MIXTURE-MODELS FOR THE ANALYSIS OF REPEATED COUNT DATA

Repeated count data showing overdispersion are commonly analysed by us ing a Poisson model with varying intensity parameter. resulting in a m ixed model. A mixed model with a gamma distribution for the Poisson pa rameter does not adequately fit a data set on 721 children's spelling errors. An alternative approach is a latent class or mixture model in which the distribution of the intensity parameter is a step function. This gives a solution with many classes that is difficult to interpret . A combination of the two models, resulting in a mixture model with t wo gamma distributions, however, fits the data very well. Moreover, it yields a substantively satisfactory interpretation: two heterogeneous classes of 'good' and 'poor' spelling children can be identified. The refore, mixture models for the analysis of overdispersed repeated coun t data are proposed, where the counts have independent Poisson distrib utions conditional on the Poisson parameter whose distribution is a mi xture of gamma distributions. Combining marginal maximum likelihood me thods and the EM algorithm leads to straightforward estimations of the models, for which goodness-of-fit tests are also presented.