brglm2 {brglm2} | R Documentation |

## brglm2: Bias Reduction in Generalized Linear Models

### Description

Estimation and inference from generalized linear models using implicit and explicit bias reduction methods (Kosmidis, 2014), and other penalized maximum likelihood methods. Currently supported methods include the mean bias-reducing adjusted scores approach in Firth (1993) and Kosmidis & Firth (2009), the median bias-reduction adjusted scores approach in Kenne Pagui et al. (2017), the correction of the asymptotic bias in Cordeiro & McCullagh (1991), the mixed bias-reduction adjusted scores approach in Kosmidis et al (2020), maximum penalized likelihood with powers of the Jeffreys prior as penalty, and maximum likelihood.

### Details

In the special case of generalized linear models for binomial, Poisson and multinomial responses (both nominal and ordinal), mean and median bias reduction and maximum penalized likelihood 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 in multinomial regression). Estimation in all cases takes place via a modified Fisher scoring algorithm, and S3 methods for the construction of confidence intervals for the reduced-bias estimates are provided.

The core model fitters are implemented by the functions
`brglm_fit()`

(univariate generalized linear models),
`brmultinom()`

(baseline category logit models for nominal
multinomial responses), `bracl()`

(adjacent category logit models
for ordinal multinomial responses), and `brnb()`

for negative
binomial regression.

The similarly named **brglm** R package can only handle generalized
linear models with binomial responses. Special care has been taken
when developing **brglm2** in order not to have conflicts when the
user loads **brglm2** and **brglm** simultaneously. The development
and maintenance of the two packages will continue in parallel,
until **brglm2** incorporates all **brglm** functionality and
provides an appropriate wrapper to the `brglm::brglm()`

function.

### Author(s)

Ioannis Kosmidis `[aut, cre]`

ioannis.kosmidis@warwick.ac.uk

### References

Kosmidis I, Firth D (2021). Jeffreys-prior penalty, finiteness
and shrinkage in binomial-response generalized linear
models. *Biometrika*, **108**, 71-82. doi:10.1093/biomet/asaa052.

Cordeiro G M, McCullagh P (1991). Bias correction in generalized
linear models. *Journal of the Royal Statistical Society. Series B
(Methodological)*, **53**, 629-643. doi:10.1111/j.2517-6161.1991.tb01852.x.

Firth D (1993). Bias reduction of maximum likelihood estimates,
Biometrika, **80**, 27-38. doi:10.2307/2336755.

Kenne Pagui E C, Salvan A, Sartori N (2017). Median bias
reduction of maximum likelihood estimates. *Biometrika*, **104**,
923–938. doi:10.1093/biomet/asx046.

Kosmidis I, Kenne Pagui E C, Sartori N (2020). Mean and median bias
reduction in generalized linear models. *Statistics and Computing*,
**30**, 43-59. doi:10.1007/s11222-019-09860-6.

Kosmidis I, Firth D (2009). Bias reduction in exponential family
nonlinear models. *Biometrika*, **96**, 793-804. doi:10.1093/biomet/asp055.

Kosmidis I, Firth D (2010). A generic algorithm for reducing
bias in parametric estimation. *Electronic Journal of Statistics*,
**4**, 1097-1112. doi:10.1214/10-EJS579.

Kosmidis I (2014). Bias in parametric estimation: reduction and
useful side-effects. *WIRE Computational Statistics*, **6**,
185-196. doi:10.1002/wics.1296.

### See Also

`brglm_fit()`

, `brmultinom()`

, `bracl()`

*brglm2*version 0.9.2 Index]