Research Unit for Biostatistics, Department of Public Health, Aarhus University, Aarhus, Denmark.
Stat Med. 2020 Sep 30;39(22):2962-2979. doi: 10.1002/sim.8587. Epub 2020 Jul 17.
Bivariate observations of binary and ordinal data arise frequently and require a bivariate modeling approach in cases where one is interested in aspects of the marginal distributions as separate outcomes along with the association between the two. We consider methods for constructing such bivariate models based on latent variables with logistic marginals and propose a model based on the Ali-Mikhail-Haq bivariate logistic distribution. We motivate the model as an extension of that based on the Gumbel type 2 distribution as considered by other authors and as a bivariate extension of the logistic distribution, which preserves certain natural characteristics. Basic properties of the obtained model are studied and the proposed methods are illustrated through analysis of two data sets: a basic science cognitive experiment of visual recognition and awareness and a clinical data set describing assessments of walking disability among multiple sclerosis patients.
二元数据和有序数据的双变量观察经常出现，并且在人们对边际分布的各个方面作为单独的结果以及两者之间的关联感兴趣的情况下，需要采用双变量建模方法。我们考虑了基于具有逻辑边缘的潜在变量构建此类双变量模型的方法，并提出了一种基于 Ali-Mikhail-Haq 双变量逻辑分布的模型。我们将该模型作为其他作者所考虑的基于 Gumbel 类型 2 分布的模型的扩展，并作为逻辑分布的双变量扩展，保留了某些自然特征。研究了所得到的模型的基本性质，并通过对两个数据集的分析说明了所提出的方法：一个是关于视觉识别和意识的基础科学认知实验，另一个是描述多发性硬化症患者行走障碍评估的临床数据集。
