A Generalized Two-Dimensional Index to Measure the Degree of Deviation from Double Symmetry in Square Contingency Tables

The double symmetry model satisfies both the symmetry and point symmetry models simultaneously. To measure the degree of deviation from the double symmetry model, a two-dimensional index that can concurrently measure the degree of deviation from symmetry and point symmetry is considered. This two-di...

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Autores principales:	Shuji Ando, Hikaru Hoshi, Aki Ishii, Sadao Tomizawa
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	confidence region measure point symmetry power divergence symmetry Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/a7e87f5d419d4a0796b97418452ca607
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id	oai:doaj.org-article:a7e87f5d419d4a0796b97418452ca607
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spelling	oai:doaj.org-article:a7e87f5d419d4a0796b97418452ca6072021-11-25T19:06:28ZA Generalized Two-Dimensional Index to Measure the Degree of Deviation from Double Symmetry in Square Contingency Tables10.3390/sym131120672073-8994https://doaj.org/article/a7e87f5d419d4a0796b97418452ca6072021-11-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2067https://doaj.org/toc/2073-8994The double symmetry model satisfies both the symmetry and point symmetry models simultaneously. To measure the degree of deviation from the double symmetry model, a two-dimensional index that can concurrently measure the degree of deviation from symmetry and point symmetry is considered. This two-dimensional index is constructed by combining two existing indexes. Although the existing indexes are constructed using power divergence, the existing two-dimensional index that can concurrently measure both symmetries is constructed using only Kullback-Leibler information, which is a special case of power divergence. Previous studies note the importance of using several indexes of divergence to compare the degrees of deviation from a model for several square contingency tables. This study, therefore, proposes a two-dimensional index based on power divergence in order to measure deviation from double symmetry for square contingency tables. Numerical examples show the utility of the proposed two-dimensional index using two datasets.Shuji AndoHikaru HoshiAki IshiiSadao TomizawaMDPI AGarticleconfidence regionmeasurepoint symmetrypower divergencesymmetryMathematicsQA1-939ENSymmetry, Vol 13, Iss 2067, p 2067 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	confidence region measure point symmetry power divergence symmetry Mathematics QA1-939
spellingShingle	confidence region measure point symmetry power divergence symmetry Mathematics QA1-939 Shuji Ando Hikaru Hoshi Aki Ishii Sadao Tomizawa A Generalized Two-Dimensional Index to Measure the Degree of Deviation from Double Symmetry in Square Contingency Tables
description	The double symmetry model satisfies both the symmetry and point symmetry models simultaneously. To measure the degree of deviation from the double symmetry model, a two-dimensional index that can concurrently measure the degree of deviation from symmetry and point symmetry is considered. This two-dimensional index is constructed by combining two existing indexes. Although the existing indexes are constructed using power divergence, the existing two-dimensional index that can concurrently measure both symmetries is constructed using only Kullback-Leibler information, which is a special case of power divergence. Previous studies note the importance of using several indexes of divergence to compare the degrees of deviation from a model for several square contingency tables. This study, therefore, proposes a two-dimensional index based on power divergence in order to measure deviation from double symmetry for square contingency tables. Numerical examples show the utility of the proposed two-dimensional index using two datasets.
format	article
author	Shuji Ando Hikaru Hoshi Aki Ishii Sadao Tomizawa
author_facet	Shuji Ando Hikaru Hoshi Aki Ishii Sadao Tomizawa
author_sort	Shuji Ando
title	A Generalized Two-Dimensional Index to Measure the Degree of Deviation from Double Symmetry in Square Contingency Tables
title_short	A Generalized Two-Dimensional Index to Measure the Degree of Deviation from Double Symmetry in Square Contingency Tables
title_full	A Generalized Two-Dimensional Index to Measure the Degree of Deviation from Double Symmetry in Square Contingency Tables
title_fullStr	A Generalized Two-Dimensional Index to Measure the Degree of Deviation from Double Symmetry in Square Contingency Tables
title_full_unstemmed	A Generalized Two-Dimensional Index to Measure the Degree of Deviation from Double Symmetry in Square Contingency Tables
title_sort	generalized two-dimensional index to measure the degree of deviation from double symmetry in square contingency tables
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/a7e87f5d419d4a0796b97418452ca607
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A Generalized Two-Dimensional Index to Measure the Degree of Deviation from Double Symmetry in Square Contingency Tables

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