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 neighbouring regions dissimilar. We develop a flexible Bayesian approach for learning from spatial data in which units are close in an unobserved socio‐demographic space and hence which units are similar. While classic approaches based on nearest‐neighbour adjacency matrices may not fully capture all of the spatial correlation, the proposed approach learns neighbourhoods from data, and averages over all possible neighbourhood structures. We demonstrate the advantages of the proposed approach by presenting simulations along with applications to county‐level American Community Survey data on median household income in the US states of Florida, North Carolina and South Carolina.