References

GENERALIZED DIAGONAL EXPONENT SYMMETRY MODEL AND ITS ORTHOGONAL DECOMPOSITION FOR SQUARE CONTINGENCY TABLES WITH ORDERED CATEGORIES


[1] V. P. Bhapkar and J. N. Darroch, Marginal symmetry and quasi symmetry of general order, Journal of Multivariate Analysis 34 (1990), 173-184.

[2] Y. M. M. Bishop, S. E. Fienberg and P. W. Holland, Discrete Multivariate Analysis: Theory and Practice, Cambridge: The MIT Press, 1975.

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

[4] H. Caussinus, Contribution à l’analyse statistique des tableaux de correlation, Annales de la Faculté des Sciences de l’Université de Toulouse 29 (1965), 77-182.

[5] J. N. Darroch and S. D. Silvey, On testing more than one hypothesis, Annals of Mathematical Statistics 34 (1963), 555-567.

[6] J. N. Darroch and D. Ratcliff, Generalized iterative scaling for log-linear models, Annals of Mathematical Statistics 43 (1972), 1470-1480.

[7] L. A. Goodman, Association models and the bivariate normal for contingency tables with ordered categories, Biometrika 68 (1981), 347-355.

[8] M. Haber, Maximum likelihood methods for linear and log-linear models in categorical data, Computational Statistics and Data Analysis 3 (1985), 1-10.

[9] S. J. Haberman, The Analysis of Frequency Data, The University of Chicago Press, 1974.

[10] K. Iki, A. Shibuya and S. Tomizawa, Extended diagonal exponent symmetry model and its orthogonal decomposition in square contingency tables with ordered categories, Open Journal of Statistics 5 (2015), 262-272.

[11] K. Iki, K. Yamamoto and S. Tomizawa, Quasi-diagonal exponent symmetry model for square contingency tables with ordered categories, Statistics and Probability Letters 92 (2014), 33-38.

[12] S. Kullback, Marginal homogeneity of multidimensional contingency tables, Annals of Mathematical Statistics 42 (1971), 594-606.

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

[14] A. Stuart, A test for homogeneity of the marginal distributions in a two-way classification, Biometrika 42 (1955), 412-416.

[15] K. Tahata and S. Tomizawa, Symmetry and asymmetry models and decompositions of models for contingency tables, SUT Journal of Mathematics 50 (2014), 131-165.

[16] S. Tomizawa, A model of symmetry with exponents along every subdiagonal and its application to data on unaided vision of pupils at Japanese elementary schools, Journal of Applied Statistics 19 (1992), 509-512.