Spatially Clustered Compositional Regression: A Nonparametric Bayesian Approach

The analysis of compositional data often requires methods that account for the relative nature of its components while also exploring spatial heterogeneity. In this article, a compositional regression with spatially clustered coefficients is proposed to assess the varying importance of compositional predictors across spatial locations within a nonparametric Bayesian framework. Specifically, a Markov random field constraint with a mixture of finite mixtures prior is developed for Bayesian log contrast regression with compositional covariates, allowing for the identification of both spatially contiguous and discontinuous clusters. Furthermore, an efficient Markov chain Monte Carlo algorithm is introduced for posterior sampling, enabling simultaneous inference on both cluster configurations and cluster-wise parameters. The proposed method’s performance is validated through extensive simulation studies and an application to compositional data from the 2019 Bureau of Economic Analysis for the 50 states and Washington DC of the United States. Supplementary materials for this article are available online.