# brglm2

**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`

).

### Installation

Install the development version from github:

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

### Solving adjusted score equations using quasi-Fisher scoring

The workhorse function in **brglm2** is
`brglmFit`

,
which can be passed directly to the `method`

argument of the `glm`

function. `brglmFit`

implements a quasi Fisher
scoring procedure,
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).

### 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.

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**