A class of ordinal quasi-symmetry models for square contingency tables. (English) Zbl 1116.62067

Summary: M. Kateri and S. Papaioannou [Asymmetry models for contingency tables. J. Am. Stat. Assoc. 92, No. 439, 1124–1131 (1997; Zbl 0889.62050)] proved that, under certain conditions, quasi-symmetry is the closest model to symmetry. A simpler ordinal quasi-symmetry model is the closest to symmetry, under a weaker condition of unequal marginal mean scores. It is a special case of a class of ordinal models based on f-divergence.


62H17 Contingency tables


Zbl 0889.62050
Full Text: DOI


[1] Agresti, A., A simple diagonals-parameters symmetry and quasi-symmetry model, Statist. probab. lett., 1, 313-316, (1983) · Zbl 0528.62050
[2] Agresti, A., Computing conditional maximum likelihood estimates for generalized rasch models using simple loglinear models with diagonals parameters, Scand. J. statist., 20, 63-71, (1993) · Zbl 0770.62095
[3] Agresti, A., Categorical data analysis, (2002), Wiley New York · Zbl 1018.62002
[4] CsiszĂ r, I., Eine informationstheoretische ungleichung und ihre anwendungen auf den beweis der ergozitat von markoffschen ketten, A mayar tudomanyos academia mathematikai kutato intezelent kozlemezyri, 8, 85-108, (1963) · Zbl 0124.08703
[5] Gilula, Z.; Krieger, A.M.; Ritov, Y., Ordinal association in contingency tables: some interpretive aspects, J. amer. statist. assoc., 83, 540-545, (1988) · Zbl 0644.62065
[6] Goodman, L.A., Multiplicative models for square contingency tables with ordered categories, Biometrika, 66, 413-418, (1979)
[7] Goodman, L.A., The analysis of cross-classified data having ordered and/or unordered categories: association models, correlation models, and asymmetry models for contingency tables with or without missing entries, Ann. statist., 13, 10-69, (1985) · Zbl 0613.62070
[8] Kateri, M.; Papaioannou, T., Asymmetry models for contingency tables, J. amer. statist. assoc., 92, 1124-1131, (1997) · Zbl 0889.62050
[9] Read, T.R.C.; Cressie, N.A.C., Goodness-of-fit statistics for discrete multivariate data, (1988), Springer New York
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.