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Graphical and recursive models for contingency tables. (English) Zbl 0541.62038
The graphical models are a subclass of hierarchical log linear models such that they can be represented by an undirected graph. The recursive models arise from a factorization of the joint distribution in terms of response variables and each of such models corresponds to a particular kind of a directed graph. E.g., in a three-dimensional contingency table the factorization \(p_{ijk}=p_{i| jk}p_{.jk}\) gives the recursive system with one response (variable 1), and \(p_{ijk}=p_{i| jk}p_{j| k}p_{..k}\) the recursive system with two responses (variables 1 and 2).
The authors characterize the class of models in which each zero partial association coincides with a zero partial dependence. The result can be used in the exploratory analysis and in the model interpretation.
Reviewer: J.Anděl

MSC:
62H17 Contingency tables
05C20 Directed graphs (digraphs), tournaments
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