ENH/TST: GLM, discrete, saturated model, perfect prediction

[josef-pkt]

corner case behavior if we have a model with perfect prediction by design

(I thought I already have an issue, but don't find it right now.
trigger for issue right now: according to their documentation, SPSS handles zero cases in loglike and deviance separately, dropping terms instead of "fixing" them as we do)

examples:

• contingency table, loglinear model with saturated exog
• computing saturated reference case for deviance, (I needed to add an epsilon to avoid corners)
• model with aggregated or averaged data using freq_weights or var_weights

Those would make good test cases for the currently open issues of zero division and similar in GLM families.

[josef-pkt]

bump

I just ran into the same problem replicating two sample proportion tests with GLM Binomial PR #6675

see #2680 for disabling perfect separation exception when using irls

I also got a zero division warning (raised only once ?)

en = np.array([[count1, nobs1 - count1], [count2, nobs2 - count2]])
ex = np.array([[1., 1], [1, 0]])
mod_glm = GLM(en, ex, family=families.Binomial())
res_glm = mod_glm.fit(method='bfgs', tol=1e-10, max_start_irls=0)

[josef-pkt]

exception when null model has perfect fit and scale=0
#7682 (comment)

[josef-pkt]

PR #8552 added option to turn off/on the perfect separation/prediction check, default changed to no exception