A Note on Collapsibility in DAG Models of Contingency Tables |
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| Authors: | SUNG-HO KIM SEONG-HO KIM |
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| Institution: | Division of Applied Mathematics, Korea Advanced Institute of Science and Technology; School of Biology, Georgia Institute of Technology |
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| Abstract: | Abstract. Necessary and sufficient conditions for collapsibility of a directed acyclic graph (DAG) model for a contingency table are derived. By applying the conditions, we can easily check collapsibility over any variable in a given model either by using the joint probability distribution or by using the graph of the model structure. It is shown that collapsibility over a set of variables can be checked in a sequential manner. Furthermore, a DAG is compared with its moral graph in the context of collapsibility. |
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| Keywords: | graphical log-linear model Markov equivalence maximum likelihood estimation model collapsibility vertex removal |
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