Open Access
June 2014 Symmetry and asymmetry models and decompositions of models for contingency tables
Kouji Tahata, Sadao Tomizawa
Author Affiliations +
SUT J. Math. 50(2): 131-165 (June 2014). DOI: 10.55937/sut/1424458569

Abstract

For analyzing square contingency tables, Bowker [14] proposed the symmetry model. Caussinus [16] proposed the quasi-symmetry model and gave a decomposition of model such that the symmetry model holds if and only if both the quasi-symmetry and the marginal homogeneity models hold. Bhapkar and Darroch [13] gave the similar theorem for multi-way contingency tables. For square tables and for multi-way tables, the present paper (1) reviews various models of symmetry and asymmetry, (2) reviews the decompositions of models, (3) gives some figures which indicate the relationships among various models, and (4) gives a new decomposition of symmetry model.

Acknowledgements

The authors would like to thank a referee for the helpful comments.

Citation

Download Citation

Kouji Tahata. Sadao Tomizawa. "Symmetry and asymmetry models and decompositions of models for contingency tables." SUT J. Math. 50 (2) 131 - 165, June 2014. https://doi.org/10.55937/sut/1424458569

Information

Received: 31 July 2014; Revised: 23 January 2015; Published: June 2014
First available in Project Euclid: 11 June 2022

Digital Object Identifier: 10.55937/sut/1424458569

Subjects:
Primary: 62H17

Keywords: Decomposition , double symmetry , marginal homogeneity , Marginal symmetry , Model , orthogonality , point-symmetry , quasi-symmetry , symmetry

Rights: Copyright © 2014 Tokyo University of Science

Vol.50 • No. 2 • June 2014
Back to Top