Check whether two coefficients in a regression differ in Python statsmodels

Question

In R, the car::linearHypothesis function can be used to test the hypothesis that two coefficients are equal (that their difference differs significantly from zero). Here's an example from its documentation:

linearHypothesis(mod.duncan, "income = education")

Per this CrossValidated answer this is also available in MATLAB as linhyptest.

Is there an equivalent for Python statsmodels regression models?

Answer 1

The results classes of most models have several methods for Wald tests.

t_test is vectorized for single hypothesis.
wald_test is for joint hypothesis.
wald_test_terms automatically tests that "terms", i.e. subset of coefficients are jointly zero, similar to a type 3 ANOVA table based on Wald tests.

See for example the docstring for t_test after OLS, but all models inherit the same method and work in the same way (*). https://www.statsmodels.org/dev/generated/statsmodels.regression.linear_model.OLSResults.t_test.html

for example

>>> t_test = results.t_test("income = education")
>>> print(t_test)

(*) There are a few models that do not follow the standard pattern where these wald tests are not yet available.

The t_test use either the normal or the t distribution, the other two wald tests use either chisquare or F distribution. The distribution can be selected using the use_t keyword in model.fit.
If use_t=True then t and F distributions are used. if it is False, then the normal and chisquare distributions are used. The default is t and F for linear regression models and normal and chisquare for all other models.