Overdispersion: Models and estimation. (English) Zbl 1042.62578

Hinde, John; Demétrio, Clarice G. B.

Comput. Stat. Data Anal. 27, No. 2, 151-170 (1998).

Summary: Overdispersion models for discrete data are considered and placed in a general framework. A distinction is made between completely specified models and those with only a mean-variance specification. Different formulations for the overdispersion mechanism can lead to different variance functions which can be placed within a general family. In addition, many different estimation methods have been proposed, including maximum likelihood, moment methods, extended quasi-likelihood, pseudo-likelihood and non-parametric maximum likelihood. We explore the relationships between these methods and examine their application to a number of standard examples for count and proportion data. A simple graphical method using half-normal plots is used to examine different overdispersion models.

MSC:

62J12	Generalized linear models (logistic models)
62F10	Point estimation
62G08	Nonparametric regression and quantile regression
62A09	Graphical methods in statistics

Keywords:

Generalized linear models; Overdispersion; Binomial; Beta-binomial; Poisson; Negative binomial

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