Hierarchical Poisson models for spatial count data

This work proposes a class of hierarchical models for geostatistical count data that includes the model proposed by Diggle et al. (1998)  [13] as a particular case. For this class of models the main second-order properties of the count variables are derived, and three models within this class are studied in some detail. It is shown that for this class of models there is a close connection between the correlation structure of the counts and their overdispersions, and this property can be used to explore the flexibility of the correlation structures of these models. It is suggested that the models in this class may not be adequate to represent data consisting mostly of small counts with substantial spatial correlation. Three geostatistical count datasets are used to illustrate these issues and suggest how the results might be used to guide the selection of a model within this class.