Correlated binary data are prevalent in a wide range of scientific disciplines, including healthcare and medicine. The generalized estimating equations (GEEs) and the multivariate probit (MP) model are two of the popular methods for analyzing such data. However, both methods have some significant drawbacks. The GEEs may not have an underlying likelihood and the MP model may fail to generate a multivariate binary distribution with specified marginals and bivariate correlations. In this paper, we study multivariate binary distributions that are based on D-vine pair-copula models as a superior alternative to these methods. We elucidate the construction of these binary distributions in two and three dimensions with numerical examples. For higher dimensions, we provide a method of constructing a multidimensional binary distribution with specified marginals and equicorrelated correlation matrix. We present a real-life data analysis to illustrate the application of our results.

中文翻译：

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对关联生成的相关二元变量的多元分布

相关二进制数据在包括医疗保健和医学在内的许多科学学科中普遍存在。广义估计方程（GEE）和多元概率模型（MP）模型是分析此类数据的两种流行方法。但是，这两种方法都有一些明显的缺点。GEE可能没有潜在的可能性，MP模型可能无法生成具有指定边际和双变量相关性的多元二元分布。在本文中，我们研究基于D-vine对-copula模型的多元二元分布，作为这些方法的替代方法。我们用数值示例阐明了这些二维分布在二维和三维中的构造。对于更大的尺寸，我们提供了一种使用指定的边际和等相关的相关矩阵构造多维二元分布的方法。我们提供了现实生活中的数据分析，以说明我们的结果的应用。