Longitudinal studies often involve multiple mixed response variables measured repeatedly over time. Although separate modeling of these multiple mixed response variables can be easily performed, they may lead to inefficient estimates and consequently, misleading inferences. For obtaining correct inference, one needs to model multiple mixed responses jointly. In this paper, we use copula models for defining a multivariate distribution for multiple mixed outcomes at each time point. Then, we use transition model for considering association between longitudinal measurements. Two simulation studies are performed for illustration of the proposed approach. The results of the simulation studies show that the use of the separate models instead of the joint modeling leads to inefficient parameter estimates. The proposed approach is also used for analyzing two real data sets. The first data set is a part of the British Household Panel Survey. In this data set, annual income and life satisfaction are considered as the continuous and the ordinal correlated longitudinal responses, respectively. The second data set is a longitudinal data about heart failure patients. This study is a treatment–control study, where the effect of a treatment is simultaneously investigated on readmission and referral to doctor as two binary associated longitudinal responses.

中文翻译：

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高斯copula方法分析多元纵向数据的过渡模型。

纵向研究通常涉及多个混合响应变量，这些变量会随时间重复测量。尽管可以轻松地对这些多个混合响应变量进行单独建模，但它们可能导致估算效率低下，从而导致误导性推断。为了获得正确的推论，需要共同对多个混合响应建模。在本文中，我们使用关联模型来定义每个时间点的多个混合结果的多元分布。然后，我们使用过渡模型来考虑纵向测量之间的关联。进行了两个仿真研究，以说明所提出的方法。仿真研究的结果表明，使用单独的模型而不是联合模型会导致效率低下的参数估计。所提出的方法还用于分析两个真实数据集。第一个数据集是英国家庭面板调查的一部分。在此数据集中，年收入和生活满意度分别被认为是连续和有序相关的纵向响应。第二个数据集是有关心力衰竭患者的纵向数据。这项研究是一种治疗-对照研究，其中同时研究了治疗对再入院的影响，并转介给医生作为两个二进制相关的纵向反应。第二个数据集是有关心力衰竭患者的纵向数据。这项研究是一种治疗-对照研究，其中同时研究了治疗对再入院的影响，并转介给医生作为两个二进制相关的纵向反应。第二个数据集是有关心力衰竭患者的纵向数据。这项研究是一种治疗-对照研究，其中同时研究了治疗对再入院的影响，并转介给医生作为两个二进制相关的纵向反应。