Overdispersion: Models and estimation. (English) Zbl 1042.62578

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.


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


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