1. bookVolume 58 (2021): Issue 1 (June 2021)
Journal Details
License
Format
Journal
First Published
17 Aug 2013
Publication timeframe
2 times per year
Languages
English
access type Open Access

Asymmetry models based on ordered score and separations of symmetry model for square contingency tables

Published Online: 24 Jun 2021
Page range: 27 - 39
Journal Details
License
Format
Journal
First Published
17 Aug 2013
Publication timeframe
2 times per year
Languages
English
Summary

This study proposes two original asymmetry models based on ordered scores for square contingency tables with the same row and column ordinal classifications. The proposed models can be applied to cases in which the scores of all categories are known or unknown. In the proposed models, the log odds for an observation falling in the (i, j)th cell instead of the (j, i)th cell are inversely proportional to the difference of the ordered scores corresponding to categories i and j. The asymmetry parameter of the proposed model can be useful for inferring whether the row variable is stochastically greater than the column variable or vice versa. The proposed models constantly hold when the symmetry model holds, but the converse is not necessarily true. This study also examines what is necessary for a model, in addition to the proposed models, to satisfy the symmetry model, and gives separations of the symmetry model using the proposed and marginal mean equality models. We apply real data to show the utility of the proposed models. The proposed models provide a better fit than that of the existing models.

Keywords

Agresti A. (1983): A simple diagonals-parameter symmetry and quasi-symmetry model. Statistics and Probability Letters 1: 313–316. Search in Google Scholar

Agresti A. (2002): Categorical Data Analysis, 2nd edition. Wiley, New York. Search in Google Scholar

Bagheban A.A., Zayeri,F. (2010): A generalization of the uniform association model for assessing rater agreement in ordinal scales. Journal of Applied Statistics 37: 1265–1273. Search in Google Scholar

Bishop Y.M.M., Fienberg S.E., Holland P.W. (1975): Discrete multivariate analysis: theory and practice. The MIT Press, Cambridge: Massachusetts. Search in Google Scholar

Bowker A.H. (1948): A test for symmetry in contingency tables. Journal of the American Statistical Association 43: 572–574. Search in Google Scholar

Bross I.D.J. (1958): How to use ridit analysis. Biometrics 14: 18–38. Search in Google Scholar

Graubard B.I., Korn E.L. (1987): Choice of column scores for testing independence in ordered 2 × K contingency tables. Biometrics 43: 471–476. Search in Google Scholar

Iki K., Tahata K., Tomizawa S. (2009): Ridit score type quasi-symmetry and decomposition of symmetry for square contingency tables with ordered categories. Austrian Journal of Statistics 38: 183–192. Search in Google Scholar

Senn S. (2007): Drawbacks to noninteger scoring for ordered categorical data. Biometrics 63: 296–299. Search in Google Scholar

Tomizawa S. (1984): Three kinds of decompositions for the conditional symmetry model in a square contingency table. Journal of the Japan Statistical Society 14: 35–42. Search in Google Scholar

Tomizawa S. (1990): Another linear diagonals-parameter symmetry model for square contingency tables with ordered categories. South African Statistical Journal 24: 117–125. Search in Google Scholar

Tomizawa S., Miyamoto N., Iwamoto M. (2006): Linear column-parameter symmetry model for square contingency tables: Application to decayed teeth data. Biometrical Letters 43: 91–98. Search in Google Scholar

Yamamoto H., Iwashita T., Tomizawa S. (2007): Decomposition of symmetry into ordinal quasi-symmetry and marginal equimoment for multi-way tables. Austrian Journal of Statistics 36: 291–306. Search in Google Scholar

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