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：本文提出因子连接函数方法来对非高斯（连续/离散）纵向数据的时间依赖性进行建模。因子连接函数模型是一种典范藤连接函数，它通过潜变量解释多元数据背后的依赖结构，因此易于解释并适用于非平衡纵向数据。通过使用带有主体特异性潜变量的因子连接函数构造，我们开发了包含协变量的连续、二元和有序纵向数据的回归模型。考虑到同质的主体内部依赖性，我们提出的模型允许在中等至高维情况下使用两阶段（IFM）估计方法进行可行的参数推断。我们通过广泛的模拟研究评估了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数据集的纵向响应。此外，我们使用标准模型选择技术将这些模型的性能与一些广泛使用的随机效应模型进行比较，并发现显著的改进。我们的研究表明，因子连接函数模型可以成为随机效应模型的良好替代方案，并能更深入地洞察任意性质纵向数据的时间依赖性。