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A Note on Collapsibility in DAG Models of Contingency Tables
Author(s) -
KIM SUNGHO,
KIM SEONGHO
Publication year - 2006
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2005.00490.x
Subject(s) - directed acyclic graph , mathematics , contingency table , graph , joint probability distribution , graphical model , moral graph , statistics , combinatorics , line graph , voltage graph
. 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.