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Some collapsibility results for n-dimensional contingency tables

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Title Some collapsibility results for n-dimensional contingency tables
 
Creator VELLAISAMY, P
VIJAY, V
 
Subject collapsibility
conditional independence
contingency table
log-linear model
mobius inversion
simpson's paradox
strict collapsibility
 
Description For a multidimensional contingency table, we obtain several necessary and sufficient conditions for collapsibility and strict collapsibility, using the technique of Mobius inversion formula. As a consequence, the results of Whittemore (Journal of the Royal Statistical Society B, 40, 328-340, 1978) are stated in a form which is easy to understand and the proofs are much simpler and straightforward. Several new results on collapsibility and strict collapsibility with respect to more than one interaction parameter, are established, and their relationships to conditional independence are also pointed out. As applications of our results, several typical examples on collapsibility, strict collapsibility and conditional independence are discussed. It is also shown that Bishop et al. (Discrete Multivariate Analysis: Theory and Practice, MIT Press, Cambridge, 1975) conditions are necessary and sufficient for strict collapsibility with respect to a set of interaction factors.
 
Publisher SPRINGER HEIDELBERG
 
Date 2011-08-30T05:26:07Z
2011-12-26T12:58:47Z
2011-12-27T05:49:19Z
2011-08-30T05:26:07Z
2011-12-26T12:58:47Z
2011-12-27T05:49:19Z
2007
 
Type Article
 
Identifier ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS, 59(3), 557-576
0020-3157
http://dx.doi.org/10.1007/s10463-006-0058-4
http://dspace.library.iitb.ac.in/xmlui/handle/10054/12207
http://hdl.handle.net/10054/12207
 
Language en