  The Gini coefficient is an universally used measurement of income inequality.
Intersectoral GDP contributions reveal the economic development of different
sectors of the national economy. Linking intersectoral GDP contributions to
Gini coefficients will provide better understandings of how the Gini
coefficient is influenced by different industries. In this paper, a
compositional regression with spatially clustered coefficients is proposed to
explore heterogeneous effects over spatial locations under nonparametric
Bayesian framework. Specifically, a Markov random field constraint mixture of
finite mixtures prior is designed for Bayesian log contrast regression with
compostional covariates, which allows for both spatially contiguous clusters
and discontinous clusters. In addition, an efficient Markov chain Monte Carlo
algorithm for posterior sampling that enables simultaneous inference on both
cluster configurations and cluster-wise parameters is designed. The compelling
empirical performance of the proposed method is demonstrated via extensive
simulation studies and an application to 51 states of United States from 2019
Bureau of Economic Analysis.
