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

TLDR

When only one variable type is present, the models reduce to standard contingency table or covariance structure models. The study defines and investigates classes of statistical models for mixed qualitative and quantitative variables, focusing on a subclass of decomposable models with particularly simple theory. The models are represented as graphs where vertices correspond to variables, edges (arrows or lines) indicate directional or symmetric associations, and non‑adjacent vertices are conditionally independent given appropriate subsets. The authors identify a subclass of decomposable models with especially simple statistical theory.

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.