Relative-shift regression provides a principled framework for modeling compositional covariates by quantifying how the response changes when mass is reallocated from one component to another. Yet many emerging compositional data problems extend beyond this classical setting, involving high-dimensional predictors and regression effects that vary across latent subpopulations. This complexity poses a dual challenge unmet by existing methods: recovering latent cluster structure while simultaneously achieving dimension reduction within each cluster. We propose a Bayesian heterogeneous relative-shift regression model that jointly learns latent clusters and parsimonious effect structures. Methodologically, we combine a projection-based shrinkage prior on identifiable contrasts, which induces exact coefficient ties within mixture components, with a mixture of finite mixtures prior that infers the number of clusters. Computationally, we develop a scalable hybrid MCMC algorithm that embeds a deterministic surrogate collapse operator within NUTS. Theoretically, we establish posterior consistency for both the latent partition and cluster-specific effect structures. Simulations confirm accurate recovery and strong predictive performance, and applications to cross-country macroeconomic data and spatial transcriptomics demonstrate the method's interpretability and practical utility.

翻译：相对偏移回归为建模成分数据协变量提供了一个原则性框架，其通过量化质量从一个组分重新分配至另一个组分时响应变量的变化方式来实现。然而，许多新兴的成分数据问题已超出这一经典设定，涉及高维预测变量以及随潜在子群体变化的回归效应。这种复杂性带来了现有方法无法应对的双重挑战：在恢复潜在聚类结构的同时，在每个聚类内实现降维。我们提出一种贝叶斯异质性相对偏移回归模型，该模型联合学习潜在聚类和简约效应结构。在方法论上，我们将基于投影的可识别对比度稀疏先验（该先验在混合成分内部诱导精确系数连接）与推断聚类数量的有限混合先验相结合。在计算上，我们开发了一种可扩展的混合马尔可夫链蒙特卡洛算法，该算法在NUTS算法内嵌入确定性替代塌陷算子。在理论上，我们建立了关于潜在划分和聚类特定效应结构的后验一致性。模拟实验证实了准确的恢复能力和强大的预测性能，而对跨国宏观经济数据和空间转录组学的应用则展示了该方法的可解释性和实际效用。