Extended asymmetry model based on logit transformation and decomposition of symmetry for square contingency tables with ordered categories


Abstract


The issues of symmetry (or asymmetry) arises naturally for the analysis of square contingency tables. Many existing asymmetry models do not have the constraints on the main diagonal cells. Thus, the observations on the main diagonal cells do not contribute to the likelihood ratio chi-squared test statistics. Herein we propose a model that indicates the asymmetry for the log odds.It can utilize the information in the main diagonal cells. Also, the symmetry model is separated into some models including the proposed model.

DOI Code: 10.1285/i20705948v14n1p1

Keywords: conditional symmetry model, contingency table analysis, symmetry model

References


Agresti, A. (1983). A simple diagonals-parameter symmetry and quasi-symmetry model. Statistics and Probability Letters, 1, 313--316.

Bowker, A. H. (1948). A test for symmetry in contingency tables. Journal of the American Statistical Association, 43, 572--574.

Caussinus, H. (1965). Contribution a l'analyse statistique des tableaux de correlation. Annales de la Facult¥'{e des Sciences de l'Universit¥'{e de Toulouse, 29, 77--182.

Fujisawa, K. and Tahata, K. (2018). Asymmetry models based on logit transformations for square contingency tables with ordinal categories. Journal of the Japanese Society of Computational Statistics, 30, 55--64.

McCullagh, P. (1978). A class of parametric models for the analysis of square contingency tables with ordered categories. Biometrika, 65, 45--55.

Read, C. B. (1977). Partitioning chi-square in contingency tables: A teaching approach. Communications in Statistics-Theory and Methods, 6, 553--562.

Seiyama, K. Social Stratification and Social Mobility Research Group, Social Stratification and Mobility (SSM95B). SRDQ Office ed., SRDQ: Social Research Database on Questionnaires, 1995. (Available at http://srdq.hus.osaka-u.ac.jp, [27 June, 2019]).

Stuart, A. (1955). A test for homogeneity of the marginal distributions in a two-way classification.

Biometrika, 42, 412--416.

Tahata, K. and Tomizawa, S. (2008). Generalized marginal homogeneity model and its relation to marginal equimoments for square contingency tables with ordered categories. Advances in Data Analysis and Classification, 2, 295--311.

Tahata, K. and Tomizawa, S. (2015). Modeling of symmetry for statistical analysis of multiway contingency tables. SUGAKU EXPOSITIONS, 28, 29--47.

Tomizawa, S. (1987). Decompositions for 2-ratios-parameter symmetry model in square contingency tables with ordered categories. Biometrical Journal, 29, 45--55.


Full Text: pdf
کاغذ a4
Bookmark and Share


Creative Commons License
This work is licensed under a Creative Commons Attribuzione - Non commerciale - Non opere derivate 3.0 Italia License.