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Separation of symmetry for square tables with ordinal categorical data. (English) Zbl 1460.62089

Summary: The present paper considers a model that indicates the structure of asymmetry for cell probabilities for square contingency tables with ordered categories. The model is the closest to the symmetry model in terms of the \(f\)-divergence under certain conditions and incorporates existing asymmetry models in special cases. A theorem that the symmetry model can be separated into two models which have weaker restrictions than the symmetry model is given. Also, a property between test statistics for goodness of fit is discussed.

MSC:

62H17 Contingency tables
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[1] Agresti, A., A simple diagonals-parameter symmetry and quasi-symmetry model, Statistics and Probability Letters, 1, 313-316 (1983) · Zbl 0528.62050
[2] Agresti, A., Analysis of ordinal categorical data (1984), New York: Wiley, New York · Zbl 0647.62052
[3] Aitchison, J., Large-sample restricted parametric tests, Journal of the Royal Statistical Society Series B, 24, 234-250 (1962) · Zbl 0113.13604
[4] Bhapkar, VP, A note on the equivalence of two test criteria for hypotheses in categorical data, Journal of the American Statistical Association, 61, 228-235 (1966) · Zbl 0147.18402
[5] Bishop, YMM; Fienberg, SE; Holland, PW, Discrete multivariate analysis: Theory and practice (1975), Cambridge: The MIT Press, Cambridge · Zbl 0332.62039
[6] Bowker, AH, A test for symmetry in contingency tables, Journal of the American Statistical Association, 43, 572-574 (1948) · Zbl 0032.17500
[7] Caussinus, H., Contribution à l’analyse statistique des tableaux de corrélation, Annales de la Faculté des Sciences de l’Université de Toulouse, Série, 4, 29, 77-182 (1965) · Zbl 0168.39904
[8] Csiszár, I.; Shields, PC, Information theory and statistics: A tutorial (2004), Hanover: Now Publishers, Hanover
[9] Darroch, JN; Silvey, SD, On testing more than one hypothesis, The Annals of Mathematical Statistics, 34, 555-567 (1963) · Zbl 0115.14003
[10] Gilula, Z.; Krieger, AM; Ritov, Y., Ordinal association in contingency tables: Some interpretive aspects, Journal of the American Statistical Association, 83, 540-545 (1988) · Zbl 0644.62065
[11] Good, IJ, Maximum entropy for hypothesis formulation, especially for multidimensional contingency tables, The Annals of Mathematical Statistics, 34, 911-934 (1963) · Zbl 0143.40705
[12] Ireland, CT; Ku, HH; Kullback, S., Symmetry and marginal homogeneity of an \(r \times r\) contingency table, Journal of the American Statistical Association, 64, 1323-1341 (1969)
[13] Kateri, M., Contingency table analysis. Methods and implementation using R (2014), Switzerland: Birkhäuser Basel, Switzerland · Zbl 1291.62012
[14] Kateri, M.; Agresti, A., A class of ordinal quasi-symmetry models for square contingency tables, Statistics and Probability Letters, 77, 598-603 (2007) · Zbl 1116.62067
[15] Kateri, M.; Papaioannou, T., Asymmetry models for contingency tables, Journal of the American Statistical Association, 92, 1124-1131 (1997) · Zbl 0889.62050
[16] Rao, CR, Linear statistical inference and its applications (1973), New York: Wiley, New York · Zbl 0256.62002
[17] Read, TRC; Cressie, NAC, Goodness-of-fit statistics for discrete multivariate data (1988), New York: Springer, New York
[18] Saigusa, Y.; Tahata, K.; Tomizawa, S., Orthogonal decomposition of symmetry model using the ordinal quasi-symmetry model based on \(f\)-divergence for square contingency tables, Statistics and Probability Letters, 101, 33-37 (2015) · Zbl 1328.62362
[19] Stuart, A., A test for homogeneity of the marginal distributions in a two-way classification, Biometrika, 42, 412-416 (1955) · Zbl 0066.12502
[20] Tahata, K., On asymmetry models and decompositions of symmetry for square contingency tables with ordered categories, Proceedings of the 32nd International Workshop on Statistical Modelling, 2, 231-234 (2017)
[21] Tahata, K.; Tomizawa, S., 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 (2008) · Zbl 1284.62337
[22] Tahata, K.; Tomizawa, S., Generalized linear asymmetry model and decomposition of symmetry for multiway contingency tables, Biometrics and Biostatistics, 2, 1-6 (2011)
[23] Tan, TK, Doubly classified model with R (2017), Singapore: Springer, Singapore · Zbl 1383.62007
[24] Tomizawa, S., An extended linear diagonals-parameter symmetry model for square contingency tables with ordered categories, Metron, 49, 401-409 (1991)
[25] Tomizawa, S.; Tahata, K., 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 (2007) · Zbl 1441.62153
[26] Yamamoto, H.; Iwashita, T.; Tomizawa, S., Decomposition of symmetry into ordinal quasi-symmetry and marginal equimoment for multi-way tables, Austrian Journal of Statistics, 36, 291-306 (2007)
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