×

Marginal symmetry and quasi symmetry of general order. (English) Zbl 0735.62057

Bei \(s\) Variablen \(R_ k\), die \(r\) Werte annehmen, sei \(\pi({\mathbf i})=P({\mathbf R}={\mathbf i})\), wobei \({\mathbf R}=(R_ 1,\dots,R_ s)\) und \(i=(i_ 1,\dots,i_ s)\) ist. In der \(r^ s\) Kontingenztafel \(\pi=[\pi({\mathbf i}), i_ \sigma=i,\dots,r; \sigma=1,\dots,s]\) bedeutet totale Symmetrie, daß \(\pi\) unverändert ist, wenn die Komponenten permutiert werden, marginale Symmetrie der Ordnung k bedeutet totale Symmetrie aller Untervektoren der Ordnung \(k\). Quasisymmetrie ist definiert auf log-linearen Wechselwirkungen von \(\pi\).
Zusätzlich zum Hauptresultat, daß marginale und Quasisymmetrie zusammen gleichwertig mit totaler Symmetrie sind, wird bewiesen, daß sie parametrisch komplementär sind.
Reviewer: P.Nüsch

MSC:

62H17 Contingency tables
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Bhapkar, V. P., On Hypotheses and Test of Marginal Symmetry and Quasi-Symmetry in Multidimensional Contingency Tables (1978), University of Kentucky, Department of Statistics Technical Report No. 131
[2] Bhapkar, V. P., On tests of marginal symmetry and quasi-symmetry in two and three-dimensional contingency tables, Biometrics, 35, 417-426 (1979) · Zbl 0419.62045
[3] Bhapkar, V. P., On tests of symmetry when higher order interactions are absent, J. Indian Statist. Assoc., 17, 17-26 (1979)
[4] Bishop, Y. P.; Fienberg, S. E.; Holland, P. W., (Discrete Multivariate Analysis (1975), The M.I.T. Press: The M.I.T. Press Cambridge, Massachusetts)
[5] Darroch, J. N., The Mantel-Haenszel test and tests of marginal symmetry; Fixed effects and mixed models for a categorical response, Internat. Statist. Rev., 49, 285-307 (1981) · Zbl 0484.62067
[6] Darroch, J. N.; McCloud, P. I., Category distinguishability and observer agreement, Austral. J. Statist., 28, 371-388 (1986) · Zbl 0609.62140
[7] Darroch, J. N.; Speed, T. P., Additive and multiplicative models and interactions, Ann. Statist., 11, 724-738 (1983) · Zbl 0556.62032
[8] McCloud, P. I., Unpublished Ph.D. thesis (1987)
[9] McCullagh, P., Some applications of quasisymmetry, Biometrika, 69, 303-308 (1982) · Zbl 0497.62051
[10] Barndorff-Nielsen, (Information and Exponential Families in Statistical Theory (1978), Wiley: Wiley New York) · Zbl 0387.62011
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.