Finite Mixtures of Generalized Estimating Equations for Clustering Multivariate Correlated Outcomes

2026-09-04

AI Summary

本文提出了一种有限混合广义估计方程(MixGEE)方法，用于解决多变量相关结果的聚类问题，特别适用于生态学生物区域划分。

Abstract

Multivariate correlated outcomes occur across disciplines, including ecology, social sciences, and psychometrics. This paper focuses on clustering these outcomes across observational units, specifically, finding groups of units with the same ``outcome profile". Our motivation comes from bioregionalization in ecology, which aims to cluster sites into bioregions with the same species profiles, where site membership can depend on environmental or habitat covariates. To accomplish this, we propose finite mixtures of generalized estimating equations (MixGEE). Unlike existing approaches to model-based bioregionalization, MixGEE partitions sites into regions while accounting for between-species correlations through a region-specific working correlation structure. Thus, each region is characterized by a marginal species mean vector and a between-species correlation matrix. Unlike likelihood-based finite mixture models, MixGEE does not require a full joint distribution of the multivariate outcomes. Instead, we construct a pseudo-posterior probability for region membership motivated by the large-sample distribution of the estimating equation. This leads to an iterative algorithm alternating between updating these probabilities and solving weighted estimating equations. We determine the number of regions using cross-validation based on predictive performance for held-out sites and species components, and use a clustered Dirichlet random-weight bootstrap for uncertainty quantification. Simulations demonstrate reliable estimation and inference under various correlation structures and more stable selection of the number of groups than methods that ignore dependence. Applying MixGEE to presence--absence records of fish species around the Kerguelen Plateau reveals three distinct fish assemblage profiles with heterogeneous occurrence and within-site correlation patterns.

Problem

• Clustering
• Multivariate Correlated Outcomes
• Bioregionalization

Innovation

• Finite Mixtures of Generalized Estimating Equations
• MixGEE
• region-specific working correlation structure
• pseudo-posterior probability
• cross-validation