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

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Open Access
|Dec 2021

References

  1. 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
  2. Agresti A. (1983b): Testing marginal homogeneity for ordinal categorical variables. Biometrics 39: 505–510.10.2307/2531022
  3. Aitchison J. (1962): Large-sample restricted parametric tests. Journal of the Royal Statistical Society: Series B 24: 234–250.10.1111/j.2517-6161.1962.tb00456.x
  4. 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
  5. 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
  6. Bishop Y.M., Fienberg S.E., Holland P.W. (2007): Discrete multivariate analysis: theory and practice. Springer Science & Business Media.
  7. 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
  8. 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
  9. Goodman L.A. (1979): Multiplicative models for square contingency tables with ordered categories. Biometrika 66: 413–418.10.1093/biomet/66.3.413
  10. 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
  11. Rao C.R. (1973): Linear statistical inference and its applications, 2nd ed. Wiley New York.10.1002/9780470316436
  12. 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
  13. Stuart A. (1953): The estimation and comparison of strengths of association in contingency tables. Biometrika 40: 105–110.10.2307/2333101
  14. 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
  15. 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.
  16. 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: 121–128.10.55937/sut/1393504838
  17. 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.
DOI: https://doi.org/10.2478/bile-2021-0007 | Journal eISSN: 2199-577X | Journal ISSN: 1896-3811
Language: English
Page range: 95 - 104
Published on: Dec 30, 2021
Published by: Polish Biometric Society
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 2021 Shuji Ando, published by Polish Biometric Society
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.