GNU R bias reduction in generalized linear models
Estimation and inference from generalized linear models based on various
methods for bias reduction and maximum penalized likelihood with powers
of the Jeffreys prior as penalty. The 'brglmFit' fitting method can
achieve reduction of estimation bias by solving either the mean bias-
reducing adjusted score equations in Firth (1993)
<doi:10.1093/biomet/80.1.27> and Kosmidis and Firth (2009)
<doi:10.1093/biomet/asp055>, or the median bias-reduction adjusted score
equations in Kenne et al. (2017) <doi:10.1093/biomet/asx046>, or through
the direct subtraction of an estimate of the bias of the maximum
likelihood estimator from the maximum likelihood estimates as in
Cordeiro and McCullagh (1991) <https://www.jstor.org/stable/2345592>.
See Kosmidis et al (2020) <doi:10.1007/s11222-019-09860-6> for more
details. Estimation in all cases takes place via a quasi Fisher scoring
algorithm, and S3 methods for the construction of of confidence
intervals for the reduced-bias estimates are provided. In the special
case of generalized linear models for binomial and multinomial responses
(both ordinal and nominal), the adjusted score approaches to mean and
media bias reduction have been found to return estimates with improved
frequentist properties, that are also always finite, even in cases where
the maximum likelihood estimates are infinite (e.g. complete and quasi-
complete separation; see Kosmidis and Firth, 2020
<doi:10.1093/biomet/asaa052>, for a proof for mean bias reduction in
logistic regression).
