Accurate inference in negative binomial regression

TL;DR

This paper introduces bias-reduction adjustments to negative binomial regression inference, improving estimation accuracy and numerical stability for overdispersed count data, especially in small to moderate samples.

Contribution

It proposes score function adjustments for bias reduction in negative binomial regression, enhancing inference and solving numerical issues of maximum likelihood estimates.

Findings

Significant bias reduction in dispersion parameter estimates.

Improved inference accuracy demonstrated in simulations.

Method outperforms traditional maximum likelihood approaches.

Abstract

Negative binomial regression is commonly employed to analyze overdispersed count data. With small to moderate sample sizes, the maximum likelihood estimator of the dispersion parameter may be subject to a significant bias, that in turn affects inference on mean parameters. This paper proposes inference for negative binomial regression based on adjustments of the score function aimed at mean and median bias reduction. The resulting estimating equations are similar to those available for improved inference in generalized linear models and, in particular, can be solved using a suitable extension of iterative weighted least squares. Simulation studies show a remarkable performance of the new methods, which are also found to solve in many cases numerical problems of maximum likelihood estimates. The methods are illustrated and evaluated using two case studies: an Ames salmonella assay data set and data on epileptic seizures. Inference based on adjusted scores turns out to be generally preferable to explicit bias correction.