Dependence modeling of multivariate count data has been receiving a considerable attention in recent times. Multivariate elliptical copulas are typically preferred in statistical literature to analyze dependence between repeated measurements of longitudinal data since they allow for different choices of the correlation structure. But these copulas lack in flexibility to model dependence and inference is only feasible under parametric restrictions. In this article, we propose the use of finite mixture of elliptical copulas in order to capture complex and hidden temporal dependency of discrete longitudinal data. With guaranteed model identifiability, our approach permits to use different correlation matrices in each component of the mixture copula. We theoretically examine the dependence properties of finite mixture of copulas, before applying them for constructing regression models for count longitudinal data. The inference of the proposed class of models is based on composite likelihood approach and the finite sample performance of the parameter estimates are investigated through extensive simulation studies. For model validation, besides the standard techniques we extended the t-plot method to accommodate finite mixture of elliptical copulas. Finally, our models are applied to analyze the temporal dependency of two real world longitudinal data sets and shown to provide improvements if compared against standard elliptical copulas.

翻译：多变量计数数据的相依性建模近年来受到广泛关注。在统计文献中，多元椭圆Copula通常被用于分析纵向数据重复测量间的相依性，因其允许采用不同的相关结构。但此类Copula在建模灵活性上存在不足，且推断仅在参数约束下可行。本文提出使用椭圆Copula的有限混合模型，以捕捉离散纵向数据中复杂且隐藏的时间相依性。在保证模型可识别性的前提下，我们的方法允许在混合Copula的每个分量中使用不同的相关矩阵。在将有限混合Copula应用于构建计数纵向数据的回归模型之前，我们从理论上检验了其相依性性质。所提模型类别的推断基于复合似然方法，并通过大量模拟研究考察参数估计的有限样本表现。在模型验证方面，除标准技术外，我们将t-plot方法扩展至适应有限混合椭圆Copula。最后，我们将模型应用于分析两个真实纵向数据集的时序相依性，并证明其相比标准椭圆Copula具有改进效果。