We demonstrate that many current approaches for marginal modeling of correlated binary outcomes produce likelihoods that are equivalent to the copula-based models herein. These general copula models of underlying latent threshold random variables yield likelihood-based models for marginal fixed effects estimation and interpretation in the analysis of correlated binary data with exchangeable correlation structures. Moreover, we propose a nomenclature and set of model relationships that substantially elucidates the complex area of marginalized random intercept models for binary data. A diverse collection of didactic mathematical and numerical examples are given to illustrate concepts.

中文翻译：

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相关二进制结果的边缘化随机截距模型的统一框架

我们证明了许多当前用于对相关二元结果进行边际建模的方法产生的可能性与此处基于 copula 的模型等效。在分析具有可交换相关结构的相关二进制数据时，这些潜在阈值随机变量的通用 copula 模型产生基于似然的模型，用于边际固定效应估计和解释。此外，我们提出了一个命名法和一组模型关系，它们基本上阐明了二进制数据的边缘化随机截距模型的复杂区域。提供了多种教学数学和数值示例来说明概念。