Inferential tools in penalized logistic regression for small and sparse data: A comparative study

AbstractThis paper focuses on inferential tools in the logistic regression model fitted by the Firth penalized likelihood. In thiscontext, the Likelihood Ratio statistic is often reported to be the preferred choice as compared to the ‘traditional’ Waldstatistic. In this work, we consider and discuss a wider range of test statistics, including the robust Wald, the Score, andthe recently proposed Gradient statistic. We compare all these asymptotically equivalent statistics in terms of intervalestimation and hypothesis testing via simulation experiments and analyses of two real datasets. We find out that theLikelihood ratio statistic does not appear the best inferential device in the Firth penalized logistic regression