用于聚类多变量相关结局的广义估计方程有限混合模型
Finite Mixtures of Generalized Estimating Equations for Clustering Multivariate Correlated Outcomes
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中文总结 AI 辅助
针对多变量相关结局聚类问题，提出MixGEE模型，通过区域特定工作相关结构处理物种间相关性，经模拟验证可靠，应用于凯尔盖朗高原鱼类数据得到三类群落特征。
中文摘要 AI 辅助
多变量相关结局出现在生态学、社会科学和心理测量学等多个学科领域。本文聚焦于对不同观测单元的这类结局进行聚类，具体是找到具有相同“结局特征”的单元组。研究动机来自生态学中的生物区域划分，该研究旨在将位点聚类为具有相同物种特征的生物区域，其中位点归属可依赖于环境或生境协变量。为实现这一目标，我们提出了广义估计方程有限混合模型（MixGEE）。与现有的基于模型的生物区域划分方法不同，MixGEE在位点分区时，会通过区域特定的工作相关结构考虑物种间的相关性，因此每个区域由边缘物种均值向量和物种间相关矩阵表征。与基于似然的有限混合模型不同，MixGEE不需要多变量结局的完整联合分布，而是基于估计方程的大样本分布构建区域归属的伪后验概率，这产生了一种交替更新这些概率和求解加权估计方程的迭代算法。我们使用基于预留位点和物种成分预测性能的交叉验证确定区域数量，并使用聚类狄利克雷随机权重自助法进行不确定性量化。模拟结果表明，在各种相关结构下，该方法的估计和推断可靠，且在选择组数量时比忽略相关性的方法更稳定。将MixGEE应用于凯尔盖朗高原周围鱼类物种的存在-缺失记录，揭示了三种具有不同出现情况和位点内相关模式的不同鱼类群落特征。
英文摘要
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.
发表机构
- Faculty of Economics, Keio University（庆应义塾大学经济学部）
- Research School of Finance, Actuarial Studies and Statistics, The Australian National University（澳大利亚国立大学金融、精算与统计研究学院）
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