0.522\n", "x2 0.4836 0.104 4.659 0.000 0.275 0.693\n", "x3 -0.0174 0.002 -7.507 0.000 -0.022 -0.013\n", "const 5.2058 0.171 30.405 0.000 4.861 5.550\n", "==============================================================================\n", "Omnibus: 0.655 Durbin-Watson: 2.896\n", "Prob(Omnibus): 0.721 Jarque-Bera (JB): 0.360\n", "Skew: 0.207 Prob(JB): 0.835\n", "Kurtosis: 3.026 Cond. No. 221.\n", "==============================================================================\n", "\n", "Notes:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n" ] } ], "source": [ "res = sm.OLS(y, X).fit()\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Extract other quantities of interest:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "execution": { "iopub.execute_input": "2022-11-02T17:11:19.387247Z", "iopub.status.busy": "2022-11-02T17:11:19.386139Z", "iopub.status.idle": "2022-11-02T17:11:19.393085Z", "shell.execute_reply": "2022-11-02T17:11:19.392536Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Parameters: [ 0.46872448 0.48360119 -0.01740479 5.20584496]\n", "Standard errors: [0.02640602 0.10380518 0.00231847 0.17121765]\n", "Predicted values: [ 4.77072516 5.22213464 5.63620761 5.98658823 6.25643234 6.44117491\n", " 6.54928009 6.60085051 6.62432454 6.6518039 6.71377946 6.83412169\n", " 7.02615877 7.29048685 7.61487206 7.97626054 8.34456611 8.68761335\n", " 8.97642389 9.18997755 9.31866582 9.36587056 9.34740836 9.28893189\n", " 9.22171529 9.17751587 9.1833565 9.25708583 9.40444579 9.61812821\n", " 9.87897556 10.15912843 10.42660281 10.65054491 10.8063004 10.87946503\n", " 10.86825119 10.78378163 10.64826203 10.49133265 10.34519853 10.23933827\n", " 10.19566084 10.22490593 10.32487947 10.48081414 10.66779556 10.85485568\n", " 11.01006072 11.10575781]\n" ] } ], "source": [ "print(\"Parameters: \", res.params)\n", "print(\"Standard errors: \", res.bse)\n", "print(\"Predicted values: \", res.predict())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Draw a plot to compare the true relationship to OLS predictions. Confidence intervals around the predictions are built using the ``wls_prediction_std`` command." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "execution": { "iopub.execute_input": "2022-11-02T17:11:19.397560Z", "iopub.status.busy": "2022-11-02T17:11:19.396464Z", "iopub.status.idle": "2022-11-02T17:11:19.657140Z", "shell.execute_reply": "2022-11-02T17:11:19.656497Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pred_ols = res.get_prediction()\n", "iv_l = pred_ols.summary_frame()[\"obs_ci_lower\"]\n", "iv_u = pred_ols.summary_frame()[\"obs_ci_upper\"]\n", "\n", "fig, ax = plt.subplots(figsize=(8, 6))\n", "\n", "ax.plot(x, y, \"o\", label=\"data\")\n", "ax.plot(x, y_true, \"b-\", label=\"True\")\n", "ax.plot(x, res.fittedvalues, \"r--.\", label=\"OLS\")\n", "ax.plot(x, iv_u, \"r--\")\n", "ax.plot(x, iv_l, \"r--\")\n", "ax.legend(loc=\"best\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## OLS with dummy variables\n", "\n", "We generate some artificial data. There are 3 groups which will be modelled using dummy variables. Group 0 is the omitted/benchmark category." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "execution": { "iopub.execute_input": "2022-11-02T17:11:19.662271Z", "iopub.status.busy": "2022-11-02T17:11:19.661122Z", "iopub.status.idle": "2022-11-02T17:11:19.668889Z", "shell.execute_reply": "2022-11-02T17:11:19.668326Z" } }, "outputs": [], "source": [ "nsample = 50\n", "groups = np.zeros(nsample, int)\n", "groups[20:40] = 1\n", "groups[40:] = 2\n", "# dummy = (groups[:,None] == np.unique(groups)).astype(float)\n", "\n", "dummy = pd.get_dummies(groups).values\n", "x = np.linspace(0, 20, nsample)\n", "# drop reference category\n", "X = np.column_stack((x, dummy[:, 1:]))\n", "X = sm.add_constant(X, prepend=False)\n", "\n", "beta = [1.0, 3, -3, 10]\n", "y_true = np.dot(X, beta)\n", "e = np.random.normal(size=nsample)\n", "y = y_true + e" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Inspect the data:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "execution": { "iopub.execute_input": "2022-11-02T17:11:19.673676Z", "iopub.status.busy": "2022-11-02T17:11:19.672562Z", "iopub.status.idle": "2022-11-02T17:11:19.679914Z", "shell.execute_reply": "2022-11-02T17:11:19.679330Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[0. 