Generalized spatial structural equation models.

It is common in public health research to have high-dimensional, multivariate, spatially referenced data representing summaries of geographic regions. Often, it is desirable to examine relationships among these variables both within and across regions. An existing modeling technique called spatial factor analysis has been used and assumes that a common spatial factor underlies all the variables and causes them to be related to one another. An extension of this technique considers that there may be more than one underlying factor, and that relationships among the underlying latent variables are of primary interest. However, due to the complicated nature of the covariance structure of this type of data, existing methods are not satisfactory. We thus propose a generalized spatial structural equation model. In the first level of the model, we assume that the observed variables are related to particular underlying factors. In the second level of the model, we use the structural equation method to model the relationship among the underlying factors and use parametric spatial distributions on the covariance structure of the underlying factors. We apply the model to county-level cancer mortality and census summary data for Minnesota, including socioeconomic status and access to public utilities.