Two ways of modelling overdispersion in non-normal data

For non-normal data assumed to have distributions, such as the Poisson dist ribution, which have an a priori dispersion parameter, there are two ways o f modelling overdispersion: by a quasi-likelihood approach or with a random -effect model. The two approaches yield different variance functions for th e response, which may be distinguishable if adequate data are available. Th e epilepsy data of Thall and Vail and the fabric data of Bissell are used t o exemplify the ideas.