Regression diagnostics
This example file shows how to use a few of the statsmodels
regression diagnostic tests in a real-life context. You can learn about more tests and find out more information abou the tests here on the Regression Diagnostics page.
Note that most of the tests described here only return a tuple of numbers, without any annotation. A full description of outputs is always included in the docstring and in the online statsmodels
documentation. For presentation purposes, we use the zip(name,test)
construct to pretty-print short descriptions in the examples below.
Estimate a regression model
from __future__ import print_function from statsmodels.compat import lzip import statsmodels import numpy as np import pandas as pd import statsmodels.formula.api as smf import statsmodels.stats.api as sms import matplotlib.pyplot as plt # Load data url = 'http://vincentarelbundock.github.io/Rdatasets/csv/HistData/Guerry.csv' dat = pd.read_csv(url) # Fit regression model (using the natural log of one of the regressaors) results = smf.ols('Lottery ~ Literacy + np.log(Pop1831)', data=dat).fit() # Inspect the results print(results.summary())
Normality of the residuals
Jarque-Bera test:
name = ['Jarque-Bera', 'Chi^2 two-tail prob.', 'Skew', 'Kurtosis'] test = sms.jarque_bera(results.resid) lzip(name, test)
Omni test:
name = ['Chi^2', 'Two-tail probability'] test = sms.omni_normtest(results.resid) lzip(name, test)
Influence tests
Once created, an object of class OLSInfluence
holds attributes and methods that allow users to assess the influence of each observation. For example, we can compute and extract the first few rows of DFbetas by:
from statsmodels.stats.outliers_influence import OLSInfluence test_class = OLSInfluence(results) test_class.dfbetas[:5,:]
Explore other options by typing dir(influence_test)
Useful information on leverage can also be plotted:
from statsmodels.graphics.regressionplots import plot_leverage_resid2 fig, ax = plt.subplots(figsize=(8,6)) fig = plot_leverage_resid2(results, ax = ax)
Other plotting options can be found on the Graphics page.
Multicollinearity
Condition number:
np.linalg.cond(results.model.exog)
Heteroskedasticity tests
Breush-Pagan test:
name = ['Lagrange multiplier statistic', 'p-value', 'f-value', 'f p-value'] test = sms.het_breushpagan(results.resid, results.model.exog) lzip(name, test)
Goldfeld-Quandt test
name = ['F statistic', 'p-value'] test = sms.het_goldfeldquandt(results.resid, results.model.exog) lzip(name, test)
Linearity
Harvey-Collier multiplier test for Null hypothesis that the linear specification is correct:
name = ['t value', 'p value'] test = sms.linear_harvey_collier(results) lzip(name, test)
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