相依有序数据下分层阿基米德Copula模型的研究

Analysis for dependent ordinal data based on hierarchical Archimedean copula

异质性变量间非对称相依关系的存在,使多元有序数据相依模型的建立变得复杂。本文重点研究了当响应变量为有序多分类数据时,基于不同生成元组合的分层阿基米德Copula(Hierarchical Archime⁃dean Copula,HAC)相依模型的构建。通过潜变量建模得到有序边际的边缘概率模型,进而建立非对称的相依结构。利用数值模拟比较了组合HAC和单一类型阿基米德生成元构成的HAC在参数估计和模型拟合上的效果,并将其应用于自评健康等级数据集的分析工作中。结果表明组合HAC在实际应用中的有效性和优越性,为研究有序数据的非对称相依结构提供了新思路。

The existence of asymmetric dependence among heterogeneous variables makes a challenging task to estab⁃lish a multivariate ordinal dependent model.This paper focuses on the construction of hierarchical Archimedean copula(HAC)based on different generator combinations when the response variables are ordinal.The marginal probability mod⁃el of ordinal margin is obtained through latent variable modeling,and then the asymmetric dependence structure is estab⁃lished.The effects of combined HAC and single HAC on parameter estimation and model fitting are compared through numerical simulation.And a real-data application related to self-assessment health status is used.The results show the ef⁃fectiveness and superiority of the combined HAC in practical application,and provide an insight for the study of the asymmetric dependence structure of ordinal data.