Advances and Applications in Statistics
Volume 5, Issue 3, Pages 301 - 312
(December 2005)
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A NOTE ON DIFFERENT SELECTION OF BEST-FITTING MODEL BY LIKELIHOOD RATIO TEST AND AKAIKE INFORMATION CRITERION FOR THE ANALYSIS OF CONTINGENCY TABLES
Nobuko Miyamoto (Japan), Satoshi Shinohara (Japan), Akira Inoue (Japan) and Sadao Tomizawa (Japan)
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Abstract: For the analysis of contingency tables, various models are applied to see the structure of the data. The likelihood ratio test (LRT) or Akaike Information Criterion (AIC) are used to select the best-fitting model among several models. In this paper, we consider what case the different models are selected by LRT and AIC each other as the best-fitting model in, and point out that there are two kinds of types of different model selections. When the different model selection occurs, this paper gives the range such that the difference between the likelihood ratio statistics for two models or the difference between the AICs for two models always exist. We describe the model selection by AIC, and indicate an example of analysis of the unaided distance vision data of pupils in the elementary schools, Japan, in which different model selections occurred. |
Keywords and phrases: AIC, contingency table, likelihood ratio test, model selection. |
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