Bayesian modelling strategies for spatially varying regression coefficients: A multivariate perspective for multiple outcomes

The modelling of spatially varying regression effects for multivariate mortality count outcomes is investigated. Alternative approaches to spatial regression heterogeneity are considered: the multivariate normal conditional autoregressive (MCAR) model is contrasted with a flexible set of priors based on the multiple membership approach. These include spatial factor priors and a non-parametric approach based on the Dirichlet process. A case study considers varying regression effects for a bivariate suicide outcome, namely male and female suicides in 354 English local authorities with social deprivation, social fragmentation and rurality as predictors.