Penalized logistic regression for small or sparse data: interval estimators revisited

Abstract

This paper focuses on interval estimation in logistic regression models fitted through the Firth penalized log-likelihood. In this context, many authors have claimed superiority of the Likelihood ratio statistic with respect to the (wrong) Wald statistic via simulation evidence. We re-assess such findings by detailing the inferential tools also including in the comparisons the (right) Wald statistic and other statistics neglected in previous literature. In particular, we assess performances of the CIs estimators by simulation and compare them in a real data set. Differently from previous findings, the Likelihood ratio statistic does not appear to be the best inferential device in Firth penalized logistic regression.