This article presents factor copula approaches to model temporal dependency of non-Gaussian (continuous/discrete) longitudinal data. Factor copula models are canonical vine copulas which explain the underlying dependence structure of a multivariate data through latent variables, and therefore can be easily interpreted and implemented to unbalanced longitudinal data. We develop regression models for continuous, binary and ordinal longitudinal data including covariates, by using factor copula constructions with subject-specific latent variables. Considering homogeneous within-subject dependence, our proposed models allow for feasible parametric inference in moderate to high dimensional situations, using two-stage (IFM) estimation method. We assess the finite sample performance of the proposed models with extensive simulation studies. In the empirical analysis, the proposed models are applied for analysing different longitudinal responses of two real world data sets. Moreover, we compare the performances of these models with some widely used random effect models using standard model selection techniques and find substantial improvements. Our studies suggest that factor copula models can be good alternatives to random effect models and can provide better insights to temporal dependency of longitudinal data of arbitrary nature.

翻译：本文提出因子copula方法来模拟非高斯（连续/离散）纵向数据的时间依赖性。因子copula模型是典范藤copula，通过潜变量解释多元数据的潜在依赖结构，因此易于解释并适用于非平衡纵向数据。我们利用包含受试者特异性潜变量的因子copula构造，开发了包含协变量的连续、二分类和有序纵向数据的回归模型。考虑同质的受试者内依赖性，所提模型采用两阶段（IFM）估计方法，在中高维情形下实现可行的参数推断。通过大量模拟研究评估所提模型的有限样本性能。在实证分析中，将所提模型应用于分析两个真实世界数据集的纵向响应。此外，采用标准模型选择技术，将模型性能与广泛使用的随机效应模型进行比较，发现显著改进。研究表明，因子copula模型可作为随机效应模型的良好替代方案，并能更深入地揭示任意性质纵向数据的时间依赖性。