Lauritzen, S. L.; Wermuth, N. Graphical models for associations between variables, some of which are qualitative and some quantitative. (English) Zbl 0669.62045 Ann. Stat. 17, No. 1, 31-57 (1989). 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. Cited in 2 ReviewsCited in 107 Documents MSC: 62H99 Multivariate analysis 62J99 Linear inference, regression 62H20 Measures of association (correlation, canonical correlation, etc.) 05C99 Graph theory Keywords:analysis of variance; conditional independence; covariance selection; exponential families; logistic regression; log-linear models; Markov random fields; path analysis; regression; recursive models; triangulated graphs; qualitative variables; quantitative variables; CG-distributions; analysis of associations; contingency tables; covariance structures; decomposable models × Cite Format Result Cite Review PDF Full Text: DOI