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Likelihood ratio tests with three-way tables

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Cheng, Philip E., Liou, Michelle and Aston, John A. D.. (2010) Likelihood ratio tests with three-way tables. Journal of the American Statistical Association, Vol.105 (No.490). pp. 740-749. ISSN 0162-1459

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Abstract

Likelihood ratio (LR) tests for association and for interaction are examined for three-way contingency tables, particularly the widely used 2 x 2 x K table. Mutual information identities are used to characterize the information decomposition and the logical relationship between the omnibus LR test for conditional independence across K strata and its two independent components. LR tests for interaction and for uniform association. The latter two tests are logically connected to formulating a natural two-step test for conditional independence. The proposed two-step test with reduced nominal levels is suggested instead of the Breslow-Day test and the Cochran-Mantel-Haenszel test. This yields efficient interval estimation for both the interaction parameter and the common odds ratio compared with using the Mantel-Haenszel estimate. This allows the development of power analysis for testing general hypotheses of varied interactions, using an invariant Pythagorean law of relative entropy.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Statistics
Journal or Publication Title: Journal of the American Statistical Association
Publisher: American Statistical Association
ISSN: 0162-1459
Official Date: June 2010
Volume: Vol.105
Number: No.490
Number of Pages: 10
Page Range: pp. 740-749
Identification Number: 10.1198/jasa.2010.tm09061
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Funder: NSC, Engineering and Physical Sciences Research Council (EPSRC)
Grant number: 2118-M-001-009, EP/H031936/1 (EPSRC)
URI: http://wrap.warwick.ac.uk/id/eprint/5504

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