We address the issue of divergent maximum likelihood estimates for logistic regression models by considering a conjugate prior penalty which always produces finite estimates. We show that the proposed method is closely related to the reduced-bias approach of Firth (1993), and that the induced penalized likelihood can be expressed as a genuine binomial likelihood, replacing the original data with pseudo-counts.
Rigon, T., Aliverti, E. (2023). Conjugate priors and bias reduction for logistic regression models. STATISTICS & PROBABILITY LETTERS, 202(November 2023) [10.1016/j.spl.2023.109901].
Conjugate priors and bias reduction for logistic regression models
Rigon, T
Primo
;
2023
Abstract
We address the issue of divergent maximum likelihood estimates for logistic regression models by considering a conjugate prior penalty which always produces finite estimates. We show that the proposed method is closely related to the reduced-bias approach of Firth (1993), and that the induced penalized likelihood can be expressed as a genuine binomial likelihood, replacing the original data with pseudo-counts.
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