A Bayesian Factor Model for Spatial Panel Data with a Separable Covariance Approach

A hierarchical Bayesian factor model for multivariate spatially and temporally correlated data is proposed. This method searches factor scores incorporating a dependence within observations due to both a geographical and a temporal structure and it is an extension of a model proposed by Mezzetti (2012) using the results of a separable covariance matrix for the spatial panel data as in Leorato and Mezzetti (2016). A Gibbs sampling algorithm is implemented to sample from the posterior distributions. We illustrate the benefit and the performance of our model by analyzing death rates for different diseases together with some socio-economical and behavioural indicators and by analyzing simulated data.