In this work we deal with multivariate spatial non-Gaussian data, by analyzing, in particular, variables for count data. Building on generalized linear mixed models, we extend these frameworks to multivariate spatial data in a new flexible fashion involving a linear factor model structure for the latent part of the model. Statistical inference is likelihood based and the parameter estimates are obtained via a stochastic version of the EM algorithm. For the mapping of the latent spatial factors, Markov Chain Monte Carlo methods are used. A deep analysis of the performance of the inferential procedure as well as an empirical evaluation of the estimates properties are carried out by a simulation study. The application to the multivariate spatial plankton data of the lake Trasimeno (Italy) allows to appreciate the efficacy of the model to detect the latent spatial structure of the observed data.
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