statsmodels.stats.diagnostic.het_breuschpagan#

statsmodels.stats.diagnostic.het_breuschpagan(resid, exog_het, robust=True)[source]#

Breusch-Pagan Lagrange Multiplier test for heteroscedasticity

The tests the hypothesis that the residual variance does not depend on the variables in x in the form

Homoscedasticity implies that $\alpha=0$.

Parameters:

residarray_like: For the Breusch-Pagan test, this should be an array of residuals from a fitted regression model.
exog_hetarray_like: This contains variables suspected of being related to heteroscedasticity in resid.
robustbool, default True: Flag indicating whether to use the Koenker version of the test (default) which assumes independent and identically distributed error terms, or the original Breusch-Pagan version which assumes residuals are normally distributed.

Returns:

lmfloat: lagrange multiplier statistic
lm_pvaluefloat: p-value of lagrange multiplier test
fvaluefloat: f-statistic of the hypothesis that the error variance does not depend on x
f_pvaluefloat: p-value for the f-statistic

Notes

Assumes x contains constant (for counting dof and calculation of R^2). In the general description of LM test, Greene mentions that this test exaggerates the significance of results in small or moderately large samples. In this case the F-statistic is preferable.

Verification

Chisquare test statistic is exactly (<1e-13) the same result as bptest in R-stats with defaults (studentize=True).

Implementation

This is calculated using the generic formula for LM test using $R^2$ (Greene, section 17.6) and not with the explicit formula (Greene, section 11.4.3), unless robust is set to False. The degrees of freedom for the p-value assume x is full rank.

References

[1]

Greene, W. H. Econometric Analysis. New Jersey. Prentice Hall; 5th edition. (2002).

[2]

Breusch, T. S.; Pagan, A. R. (1979). “A Simple Test for Heteroskedasticity and Random Coefficient Variation”. Econometrica. 47 (5): 1287-1294.

[3]

Koenker, R. (1981). “A note on studentizing a test for heteroskedasticity”. Journal of Econometrics 17 (1): 107-112.