0. 0. 1. ]\n", " [0.40816327 0. 0. 1. ]\n", " [0.81632653 0. 0. 1. ]\n", " [1.2244898 0. 0. 1. ]\n", " [1.63265306 0. 0. 1. ]]\n", "[ 9.28223335 10.50481865 11.84389206 10.38508408 12.37941998]\n", "[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", " 1 1 1 2 2 2 2 2 2 2 2 2 2]\n", "[[1 0 0]\n", " [1 0 0]\n", " [1 0 0]\n", " [1 0 0]\n", " [1 0 0]]\n" ] } ], "source": [ "print(X[:5, :])\n", "print(y[:5])\n", "print(groups)\n", "print(dummy[:5, :])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Fit and summary:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "execution": { "iopub.execute_input": "2022-11-02T17:11:19.684659Z", "iopub.status.busy": "2022-11-02T17:11:19.683539Z", "iopub.status.idle": "2022-11-02T17:11:19.696623Z", "shell.execute_reply": "2022-11-02T17:11:19.696013Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: y R-squared: 0.978\n", "Model: OLS Adj. R-squared: 0.976\n", "Method: Least Squares F-statistic: 671.7\n", "Date: Wed, 02 Nov 2022 Prob (F-statistic): 5.69e-38\n", "Time: 17:11:19 Log-Likelihood: -64.643\n", "No. Observations: 50 AIC: 137.3\n", "Df Residuals: 46 BIC: 144.9\n", "Df Model: 3 \n", "Covariance Type: nonrobust \n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "x1 0.9999 0.060 16.689 0.000 0.879 1.121\n", "x2 2.8909 0.569 5.081 0.000 1.746 4.036\n", "x3 -3.2232 0.927 -3.477 0.001 -5.089 -1.357\n", "const 10.1031 0.310 32.573 0.000 9.479 10.727\n", "==============================================================================\n", "Omnibus: 2.831 Durbin-Watson: 1.998\n", "Prob(Omnibus): 0.243 Jarque-Bera (JB): 1.927\n", "Skew: -0.279 Prob(JB): 0.382\n", "Kurtosis: 2.217 Cond. No. 96.3\n", "==============================================================================\n", "\n", "Notes:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n" ] } ], "source": [ "res2 = sm.OLS(y, X).fit()\n", "print(res2.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Draw a plot to compare the true relationship to OLS predictions:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "execution": { "iopub.execute_input": "2022-11-02T17:11:19.701501Z", "iopub.status.busy": "2022-11-02T17:11:19.700373Z", "iopub.status.idle": "2022-11-02T17:11:19.953737Z", "shell.execute_reply": "2022-11-02T17:11:19.953045Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pred_ols2 = res2.get_prediction()\n", "iv_l = pred_ols.summary_frame()[\"obs_ci_lower\"]\n", "iv_u = pred_ols.summary_frame()[\"obs_ci_upper\"]\n", "\n", "fig, ax = plt.subplots(figsize=(8, 6))\n", "\n", "ax.plot(x, y, \"o\", label=\"Data\")\n", "ax.plot(x, y_true, \"b-\", label=\"True\")\n", "ax.plot(x, res2.fittedvalues, \"r--.\", label=\"Predicted\")\n", "ax.plot(x, iv_u, \"r--\")\n", "ax.plot(x, iv_l, \"r--\")\n", "legend = ax.legend(loc=\"best\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Joint hypothesis test\n", "\n", "### F test\n", "\n", "We want to test the hypothesis that both coefficients on the dummy variables are equal to zero, that is, $R \\times \\beta = 0$. An F test leads us to strongly reject the null hypothesis of identical constant in the 3 groups:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "execution": { "iopub.execute_input": "2022-11-02T17:11:19.959138Z", "iopub.status.busy": "2022-11-02T17:11:19.957944Z", "iopub.status.idle": "2022-11-02T17:11:19.966487Z", "shell.execute_reply": "2022-11-02T17:11:19.965881Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[0 