Dependence modeling of multivariate count data has garnered significant attention in recent years. 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 employing finite mixtures of elliptical copulas to better capture the intricate and hidden temporal dependencies present in discrete longitudinal data. Our approach allows for the utilization of different correlation matrices within each component of the mixture copula. We theoretically explore the dependence properties of finite mixtures of copulas before employing them to construct regression models for count longitudinal data. Inference for this proposed class of models is based on a composite likelihood approach, and we evaluate the finite sample performance of parameter estimates through extensive simulation studies. To validate our models, we extend traditional techniques and introduce the t-plot method to accommodate finite mixtures of elliptical copulas. Finally, we apply our models to analyze the temporal dependence within two real-world longitudinal datasets and demonstrate their superiority over standard elliptical copulas.

翻译：近年来，多元计数数据的相依性建模受到广泛关注。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关系，因其允许选择不同的相关结构。然而这些Copula在相依性建模方面缺乏灵活性，且推断仅在参数限制条件下可行。本文提出采用椭圆Copula的有限混合模型，以更好地捕捉离散纵向数据中复杂且隐含的时间相依性。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。在将其应用于构建纵向计数数据回归模型之前，我们从理论上探讨了有限混合Copula的相依特性。针对此类模型的推断基于复合似然方法，并通过大量模拟研究评估参数估计的有限样本性能。为验证模型，我们扩展了传统技术并引入t-plot方法以适应椭圆Copula的有限混合结构。最后，我们将模型应用于两个真实世界纵向数据集的时间相依性分析，并证明其相对于标准椭圆Copula的优越性。