A COUNT DATA MODEL WITH UNOBSERVED HETEROGENEITY

A count data model is defined via the distribution of the durations be tween successive events. It is assumed that the durations follow indep endent exponential distributions conditionally to a set of variables. The parameters of these distributions depend not only on observed and unobserved individual specific factors, but also on unobserved spell-s pecific factors. The count data model is therefore a natural extension of the compound Poisson model. A local version of the count data mode l is used to analyse the effects of unobserved spell specific factors. In particular, it is shown that spell-specific heterogeneity can indu ce not only overdispersion, but also underdispersion. The local model is also used to construct a score test for spell-specific heterogeneit y in the Poisson model. The results are applied on purchase data of a consumption good.