Diagnostics in Nonlinear Negative Binomial Models

Abstract

Nonlinear negative binomial models represent a general class of nonlinear regression models that may be applied to fit growth curves for overdispersed count data. We discuss in this article application of local influence and residual analysis through deviance residual in nonlinear negative binomial models. We derive the appropriate matrices for assessing the local influence on the parameter estimates by considering as influence measure the likelihood displacement. An example in which different growth curves for count data are compared is given for illustration.

Keywords:

• Count data
• Influence diagnostic
• Lack-of-fit
• Likelihood displacement
• Offset-facility
• Residual analysis
• Overdispersion

Acknowledgments

This work was supported by CNPq and FAPESP-Brazil. The authors are grateful to one referee for helpful comments and suggestions.