Diagnostic tools for a multivariate negative binomial model for fitting correlated data with overdispersion

TL;DR

This paper introduces diagnostic tools and an R package for a multivariate negative binomial regression model that detects influential subjects and assesses model adequacy for correlated overdispersed count data.

Contribution

It develops a new multivariate negative binomial model derived from a Poisson mixed model with a generalized log-gamma distribution and provides diagnostic tools and an R package for practical application.

Findings

The MNB model effectively detects influential subjects.

The randomized quantile residual assesses model adequacy.

Applications demonstrate the model's utility in real data analysis.

Abstract

We focus on the development of diagnostic tools and an R package called MNB for a multivariate negative binomial (MNB) regression model for detecting atypical and influential subjects. The MNB model is deduced from a Poisson mixed model in which the random intercept follows the generalized log-gamma (GLG) distribution. The MNB model for correlated count data leads to an MNB regression model that inherits the features of a hierarchical model to accommodate the intraclass correlation and the occurrence of overdispersion simultaneously. The asymptotic consistency of the dispersion parameter estimator depends on the asymmetry of the GLG distribution. Inferential procedures for the MNB regression model are simple, although it can provide inconsistent estimates of the asymptotic variance when the correlation structure is misspecified. We propose the randomized quantile residual for checking the adequacy of the multivariate model, and derive global and local influence measures from the multivariate model to assess influential subjects. Finally, two applications are presented in the data analysis section. The code for installing the MNB package and the code used in the two examples is exhibited in the Appendix.