Marginal models involve restrictions on the conditional and marginal association structure of a set of categorical variables. They generalize log-linear models for contingency tables, which are the fundamental tools for modelling the conditional association structure. This chapter gives an overview of the development of marginal models during the past 20 years. After providing some motivating examples, the first few sections focus on the definition and characteristics of marginal models. Specifically, we show how their fundamental properties can be understood from the properties of marginal log-linear parameterizations. Algorithms for estimating marginal models are discussed, focussing on the maximum likelihood and the generalized estimating equations approaches. It is shown how marginal models can help to understand directed graphical and path models, and a description is given of marginal models with latent variables.

翻译：边际模型涉及对一组分类变量的条件与边际关联结构的约束。它们推广了用于列联表的对数线性模型，后者是建模条件关联结构的基本工具。本章概述了过去20年间边际模型的发展。在给出若干启发式案例后，前几节重点阐述边际模型的定义与特性。具体而言，我们展示了如何通过边际对数线性参数化的性质理解其基本属性。本文讨论了边际模型的估计算法，重点聚焦极大似然法与广义估计方程方法。同时阐释了边际模型如何帮助理解有向图模型与路径模型，并描述了包含潜变量的边际模型。