Bias Reduction in Generalized Linear Models

Estimation and inference from generalized linear models based on various methods for bias reduction. The 'brglmFit' fitting method can achieve reduction of estimation bias by solving either the mean bias-reducing adjusted score equations in Firth (1993) and Kosmidis and Firth (2009) , or the median bias-reduction 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 in Cordeiro and McCullagh (1991) < http://www.jstor.org/stable/2345592>. 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, the adjusted score approaches 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 detecting separation and infinite maximum likelihood estimates in binomial response generalized linear models.


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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 ?detect_separation and ?check_infinite_estimates).

Install the development version from github:

# install.packages("devtools")
devtools::install_github("ikosmidis/brglm2")

Quasi Fisher scoring for solving adjusted score equations

The workhorse function in brglm2 is brglmFit, which can be passed directly to the method argument of the glm function and . brglmFit implements a quasi Fisher scoring procedure, whose special cases result in various explicit and implicit bias reduction methods for generalized linear models.

The iteration vignette describes the iteration and gives the 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).

References and resources

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.

News

brglm2 0.1.5

Bug fixes

New functionality

  • Added type = AS_mixed as 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
  • check_infinite_estimates now accepts brmultinom objects
  • Added singular.ok argument to brglmFit and detect_separation methods in line with the update of glm.fit

Other improvements, updates and addition

  • less strict tolerance in brglm_control
  • Updates to help files
  • Fixed typos in iteration vignette
  • Added URL and bugreports in Description
  • Added new tests

brglm2 0.1.4

Bug fixes

  • brglmControl is now exported
  • slowit did nothing; now included in iteration

New functionality

  • The detect_separation method for the glm function can be used to check for separation in binomial response settings without fitting the model. This relies on a port of Kjell Konis' safeBinaryRegression:::separator function (see ?detect_separation)
  • brglm2 provides estimation via median-bias reducing score functions with type = "AS_median"
  • brglm2 provides camel and underscored aliases for basic methods (brglmFit, brglm_fit, detectSeparation, detect_separation, brglm_control, brglmControl, detectSeparationControl, detect_separation_control, checkInfiniteEstimates, check_infinite_estimates)

Other improvements, updates and additions

  • Minor enhancements in the codebase
  • The inverse expected information matrix is computed internally using cho2inv
  • Internal changes to have more meaningful variable names
  • Renamed detect_infinite* to check_infinite

brglm2 0.1.3

Bug fixes

New functionality

Other improvements, updates and additions

  • Fixed typo in f_{Y_i}(y) in iteration vignette (thanks to Eugene Clovis Kenne Pagui for spotting)

brglm2 0.1.2

  • First release

Reference manual

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install.packages("brglm2")

0.1.8 by Ioannis Kosmidis, 8 days ago


https://github.com/ikosmidis/brglm2


Report a bug at https://github.com/ikosmidis/brglm2/issues


Browse source code at https://github.com/cran/brglm2


Authors: Ioannis Kosmidis [aut, cre], Kjell Konis [ctb], Euloge Clovis Kenne Pagui [ctb], Nicola Sartori [ctb]


Documentation:   PDF Manual  


GPL-3 license


Imports MASS, stats, Matrix, graphics, nnet, enrichwith, lpSolveAPI

Suggests testthat, knitr, rmarkdown, covr


Imported by SOIL.


See at CRAN