BUG/ENH: constrained/collinear fit and degrees of freedom for terms, df_terms, anova

[josef-pkt]

followup question to #8506 and #8336

If we (semi-) automatically drop exog columns (e.g. fit_colinear), estimated (pinv) regularized params or fit under constraints, then this can effect hypothesis tests for terms.

question is what is the relevant number of constraints for a joint hypothesis that affect terms.
Hypothesis tests on individual columns or on all params will effectively not be affected, I think. Those hypotheses we already have now.

With categorical exog and two way effects, especially nested effects, we might have zero cells, i.e. a column of zeros.
If we drop those, then the df of the term will be reduced.

AFAIR, we don't have any support for keeping track of df, number of effective parameters for terms (except, AFAIR we added it to GAM)

That is we need effective number of parameters for each term.

im_ratio might apply for pinv OLS
When we only drop columns, then we would just need to keep track of "nonzero" or unrestricted columns.

I don't have any idea (for now) what would be useful for general affine transformation of params as in fit_constrained.

In general, maybe just looking at the matrix rank of the sub-exog or terms would be enough.
I think, I do this already in some specification, lm tests, using rank to determine df_constrained for chi2 test.