BUG/ENH: wald test, wald_test_terms, degrees of freedom for rank-deficient cases #9686

related to #1717
update directly related general issue #8512

I'm using an over-parameterized model (columns of zeros) estimated with fit_zeros.
I get a rank warning when I use wald_test_terms

example

res3z.wald_test_terms(scalar=True)
...\statsmodels\base\model.py:1902: ValueWarning: covariance of constraints does not have full rank. 
The number of constraints is 24, but rank is 8
  warnings.warn('covariance of constraints does not have full '
<class 'statsmodels.stats.contrast.WaldTestResults'>
                                 F           P>F  df constraint  df denom
Intercept               232.071429  8.844181e-15              1      27.0
C(fertilizer)            32.595238  6.311739e-08              2      27.0
C(fertilizer):C(tech0)   14.446429  6.061365e-08             24      27.0

It looks like it is using the wrong df_constraint.
When I parameterize the model in a different way so that it is not rank-deficient, then the df are the reduced ones, e.g. 8 instead of 24.

I have not verified yet, what the result is supposed to be.

I guess the same will be the case with just wald_test for a joint hypothesis.

Aside:
F-statistic, AIC and BIC in the summary table seems to be correct, they are the same between over-parameterized and not over-parameterized models. It looks like they use rank of exog and not the number of columns.