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Title: The analysis of asymmetry based on ordered scores for square contingency tables Authors:  Hiroyuki Kurakami - Tokyo University of Science (Japan) [presenting]
Shuji Ando - Novartis Pharma KK (Japan)
Abstract: For the analysis of square contingency tables with same row and column ordinal classifications, the symmetry (S) model has been considered. The S model indicates that the cell probabilities of the table are symmetric with respect to the main diagonal line in a square contingency table. As an extension of the S model, some models having the structure of asymmetry based on the integer scores has been considered. We focus on the asymmetry models based on the ordered scores. We propose a new model based on the ordered scores. The proposed model indicates that the log odds of the symmetric cell probabilities decreases depending on the difference between the ordered scores. Also, we give the decomposition of the S model using the proposed model, and show that the test statistic for the S model is approximately equivalent to the sum of those for decomposed models. Additionally, the simulation study about the relationship between the new model and continuous distributions is given.