statsmodels.sandbox.regression.gmm.IVGMMResults.wald_test

IVGMMResults.wald_test(r_matrix, cov_p=None, scale=1.0, invcov=None, use_f=None, df_constraints=None)

Compute a Wald-test for a joint linear hypothesis.

Parameters:
  • r_matrix (array-like, str, or tuple) –
    • array : An r x k array where r is the number of restrictions to test and k is the number of regressors. It is assumed that the linear combination is equal to zero.
    • str : The full hypotheses to test can be given as a string. See the examples.
    • tuple : A tuple of arrays in the form (R, q), q can be either a scalar or a length p row vector.
  • cov_p (array-like, optional) – An alternative estimate for the parameter covariance matrix. If None is given, self.normalized_cov_params is used.
  • scale (float, optional) – Default is 1.0 for no scaling.
  • invcov (array-like, optional) – A q x q array to specify an inverse covariance matrix based on a restrictions matrix.
  • use_f (bool) – If True, then the F-distribution is used. If False, then the asymptotic distribution, chisquare is used. If use_f is None, then the F distribution is used if the model specifies that use_t is True. The test statistic is proportionally adjusted for the distribution by the number of constraints in the hypothesis.
Returns:

res – The results for the test are attributes of this results instance.

Return type:

ContrastResults instance

Notes

The matrix r_matrix is assumed to be non-singular. More precisely,

r_matrix (pX pX.T) r_matrix.T

is assumed invertible. Here, pX is the generalized inverse of the design matrix of the model. There can be problems in non-OLS models where the rank of the covariance of the noise is not full.