Detecting discrete spatial heterogeneity in compositional data via generalized group minimax concave penalty regularization

Compositional data comprises data where each value represents a fraction, ratio, or percentage of a whole. These values describe how different components contribute while maintaining relative proportions. In spatial contexts, these compositions can vary across regions owing to differing local influences. Capturing such area-specific variations in the compositional data is essential for understanding regional characteristics. However, analyzing spatial heterogeneity in compositional data is challenging because it must respect the simplex structure while detecting region-specific shifts. We introduce a novel statistical framework combining orthonormal log-ratio transformation and generalized group minimax concave penalty (MCP) regularization to detect discrete spatial heterogeneity, that is, spatial stratified heterogeneity, in compositional datasets. Extending the generalized lasso framework for discrete spatial heterogeneity analysis, our method enables simultaneous detection of local deviations and common spatial patterns, while addressing variable selection bias through MCP. We develop an estimation algorithm based on the majorize–minimization algorithm. Simulation studies under diverse spatial settings show high detection accuracy for moderate-to-strong heterogeneity, with power above 75% and a median false discovery rate of zero in every setting examined. The framework performs robustly even in complex spatial patterns. Application to municipal-level voting data from Japan’s 2024 general election reveals clear regional clusters linked to local political trends. Our approach offers a flexible tool, grounded in the CoDa and sparse modeling frameworks for spatial compositional data analysis and provides a basis for integrating with continuous heterogeneity analysis in future research.