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 art{i}culo propone una medida para representar el grado de alejamiento del modelo extendido cuasisim{e}trico (EQS, por su sigla en inglés) para tablas de contingencia con categor{i}as ordenadas. Esta medida se expresa mediante el uso de la divergencia de potencia de Cressie-Read o el {i}ndice de diversidad Patil-Taillie. Nuestro trabajo tambi{e}n define el m{a}ximo alejamiento de EQS, el cual indica el alejamiento m{a}ximo de la uniformidad de razones de odds-ratios simétricos. La medida cae entre 0 y 1 y es {u}til no solo para determinar el grado de alejamiento de EQS en una tabla, sino tambi{e}n 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}
}