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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. doi:10.1198/jasa.2010.tm09061 ISSN 0162-1459.
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Official URL: http://dx.doi.org/10.1198/jasa.2010.tm09061
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, Engineering and Medicine > Science > Statistics | ||||
| Journal or Publication Title: | Journal of the American Statistical Association | ||||
| Publisher: | American Statistical Association | ||||
| ISSN: | 0162-1459 | ||||
| Official Date: | June 2010 | ||||
| Dates: |
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| Volume: | Vol.105 | ||||
| Number: | No.490 | ||||
| Number of Pages: | 10 | ||||
| Page Range: | pp. 740-749 | ||||
| DOI: | 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) |
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