Graphical Models for Associations between Variables, some of which are Qualitative and some Quantitative

The Annals of Statistics · 1989 · Volume 17 · Issue 1

Abstract

We define and investigate classes of statistical models for the analysis of associations between variables, some of which are qualitative and some quantitative. In the cases where only one kind of variables is present, the models are well-known models for either contingency tables or covariance structures. We characterize the subclass of decomposable models where the statistical theory is especially simple. All models can be represented by a graph with one vertex for each variable. The vertices are possibly connected with arrows or lines corresponding to directional or symmetric associations being present. Pairs of vertices that are not connected are conditionally independent given some of the remaining variables according to specific rules.

Keywords

62H99, 62J99, Analysis of variance, Conditional independence, Contingency tables, covariance selection, exponential families, logistic regression, log-linear models, Markov random fields, Multivariate analysis, path analysis, recursive models, regression, triangulated graphs

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