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Generalized common spatial factor model.

There are often two types of correlations in multivariate spatial data: correlations between variables measured at the same locations, and correlations of each variable across the locations. We hypothesize that these two types of correlations are caused by a common spatially correlated underlying factor. Under this hypothesis, we propose a generalized common spatial factor model. The parameters are estimated using the Bayesian method and a Markov chain Monte Carlo computing technique. Our main goals are to determine which observed variables share a common underlying spatial factor and also to predict the common spatial factor. The model is applied to county-level cancer mortality data in Minnesota to find whether there exists a common spatial factor underlying the cancer mortality throughout the state.