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.

中文翻译：

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基于潜在变量的双变量逻辑回归模型。

对二值和有序数据的双变量观测经常出现，并且在人们对边缘分布的各个方面以及作为二者之间的关联的结果感兴趣的情况下，需要采用双变量建模方法。我们考虑了基于具有逻辑对数边际潜变量的双变量模型构建方法，并提出了基于Ali-Mikhail-Haq双变量对数分布的模型。我们将模型作为其他作者考虑的基于Gumbel 2型分布的模型的扩展以及作为逻辑分布的双变量扩展的动机，该模型保留了某些自然特征。研究了所得模型的基本性质，并通过分析两个数据集说明了所提出的方法：