Objectives that are used in profile.brglm
penalizedDeviance(fm, X, dispersion = 1)modifiedScoreStatistic(fm, X, dispersion = 1)
the restricted fit.
the model matrix of the fit on all parameters.
the dispersion parameter.
A scalar.
These objectives follow the specifications for objectives in the
profileModel package and are used from profile.brglm.
penalizedDeviance returns a deviance-like value corresponding
to a likelihood function penalized by Jeffreys invariant prior. It
has been used by Heinze & Schemper (2002) and by Bull et. al. (2002)
for the construction of confidence intervals for the bias-reduced
estimates in logistic regression. The X argument is the
model matrix of the full (not the restricted) fit.
modifiedScoreStatistic mimics RaoScoreStatistic
in profileModel, but with the ordinary scores replaced with the
modified scores used for bias reduction. The argument X has
the same interpretation as for penalizedDeviance.
Kosmidis, I. and Firth, D. (2020). Jeffreys-prior penalty, finiteness and shrinkage in binomial-response generalized linear models. Biometrika. https://doi.org/10.1093/biomet/asaa052
Bull, S. B., Lewinger, J. B. and Lee, S. S. F. (2007). Confidence intervals for multinomial logistic regression in sparse data. Statistics in Medicine 26, 903--918.
Heinze, G. and Schemper, M. (2002). A solution to the problem of separation in logistic regression. Statistics in Medicine 21, 2409--2419.