GLMGamResults.score_test(exog_extra=None, params_constrained=None, hypothesis='joint', cov_type=None, cov_kwds=None, k_constraints=None, observed=True)

score test for restrictions or for omitted variables

Null Hypothesis : constraints are satisfied

Alternative Hypothesis : at least one of the constraints does not hold

This allows to specify restricted and unrestricted model properties in three different ways

  • fit_constrained result: model contains score and hessian function for the full, unrestricted model, but the parameter estimate in the results instance is for the restricted model. This is the case if the model was estimated with fit_constrained.

  • restricted model with variable addition: If exog_extra is not None, then it is assumed that the current model is a model with zero restrictions and the unrestricted model is given by adding exog_extra as additional explanatory variables.

  • unrestricted model with restricted parameters explicitly provided. If params_constrained is not None, then the model is assumed to be for the unrestricted model, but the provided parameters are for the restricted model. TODO: This case will currently only work for nonrobust cov_type, otherwise we will also need the restriction matrix provided by the user.

exog_extraNone or array_like

Explanatory variables that are jointly tested for inclusion in the model, i.e. omitted variables.


estimated parameter of the restricted model. This can be the parameter estimate for the current when testing for omitted variables.

hypothesisstr, ‘joint’ (default) or ‘separate’

If hypothesis is ‘joint’, then the chisquare test results for the joint hypothesis that all constraints hold is returned. If hypothesis is ‘joint’, then z-test results for each constraint is returned. This is currently only implemented for cov_type=”nonrobust”.


Warning: only partially implemented so far, currently only “nonrobust” and “HC0” are supported. If cov_type is None, then the cov_type specified in fit for the Wald tests is used. If the cov_type argument is not None, then it will be used instead of the Wald cov_type given in fit.

k_constraintsint or None

Number of constraints that were used in the estimation of params restricted relative to the number of exog in the model. This must be provided if no exog_extra are given. If exog_extra is not None, then k_constraints is assumed to be zero if it is None.


If True, then the observed Hessian is used in calculating the covariance matrix of the score. If false then the expected information matrix is used. This currently only applies to GLM where EIM is available. Warning: This option might still change.


chisquare statistic for the score test


P-value of the score test based on the chisquare distribution.


Degrees of freedom used in the p-value calculation. This is equal to the number of constraints.


Status: experimental, several options are not implemented yet or are not verified yet. Currently available ptions might also still change.

cov_type is ‘nonrobust’:

The covariance matrix for the score is based on the Hessian, i.e. observed information matrix or optionally on the expected information matrix.

cov_type is ‘HC0’

The covariance matrix of the score is the simple empirical covariance of score_obs without degrees of freedom correction.

Last update: Dec 14, 2023