title: Inferential tools in penalized logistic regression for small and sparse data: A comparative study.
abstract: This paper focuses on inferential tools in the logistic regression model fitted by the Firth penalized likelihood. In this context, the Likelihood Ratio statistic is often reported to be the preferred choice as compared to the 'traditional' Wald statistic. In this work, we consider and discuss a wider range of test statistics, including the robust Wald, the Score, and the recently proposed Gradient statistic. We compare all these asymptotically equivalent statistics in terms of interval estimation and hypothesis testing via simulation experiments and analyses of two real datasets. We find out that the Likelihood Ratio statistic does not appear the best inferential device in the Firth penalized logistic regression.
authors: Department of Scienze Economiche, Aziendali e Statistiche, University of Palermo, Italy.
authors: Marianna
authors: M
authors: Siino
authors: Department of Scienze Economiche, Aziendali e Statistiche, University of Palermo, Italy.
authors: Salvatore
authors: S
authors: Fasola
authors: Department of Scienze Economiche, Aziendali e Statistiche, University of Palermo, Italy.
authors: Vito Mr
authors: VM
authors: Muggeo
mesh_terms: D003627:Data Interpretation, Statistical; D006801:Humans; D016013:Likelihood Functions; D016015:Logistic Models; D015233:Models, Statistical; D018401:Sample Size; D013223:Statistics as Topic
keywords: Firth penalized likelihood; Logistic regression; gradient statistic; sandwich formula; score statistic