A Socio-Demographic Latent Space Approach to Spatial Data When Geography is Important but Not All-Important

Many models for spatial and spatio-temporal data assume that "near things are more related than distant things," which is known as the first law of geography. While geography may be important, it may not be all-important, for at least two reasons. First, technology helps bridge distance, so that regions separated by large distances may be more similar than would be expected based on geographical distance. Second, geographical, political, and social divisions can make neighboring regions dissimilar. We develop a flexible Bayesian approach for learning from spatial data which units are close in an unobserved socio-demographic space and hence which units are similar. As a by-product, the Bayesian approach helps quantify the relative importance of socio-demographic space relative to geographical space. To demonstrate the proposed approach, we present simulations along with an application to county-level data on median household income in the U.S. state of Florida.