Can likelihood ratio test be used for logistic regression in the case of complete separation? I understand that individual parameters can go to infinity so Wald's test is not recommended, but does that also affect likelihood ratio test? Or in other words, is likelihood (and likelihood ratios) from models with a complete separation valid?
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You can still use the likelihood ratio test with separation. This is explained at Why do my p-values differ between logistic regression output, chi-squared test, and the confidence interval for the OR?, the likelihood ratio test does not depend on approximations that throw off the Wald test and the score test.
For more details on logistic regression and separation see How to deal with perfect separation in logistic regression? and GLM high standard errors, but variables are definitely not collinear.
answered Mar 12, 2021 at 3:02