  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.
