A preliminary investigation of maximum likelihood logistic regression versus exact logistic regression

Logistic regression is used by practitioners and researchers in many fields, but is undoubtedly used most frequently in medical and biostatistical applications. Maximum likelihood is generally the estimation method of choice, but we show that maximum likelihood can produce very poor results under certain conditions. Specifically, the poor performance of maximum likelihood in the case of rare events is known and we review research on this topic. We primarily examine the performance of maximum likelihood in the presence of near separation, which has apparently not been studied. Exact logistic regression is the logical alternative to maximum likelihood. We offer a comparison of the two methods of estimation.