Bayesian analysis of areal data with unknown adjacencies using the stochastic edge mixed effects model

Abstract

Traditional conditional autoregressive (CAR) models use neighborhood information to define the adjacency matrix. Specifically, the neighborhoods are defined deterministically using the boundaries between the regions. However, covariates may inform the entries of the adjacency matrix and may not correspond to the nearest neighbor structure that is typically assumed. We propose a class of prior distributions for adjacency matrices, which incorporate covariates and can detect a relationship between two areas that do not share a boundary. Our approach is fully Bayesian, and involves a computationally efficient conjugate update of the adjacency matrix. To illustrate the high performance of our Bayesian hierarchical model, we present a simulation study, and an example using data made publicly available by the New York City Department of Health.