Generalized Sum-Asymmetry Model and Orthogonality of Test Statistic for Square Contingency Tables
DOI:
https://doi.org/10.17713/ajs.v53i2.1730Abstract
For analyzing contingency tables, we are usually interested in whether or not the independence model holds. On the other hand, for the analysis of square contingency tables, we are usually interested in whether or not the model having the structure of symmetry or asymmetry with respect to the main diagonals cells holds. This study proposes a generalized sum-asymmetry model including the exponential and relative exponential sum-symmetry models. This generalized model indicates that the cumulative probability that the sum of classes for row and column variables is s within the upper right cell of the table, is exponentially higher than the cumulative probability that the sum of classes for row and column variables is s within the lower left cell. Additionally, this study gives a separation of the sum-symmetry model using the proposed model, and reveals that the new separation satisfies the asymptotic equivalence for the test statistic. The utilities of the proposed methods are demonstrated through the real data analysis.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Shuji Ando
This work is licensed under a Creative Commons Attribution 3.0 Unported License.
The Austrian Journal of Statistics publish open access articles under the terms of the Creative Commons Attribution (CC BY) License.
The Creative Commons Attribution License (CC-BY) allows users to copy, distribute and transmit an article, adapt the article and make commercial use of the article. The CC BY license permits commercial and non-commercial re-use of an open access article, as long as the author is properly attributed.
Copyright on any research article published by the Austrian Journal of Statistics is retained by the author(s). Authors grant the Austrian Journal of Statistics a license to publish the article and identify itself as the original publisher. Authors also grant any third party the right to use the article freely as long as its original authors, citation details and publisher are identified.
Manuscripts should be unpublished and not be under consideration for publication elsewhere. By submitting an article, the author(s) certify that the article is their original work, that they have the right to submit the article for publication, and that they can grant the above license.