statsmodels.stats.diagnostic.compare_encompassing#

statsmodels.stats.diagnostic.compare_encompassing(results_x, results_z, cov_type='nonrobust', cov_kwds=None)[source]#

Davidson-MacKinnon encompassing test for comparing non-nested models

Parameters:

results_xResult instance: result instance of first model
results_zResult instance: result instance of second model
cov_typestr, default “nonrobust”: Covariance type. The default is “nonrobust” which uses the classic OLS covariance estimator. Specify one of “HC0”, “HC1”, “HC2”, “HC3” to use White’s covariance estimator. All covariance types supported by OLS.fit are accepted.
cov_kwdsdict, default None: Dictionary of covariance options passed to OLS.fit. See OLS.fit for more details.

Returns:

DataFrame: A DataFrame with two rows and four columns. The row labeled x contains results for the null that the model contained in results_x is equivalent to the encompassing model. The results in the row labeled z correspond to the test that the model contained in results_z are equivalent to the encompassing model. The columns are the test statistic, its p-value, and the numerator and denominator degrees of freedom. The test statistic has an F distribution. The numerator degree of freedom is the number of variables in the encompassing model that are not in the x or z model. The denominator degree of freedom is the number of observations minus the number of variables in the nesting model.

Notes

The null is that the fit produced using x is the same as the fit produced using both x and z. When testing whether x is encompassed, the model estimated is

\[Y = X\beta + Z_1\gamma + \epsilon\]

where \(Z_1\) are the columns of \(Z\) that are not spanned by \(X\). The null is \(H_0:\gamma=0\). When testing whether z is encompassed, the roles of \(X\) and \(Z\) are reversed.

Implementation of Davidson and MacKinnon (1993)’s encompassing test. Performs two Wald tests where models x and z are compared to a model that nests the two. The Wald tests are performed by using an OLS regression.