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.

成分数据（compositional data）的分析通常需要既能刻画其组分的相对属性，又能探究空间异质性的方法。本文提出一种带空间聚类系数的成分回归模型，用于在非参数贝叶斯框架下评估成分预测变量在不同空间位置上的重要性差异。具体而言，针对含成分协变量的贝叶斯对数对比回归模型，本文构建了一种基于有限混合的混合先验的马尔可夫随机场（Markov random field）约束，可同时识别空间连续与不连续聚类。此外，本文还提出一种高效的马尔可夫链蒙特卡洛（Markov chain Monte Carlo）算法用于后验抽样，可同时实现聚类配置与聚类层面参数的联合推断。本文通过大量模拟实验与实际应用验证了所提方法的性能，其中实际应用数据取自2019年美国经济分析局（Bureau of Economic Analysis）针对美国50个州及华盛顿哥伦比亚特区的成分数据。本文的补充材料可在线获取。