Log In Sign Up

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

by   Lizandra Castilho Fabio, et al.

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.


page 1

page 2

page 3

page 4


Poisson-Birnbaum-Saunders Regression Model for Clustered Count Data

The premise of independence among subjects in the same cluster/group oft...

Multivariate generalized linear mixed models for underdispersed count data

Researchers are often interested in understanding the relationship betwe...

Dynamical multiple regression in function spaces, under kernel regressors, with ARH(1) errors

A linear multiple regression model in function spaces is formulated, und...

Global simulation envelopes for diagnostic plots in regression models

Residual plots are often used to interrogate regression model assumption...

Backward Simulation of Multivariate Mixed Poisson Processes

The Backward Simulation (BS) approach was developed to generate, simply ...

Zero-adjusted Birnbaum-Saunders regression model

In this paper we introduce the zero-adjusted Birnbaum-Saunders regressio...