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)
brglm2 provides tools for the estimation and inference from generalized linear models using various methods for bias reduction (Kosmidis, 2014). Reduction of estimation bias is achieved by solving either the mean-bias reducing adjusted score equations in Firth (1993) and Kosmidis & Firth (2009) or the median-bias reducing adjusted score equations in Kenne et al (2016), or through the direct subtraction of an estimate of the bias of the maximum likelihood estimator from the maximum likelihood estimates as prescribed in Cordeiro and McCullagh (1991)
In the special case of generalized linear models for binomial and multinomial responses, the adjusted score equations 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).
brglm2 also provides pre-fit and post-fit methods for the detection of separation and of infinite maximum likelihood estimates in binomial response generalized linear models (see
Install the development version from github:
The workhorse function in brglm2 is
which can be passed directly to the
method argument of the
brglmFit implements a quasi Fisher
whose special cases result in a range of explicit and implicit bias
reduction methods for generalized linear models.
The iteration vignette and the paper arXiv:1710.11217 present the iteration and give mathematical details for the bias-reducing adjustments to the score functions for generalized linear models.
The classification of bias reduction methods into explicit and implicit is as given in Kosmidis (2014).
brglm2 was presented by Ioannis Kosmidis at the useR! 2016 international R User conference at University of Stanford on 16 June 2016. The presentation was titled "Reduced-bias inference in generalized linear models" and can be watched online at this link.
Motivation, details and discussion on the methods that brglm2 implements are provided in
Kosmidis, I, Kenne Pagui, E C, Sartori N. (2017). Mean and median bias reduction in generalized linear models. arXiv, arXiv:1710.11217
brglmFitnow works as expected with custom link functions (mean and median bias reduction)
brglmFitrespects the specification of the transformation argument in
quasibinomialfamilies and documentation update.
braclfor fitting adjacent category logit models for ordinal responses using maximum likelihood, mean bias reduction, and median bias reduction and associated methods (
summaryand so on)
bracl(residuals of the equivalent Poisson log-linear model)
mislink functions for accounting for misclassification in binomial response models (Neuhaus, 1999, Biometrika)
type = AS_mixedas an option to use mean-bias reducing score functions for the regression parameters and median-bias reducing score functions for the dispersion in models with uknown dispersion
detect_separationmethods in line with the update of
brglmControlis now exported
slowitdid nothing; now included in iteration
glmfunction can be used to check for separation in binomial response settings without fitting the model. This relies on a port of Kjell Konis'
safeBinaryRegression:::separatorfunction (see ?detect_separation)
type = "AS_median"