A Note on Collapsibility in DAG Models of Contingency Tables

Authors: KIM, SUNG-HO¹; KIM, SEONG-HO²

Source: Scandinavian Journal of Statistics, Volume 33, Number 3, September 2006 , pp. 575-590(16)

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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.

Keywords: graphical log-linear model; Markov equivalence; maximum likelihood estimation; model collapsibility; vertex removal

Document Type: Research article

DOI: http://dx.doi.org/10.1111/j.1467-9469.2005.00490.x

Affiliations: 1: Division of Applied Mathematics, Korea Advanced Institute of Science and Technology 2: School of Biology, Georgia Institute of Technology

Publication date: 2006-09-01