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Revista Colombiana de Estadística

Print version ISSN 0120-1751

Rev.Colomb.Estad. vol.35 no.1 Bogotá Jan./June 2012

 

Measuring Degree of Departure from Extended Quasi-Symmetry for Square Contingency Tables

Medición del grado alejamiento del modelo extendido cuasi simétrico para tablas de contingencia cuadradas

KOUJI TAHATA1, KEIGO KOZAI2

1Tokyo University of Science, Faculty of Science and Technology, Department of Information Sciences, Chiba, Japan. Assistant professor. Email: kouji_tahata@is.noda.tus.ac.jp
2Tokyo University of Science, Faculty of Science and Technology, Department of Information Sciences, Chiba, Japan. Graduate student. Email: keigo14@hotmail.co.jp


Abstract

For square contingency tables with ordered categories, the present paper proposes a measure to represent the degree of departure from the extended quasi-symmetry (EQS) model. It is expressed by using the Cressie-Read power-divergence or Patil-Taillie diversity index. The present paper also defines the maximum departure from EQS which indicates the maximum departure from the uniformity of ratios of symmetric odds-ratios. The measure lies between 0 and 1, and it is useful for not only seeing the degree of departure from EQS in a table but also comparing it in several tables.

Key words: Contingency table, Kullback-Leibler information, Quasi-symmetry, Shannon entropy.


Resumen

El presente artículo propone una medida para representar el grado de alejamiento del modelo extendido cuasisimétrico (EQS, por su sigla en inglés) para tablas de contingencia con categorías ordenadas. Esta medida se expresa mediante el uso de la divergencia de potencia de Cressie-Read o el índice de diversidad Patil-Taillie. Nuestro trabajo también define el máximo alejamiento de EQS, el cual indica el alejamiento máximo de la uniformidad de razones de odds-ratios simétricos. La medida cae entre 0 y 1 y es útil no solo para determinar el grado de alejamiento de EQS en una tabla, sino también para comparar este grado de alejamiento en varias tablas.

Palabras clave: cuasi-simetría, entropía de Shannon, información de Kullback-Leibler, tablas de contingencia.


Texto completo disponible en PDF


References

1. Bishop, Y. M. M., Fienberg, S. E. & Holland, P. W. (1975), Discrete Multivariate Analysis: Theory and Practice, The MIT Press, Cambridge, Massachusetts.         [ Links ]

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

3. Caussinus, H. (1965), 'Contribution á l'analyse statistique des tableaux de corrélation', Annales de la Faculté des Sciences de l'Université de Toulouse 29, 77-182.         [ Links ]

4. Cressie, N. A. C. & Read, T. R. C. (1984), 'Multinomial goodness-of-fit tests', Journal of the Royal Statistical Society, Series B 46, 440-464.         [ Links ]

5. Hashimoto, K. (2003), Class Structure in Contemporary Japan, Trans Pacific Press, Melbourne.         [ Links ]

6. Lawal, H. B. (2004), 'Using a GLM to decompose the symmetry model in square contingency tables with ordered categories', Journal of Applied Statistics 31, 279-303.         [ Links ]

7. Patil, G. P. & Taillie, C. (1982), 'Diversity as a concept and its measurement', Journal of the American Statistical Association 77, 548-561.         [ Links ]

8. Tahata, K., Miyamoto, N. & Tomizawa, S. (2004), 'Measure of departure from quasi-symmetry and Bradley-Terry models for square contingency tables with nominal categories', Journal of the Korean Statistical Society 33, 129-147.         [ Links ]

9. Tomizawa, S. (1984), 'Three kinds of decompositions for the conditional symmetry model in a square contingency table', Journal of the Japan Statistical Society 14, 35-42.         [ Links ]

10. Tomizawa, S. (1990), 'Quasi-diagonals-parameter symmetry model for square contingency tables with ordered categories', Calcutta Statistical Association Bulletin 39, 53-61.         [ Links ]

11. Tomizawa, S. (1994), 'Two kinds of measures of departure from symmetry in square contingency tables having nominal categories', Statistica Sinica 4, 325-334.         [ Links ]

12. Tomizawa, S., Miyamoto, N. & Hatanaka, Y. (2001), 'Measure of asymmetry for square contingency tables having ordered categories', Australian and New Zealand Journal of Statistics 43, 335-349.         [ Links ]

13. Tomizawa, S., Seo, T. & Yamamoto, H. (1998), 'Power-divergence-type measure of departure from symmetry for square contingency tables that have nominal categories', Journal of Applied Statistics 25, 387-398.         [ Links ]

14. Yamaguchi, K. (1990), 'Some models for the analysis of asymmetric association in square contingency tables with ordered categories', Sociological Methodology 20, 181-212.         [ Links ]

[Recibido en marzo de 2011. Aceptado en septiembre de 2011]

Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

@ARTICLE{RCEv35n1a04,
AUTHOR = {Tahata, Kouji and Kozai, Keigo},
TITLE = {{Measuring Degree of Departure from Extended Quasi-Symmetry for Square Contingency Tables}},
JOURNAL = {Revista Colombiana de Estadística},
YEAR = {2012},
volume = {35},
number = {1},
pages = {55-65}
}

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