Jeffreys-prior penalty, finiteness and shrinkage in binomial-response\n generalized linear models

2018/12/05 by Ioannis Kosmidis, David Firth, Kosmidis, Ioannis +1 · 6 citations
Agricultural and Biological Sciences · Mathematics · #62F03 #62F10 #62F12 #62J12 #Banana Cultivation and Research #FOS: Computer and information sciences #FOS: Mathematics #Genetics and Plant Breeding #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1812.01938

openalex publication_date 2018/12/05 · openalex created_date 2022/08/01 · openalex updated_date 2026/07/28

Abstract

Penalization of the likelihood by Jeffreys' invariant prior, or by a positive\npower thereof, is shown to produce finite-valued maximum penalized likelihood\nestimates in a broad class of binomial generalized linear models. The class of\nmodels includes logistic regression, where the Jeffreys-prior penalty is known\nadditionally to reduce the asymptotic bias of the maximum likelihood estimator;\nand also models with other commonly used link functions such as probit and\nlog-log. Shrinkage towards equiprobability across observations, relative to the\nmaximum likelihood estimator, is established theoretically and is studied\nthrough illustrative examples. Some implications of finiteness and shrinkage\nfor inference are discussed, particularly when inference is based on Wald-type\nprocedures. A widely applicable procedure is developed for computation of\nmaximum penalized likelihood estimates, by using repeated maximum likelihood\nfits with iteratively adjusted binomial responses and totals. These theoretical\nresults and methods underpin the increasingly widespread use of reduced-bias\nand similarly penalized binomial regression models in many applied fields.\n

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