Binary models for marginal independence
Binary models for marginal independence
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DOI：
10.1111/j.1467-9868.2007.00636.x
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发表时间：
2008-01-01
影响因子：
5.8
通讯作者：
Richardson, Thomas S.
中科院分区：
文献类型：
--
作者：
Drton, Mathias;Richardson, Thomas S.
对数线性模型是分析列联表的经典工具。特别是，图形对数线性模型的子类为条件独立性建模提供了通用框架。然而，除了特殊结构之外，这些传统模型无法适应边际独立性假设。着眼于二元变量，我们提出了一个模型类，它为列联表中的边际独立性建模提供了框架。所采用的方法是图形化的，并利用与边际独立性的多元高斯模型进行类比。对于图形模型表示，我们使用双向图，这是路径图的传统。我们展示了如何以简单的方式对模型进行参数化，以及如何使用迭代条件拟合算法的版本来执行最大似然估计。最后我们考虑将这些模型与对称限制结合起来。
Log-linear models are a classical tool for the analysis of contingency tables. In particular, the subclass of graphical log-linear models provides a general framework for modelling conditional independences. However, with the exception of special structures, marginal independence hypotheses cannot be accommodated by these traditional models. Focusing on binary variables, we present a model class that provides a framework for modelling marginal independences in contingency tables. The approach that is taken is graphical and draws on analogies with multivariate Gaussian models for marginal independence. For the graphical model representation we use bidirected graphs, which are in the tradition of path diagrams. We show how the models can be parameterized in a simple fashion, and how maximum likelihood estimation can be performed by using a version of the iterated conditional fitting algorithm. Finally we consider combining these models with symmetry restrictions.