04197186

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04197186 Frydenberg, Morten Marginalization and collapsibility in graphical interaction models. Ann. Stat. 18, No.2, 790-805 (1990). 1990 Institute of Mathematical Statistics, Beachwood, OH EN association models decomposition maximum likelihood estimate contingency tables covariance selection marginalization cut graphical interaction model necessary and sufficient condition for collapsibility

doi:10.1214/aos/1176347626

A graphical interaction model is a model for association among variables where each variable is represented by a vertex on the graph, and two vertices are connected if there is a direct association between the corresponding variables, so that two variables are not connected if they are conditionally independent given some other variables. Such a model is called collapsible onto a set of variables if the implied model for the marginal distributions for these variables is equal to the graphical interaction model given by the induced subgraph. A necessary and sufficient condition for collapsibility is found. Several implications of collapsibility are discussed. L.Weiss (Ithaca)