1 0 0]\n", " [0 0 1 0]]\n", "\n" ] } ], "source": [ "R = [[0, 1, 0, 0], [0, 0, 1, 0]]\n", "print(np.array(R))\n", "print(res2.f_test(R))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can also use formula-like syntax to test hypotheses" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "execution": { "iopub.execute_input": "2022-11-02T17:11:19.971597Z", "iopub.status.busy": "2022-11-02T17:11:19.970472Z", "iopub.status.idle": "2022-11-02T17:11:19.977809Z", "shell.execute_reply": "2022-11-02T17:11:19.977242Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "print(res2.f_test(\"x2 = x3 = 0\"))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Small group effects\n", "\n", "If we generate artificial data with smaller group effects, the T test can no longer reject the Null hypothesis: " ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "execution": { "iopub.execute_input": "2022-11-02T17:11:19.982383Z", "iopub.status.busy": "2022-11-02T17:11:19.981257Z", "iopub.status.idle": "2022-11-02T17:11:19.986712Z", "shell.execute_reply": "2022-11-02T17:11:19.986153Z" } }, "outputs": [], "source": [ "beta = [1.0, 0.3, -0.0, 10]\n", "y_true = np.dot(X, beta)\n", "y = y_true + np.random.normal(size=nsample)\n", "\n", "res3 = sm.OLS(y, X).fit()" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "execution": { "iopub.execute_input": "2022-11-02T17:11:19.991111Z", "iopub.status.busy": "2022-11-02T17:11:19.990006Z", "iopub.status.idle": "2022-11-02T17:11:19.996472Z", "shell.execute_reply": "2022-11-02T17:11:19.995910Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "print(res3.f_test(R))" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "execution": { "iopub.execute_input": "2022-11-02T17:11:20.000817Z", "iopub.status.busy": "2022-11-02T17:11:19.999719Z", "iopub.status.idle": "2022-11-02T17:11:20.006856Z", "shell.execute_reply": "2022-11-02T17:11:20.006301Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "print(res3.f_test(\"x2 = x3 = 0\"))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Multicollinearity\n", "\n", "The Longley dataset is well known to have high multicollinearity. That is, the exogenous predictors are highly correlated. This is problematic because it can affect the stability of our coefficient estimates as we make minor changes to model specification. " ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "execution": { "iopub.execute_input": "2022-11-02T17:11:20.011353Z", "iopub.status.busy": "2022-11-02T17:11:20.010238Z", "iopub.status.idle": "2022-11-02T17:11:20.024907Z", "shell.execute_reply": "2022-11-02T17:11:20.024207Z" } }, "outputs": [], "source": [ "from statsmodels.datasets.longley import load_pandas\n", "\n", "y = load_pandas().endog\n", "X = load_pandas().exog\n", "X = sm.add_constant(X)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Fit and summary:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "execution": { "iopub.execute_input": "2022-11-02T17:11:20.030343Z", "iopub.status.busy": "2022-11-02T17:11:20.029150Z", "iopub.status.idle": "2022-11-02T17:11:20.045472Z", "shell.execute_reply": "2022-11-02T17:11:20.044883Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: TOTEMP R-squared: 0.995\n", "Model: OLS Adj. R-squared: 0.992\n", "Method: Least Squares F-statistic: 330.3\n", "Date: Wed, 02 Nov 2022 Prob (F-statistic): 4.98e-10\n", "Time: 17:11:20 Log-Likelihood: -109.62\n", "No. Observations: 16 AIC: 233.2\n", "Df Residuals: 9 BIC: 238.6\n", "Df Model: 6 \n", "Covariance Type: nonrobust \n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "const -3.482e+06 8.9e+05 -3.911 0.004 -5.5e+06 -1.47e+06\n", "GNPDEFL 15.0619 84.915 0.177 0.863 -177.029 207.153\n", "GNP -0.0358 0.033 -1.070 0.313 -0.112 0.040\n", "UNEMP -2.0202 0.488 -4.136 0.003 -3.125 -0.915\n", "ARMED -1.0332 0.214 -4.822 0.001 -1.518 -0.549\n", "POP -0.0511 0.226 -0.226 0.826 -0.563 0.460\n", "YEAR 1829.1515 455.478 4.016 0.003 798.788 2859.515\n", "==============================================================================\n", "Omnibus: 0.749 Durbin-Watson: 2.559\n", "Prob(Omnibus): 0.688 Jarque-Bera (JB): 0.684\n", "Skew: 0.420 Prob(JB): 0.710\n", "Kurtosis: 2.434 Cond. No. 4.86e+09\n", "==============================================================================\n", "\n", "Notes:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "[2] The condition number is large, 4.86e+09. This might indicate that there are\n", "strong multicollinearity or other numerical problems.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/opt/hostedtoolcache/Python/3.10.8/x64/lib/python3.10/site-packages/scipy/stats/stats.py:1541: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=16\n", " warnings.warn(\"kurtosistest only valid for n>=20 ... continuing \"\n" ] } ], "source": [ "ols_model = sm.OLS(y, X)\n", "ols_results = ols_model.fit()\n", "print(ols_results.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Condition number\n", "\n", "One way to assess multicollinearity is to compute the condition number. Values over 20 are worrisome (see Greene 4.9). The first step is to normalize the independent variables to have unit length: " ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "execution": { "iopub.execute_input": "2022-11-02T17:11:20.050175Z", "iopub.status.busy": "2022-11-02T17:11:20.049044Z", "iopub.status.idle": "2022-11-02T17:11:20.055823Z", "shell.execute_reply": "2022-11-02T17:11:20.055248Z" } }, "outputs": [], "source": [ "norm_x = X.values\n", "for i, name in enumerate(X):\n", " if name == \"const\":\n", " continue\n", " norm_x[:, i] = X[name] / np.linalg.norm(X[name])\n", "norm_xtx = np.dot(norm_x.T, norm_x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then, we take the square root of the ratio of the biggest to the smallest eigen values. " ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "execution": { "iopub.execute_input": "2022-11-02T17:11:20.061060Z", "iopub.status.busy": "2022-11-02T17:11:20.059943Z", "iopub.status.idle": "2022-11-02T17:11:20.066269Z", "shell.execute_reply": "2022-11-02T17:11:20.065690Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "56240.86912116517\n" ] } ], "source": [ "eigs = np.linalg.eigvals(norm_xtx)\n", "condition_number = np.sqrt(eigs.max() / eigs.min())\n", "print(condition_number)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Dropping an observation\n", "\n", "Greene also points out that dropping a single observation can have a dramatic effect on the coefficient estimates: " ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "execution": { "iopub.execute_input": "2022-11-02T17:11:20.070748Z", "iopub.status.busy": "2022-11-02T17:11:20.069632Z", "iopub.status.idle": "2022-11-02T17:11:20.078053Z", "shell.execute_reply": "2022-11-02T17:11:20.077460Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Percentage change 4.55%\n", "Percentage change -2228.01%\n", "Percentage change 154304695.31%\n", "Percentage change 1366329.02%\n", "Percentage change 1112549.36%\n", "Percentage change 92708715.91%\n", "Percentage change 817944.26%\n", "\n" ] } ], "source": [ "ols_results2 = sm.OLS(y.iloc[:14], X.iloc[:14]).fit()\n", "print(\n", " \"Percentage change %4.2f%%\\n\"\n", " * 7\n", " % tuple(\n", " [\n", " i\n", " for i in (ols_results2.params - ols_results.params)\n", " / ols_results.params\n", " * 100\n", " ]\n", " )\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also look at formal statistics for this such as the DFBETAS -- a standardized measure of how much each coefficient changes when that observation is left out." ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "execution": { "iopub.execute_input": "2022-11-02T17:11:20.082756Z", "iopub.status.busy": "2022-11-02T17:11:20.081612Z", "iopub.status.idle": "2022-11-02T17:11:20.087165Z", "shell.execute_reply": "2022-11-02T17:11:20.086589Z" } }, "outputs": [], "source": [ "infl = ols_results.get_influence()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In general we may consider DBETAS in absolute value greater than $2/\\sqrt{N}$ to be influential observations" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "execution": { "iopub.execute_input": "2022-11-02T17:11:20.091902Z", "iopub.status.busy": "2022-11-02T17:11:20.090775Z", "iopub.status.idle": "2022-11-02T17:11:20.097587Z", "shell.execute_reply": "2022-11-02T17:11:20.097030Z" } }, "outputs": [ { "data": { "text/plain": [ "0.5" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "2.0 / len(X) ** 0.5" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "execution": { "iopub.execute_input": "2022-11-02T17:11:20.102074Z", "iopub.status.busy": "2022-11-02T17:11:20.100957Z", "iopub.status.idle": "2022-11-02T17:11:20.121864Z", "shell.execute_reply": "2022-11-02T17:11:20.121293Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " dfb_const dfb_GNPDEFL dfb_GNP dfb_UNEMP dfb_ARMED \\\n", "0 -0.016406 -169.822675 1.673981e+06 54490.318088 51447.824036 \n", "1 -0.020608 -187.251727 1.829990e+06 54495.312977 52659.808664 \n", "2 -0.008382 -65.417834 1.587601e+06 52002.330476 49078.352378 \n", "3 0.018093 288.503914 1.155359e+06 56211.331922 60350.723082 \n", "4 1.871260 -171.109595 4.498197e+06 82532.785818 71034.429294 \n", "5 -0.321373 -104.123822 1.398891e+06 52559.760056 47486.527649 \n", "6 0.315945 -169.413317 2.364827e+06 59754.651394 50371.817827 \n", "7 0.015816 -69.343793 1.641243e+06 51849.056936 48628.749338 \n", "8 -0.004019 -86.903523 1.649443e+06 52023.265116 49114.178265 \n", "9 -1.018242 -201.315802 1.371257e+06 56432.027292 53997.742487 \n", "10 0.030947 -78.359439 1.658753e+06 52254.848135 49341.055289 \n", "11 0.005987 -100.926843 1.662425e+06 51744.606934 48968.560299 \n", "12 -0.135883 -32.093127 1.245487e+06 50203.467593 51148.376274 \n", "13 0.032736 -78.513866 1.648417e+06 52509.194459 50212.844641 \n", "14 0.305868 -16.833121 1.829996e+06 60975.868083 58263.878679 \n", "15 -0.538323 102.027105 1.344844e+06 54721.897640 49660.474568 \n", "\n", " dfb_POP dfb_YEAR \n", "0 207954.113588 -31969.158503 \n", "1 25343.938290 -29760.155888 \n", "2 107465.770565 -29593.195253 \n", "3 456190.215133 -36213.129569 \n", "4 -389122.401699 -49905.782854 \n", "5 144354.586054 -28985.057609 \n", "6 -107413.074918 -32984.462465 \n", "7 92843.959345 -29724.975873 \n", "8 83931.635336 -29563.619222 \n", "9 18392.575057 -29203.217108 \n", "10 93617.648517 -29846.022426 \n", "11 95414.217290 -29690.904188 \n", "12 258559.048569 -29296.334617 \n", "13 104434.061226 -30025.564763 \n", "14 275103.677860 -36060.612522 \n", "15 -110176.960671 -28053.834556 \n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/opt/hostedtoolcache/Python/3.10.8/x64/lib/python3.10/site-packages/statsmodels/stats/outliers_influence.py:696: RuntimeWarning: invalid value encountered in sqrt\n", " return self.resid / sigma / np.sqrt(1 - hii)\n", "/opt/hostedtoolcache/Python/3.10.8/x64/lib/python3.10/site-packages/statsmodels/stats/outliers_influence.py:737: RuntimeWarning: invalid value encountered in sqrt\n", " dffits_ = self.resid_studentized_internal * np.sqrt(hii / (1 - hii))\n", "/opt/hostedtoolcache/Python/3.10.8/x64/lib/python3.10/site-packages/statsmodels/stats/outliers_influence.py:766: RuntimeWarning: invalid value encountered in sqrt\n", " dffits_ = self.resid_studentized_external * np.sqrt(hii / (1 - hii))\n" ] } ], "source": [ "print(infl.summary_frame().filter(regex=\"dfb\"))" ] } ], "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": "3.10.8" } }, "nbformat": 4, "nbformat_minor": 4 }