A hierarchical geostatistical factor model for multivariate Poisson count data

Though in the last decade many works have appeared in the literature dealing with model-based extensions of the classical (univariate) geostatistical mapping methodology based on linear Kriging, very few authors have concentrated, mainly for the inferential problems they pose, on model-based extensions of classical multivariate geostatistical techniques like the linear model of coregionalization, or the related `factorial kriging analysis'. Nevertheless, in presence of multivariate spatial non-Gaussian data, in particular count data, as in many environmental applications, the use of these classical techniques can lead to incorrect predictions about the underling factors. To recover some of the optimality properties enjoyed by the predictions supplied by these techniques in the case of Gaussian data, in particular unbiasedness and minimum mean square error, we propose a hierarchical geostatistical factor model extending, following a model-based geostatistical approach, the classical geostatistical proportional covariance model. For this model we investigate a likelihood-based inferential procedure adopting the Monte Carlo EM algorithm and show its sampling performances mainly through some thorough simulation studies. Besides, we also show how mapping of the latent factors can be efficiently carried out exploiting a linearity property of the predictions.