1. bookVolume 58 (2021): Issue 2 (December 2021)
Journal Details
License
Format
Journal
eISSN
2199-577X
First Published
17 Aug 2013
Publication timeframe
2 times per year
Languages
English
access type Open Access

Orthogonal decomposition of the sum-symmetry model for square contingency tables with ordinal categories: Use of the exponential sum-symmetry model

Published Online: 30 Dec 2021
Volume & Issue: Volume 58 (2021) - Issue 2 (December 2021)
Page range: 95 - 104
Journal Details
License
Format
Journal
eISSN
2199-577X
First Published
17 Aug 2013
Publication timeframe
2 times per year
Languages
English
Summary

In the existing decomposition theorem, the sum-symmetry model holds if and only if both the exponential sum-symmetry and global symmetry models hold. However, this decomposition theorem does not satisfy the asymptotic equivalence for the test statistic. To address the aforementioned gap, this study establishes a decomposition theorem in which the sum-symmetry model holds if and only if both the exponential sum-symmetry and weighted global-sum-symmetry models hold. The proposed decomposition theorem satisfies the asymptotic equivalence for the test statistic. We demonstrate the advantages of the proposed decomposition theorem by applying it to datasets comprising real data and artificial data.

Keywords

Agresti A. (1983a): A simple diagonals-parameter symmetry and quasi-symmetry model. Statistics & Probability Letters 1: 313–316.10.1016/0167-7152(83)90051-2 Search in Google Scholar

Agresti A. (1983b): Testing marginal homogeneity for ordinal categorical variables. Biometrics 39: 505–510.10.2307/2531022 Search in Google Scholar

Aitchison J. (1962): Large-sample restricted parametric tests. Journal of the Royal Statistical Society: Series B 24: 234–250. Search in Google Scholar

Bhapkar V.P. (1966): A note on the equivalence of two test criteria for hypotheses in categorical data. Journal of the American Statistical Association 61: 228–235.10.1080/01621459.1966.10502021 Search in Google Scholar

Bhapkar V.P. (1979): On tests of marginal symmetry and quasi-symmetry in two and three-dimensional contingency tables. Biometrics 33: 417–426.10.2307/2530344 Search in Google Scholar

Bishop Y.M., Fienberg S.E., Holland P.W. (2007): Discrete multivariate analysis: theory and practice. Springer Science & Business Media. Search in Google Scholar

Caussinus H. (1965): Contribution à l’Analyse Statistique des Tableaux de Corrélation. Annales de la Faculté des Sciences de l’Université de Toulouse 29: 77–183.10.5802/afst.519 Search in Google Scholar

Darroch J.N., Silvey S.D. (1963): On testing more than one hypothesis. The Annals of Mathematical Statistics 34: 555–567.10.1214/aoms/1177704168 Search in Google Scholar

Goodman L.A. (1979): Multiplicative models for square contingency tables with ordered categories. Biometrika 66: 413–418.10.1093/biomet/66.3.413 Search in Google Scholar

McCullagh P. (1978): A class of parametric models for the analysis of square contingency tables with ordered categories. Biometrika 65: 413–418.10.1093/biomet/65.2.413 Search in Google Scholar

Rao C.R. (1973): Linear statistical inference and its applications, 2nd ed. Wiley New York.10.1002/9780470316436 Search in Google Scholar

Read C.B. (1977): Partitioning chi-square in contingency tables: A teaching approach. Communications in Statistics – Theory and Methods 6: 553–562.10.1080/03610927708827513 Search in Google Scholar

Stuart A. (1953): The estimation and comparison of strengths of association in contingency tables. Biometrika 40: 105–110.10.2307/2333101 Search in Google Scholar

Stuart A. (1955): A test for homogeneity of the marginal distributions in a two-way classification. Biometrika 42: 412–416.10.1093/biomet/42.3-4.412 Search in Google Scholar

Tomizawa S., Tahata K. (2007): The analysis of symmetry and asymmetry: orthogonality of decomposition of symmetry into quasi-symmetry and marginal symmetry for multi-way tables. Journal de la société française de statistique 148: 3–36. Search in Google Scholar

Yamamoto K., Tanaka Y., Tomizawa S. (2013): Sum-symmetry model and its orthogonal decomposition for square contingency tables with ordered categories. SUT Journal of Mathematics 49: 121–128. Search in Google Scholar

Yamamoto K., Aizawa M., Tomizawa S. (2016): Decomposition of sum-symmetry model for ordinal square contingency tables. European Journal of Statistics and Probability 4: 12–19. Search in Google Scholar

Recommended articles from Trend MD

Plan your remote conference with Sciendo