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
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.
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.
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References
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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}
}