A count data model with unobserved heterogeneity

A count data model is defined via the distribution of the durations between successive events. It is assumed that the durations follow independent 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-specific factors. The count data model is therefore a natural extension of the compound Poisson model. A local version of the count data model is used to analyse the effects of unobserved spell specific factors. In particular, it is shown that spell-specific heterogeneity can induce not only overdispersion, but also underdispersion. The local model is also used to construct a score test for spell-specific heterogeneity in the Poisson model. The results are applied on purchase data of a consumption good.