Two-Dimensional Index of Departure from the Symmetry Model for Square Contingency Tables with Nominal Categories

In the analysis of two-way contingency tables, the degree of departure from independence is measured using measures of association between row and column variables (e.g., Yule’s coefficients of association and of colligation, Cramér’s coefficient, and Goodman and Kruskal’s coefficient). On the other...

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Autores principales:	Tomotaka Momozaki, Tomoyuki Nakagawa, Aki Ishii, Yusuke Saigusa, Sadao Tomizawa
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	asymmetry comparison geometric mean log odds measure of association Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/e7191fe9aed142cf8f1ae88dcc1e129b
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spelling	oai:doaj.org-article:e7191fe9aed142cf8f1ae88dcc1e129b2021-11-25T19:06:11ZTwo-Dimensional Index of Departure from the Symmetry Model for Square Contingency Tables with Nominal Categories10.3390/sym131120312073-8994https://doaj.org/article/e7191fe9aed142cf8f1ae88dcc1e129b2021-10-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2031https://doaj.org/toc/2073-8994In the analysis of two-way contingency tables, the degree of departure from independence is measured using measures of association between row and column variables (e.g., Yule’s coefficients of association and of colligation, Cramér’s coefficient, and Goodman and Kruskal’s coefficient). On the other hand, in the analysis of square contingency tables with the same row and column classifications, we are interested in measuring the degree of departure from symmetry rather than independence. Over past years, many studies have proposed various types of indexes based on their power divergence (or diversity index) to represent the degree of departure from symmetry. This study proposes a two-dimensional index to measure the degree of departure from symmetry in terms of the log odds of each symmetric cell with respect to the main diagonal of the table. By measuring the degree of departure from symmetry in terms of the log odds of each symmetric cell, the analysis results are easier to interpret than existing indexes. Numerical experiments show the utility of the proposed two-dimensional index. We show the usefulness of the proposed two-dimensional index by using real data.Tomotaka MomozakiTomoyuki NakagawaAki IshiiYusuke SaigusaSadao TomizawaMDPI AGarticleasymmetrycomparisongeometric meanlog oddsmeasure of associationMathematicsQA1-939ENSymmetry, Vol 13, Iss 2031, p 2031 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	asymmetry comparison geometric mean log odds measure of association Mathematics QA1-939
spellingShingle	asymmetry comparison geometric mean log odds measure of association Mathematics QA1-939 Tomotaka Momozaki Tomoyuki Nakagawa Aki Ishii Yusuke Saigusa Sadao Tomizawa Two-Dimensional Index of Departure from the Symmetry Model for Square Contingency Tables with Nominal Categories
description	In the analysis of two-way contingency tables, the degree of departure from independence is measured using measures of association between row and column variables (e.g., Yule’s coefficients of association and of colligation, Cramér’s coefficient, and Goodman and Kruskal’s coefficient). On the other hand, in the analysis of square contingency tables with the same row and column classifications, we are interested in measuring the degree of departure from symmetry rather than independence. Over past years, many studies have proposed various types of indexes based on their power divergence (or diversity index) to represent the degree of departure from symmetry. This study proposes a two-dimensional index to measure the degree of departure from symmetry in terms of the log odds of each symmetric cell with respect to the main diagonal of the table. By measuring the degree of departure from symmetry in terms of the log odds of each symmetric cell, the analysis results are easier to interpret than existing indexes. Numerical experiments show the utility of the proposed two-dimensional index. We show the usefulness of the proposed two-dimensional index by using real data.
format	article
author	Tomotaka Momozaki Tomoyuki Nakagawa Aki Ishii Yusuke Saigusa Sadao Tomizawa
author_facet	Tomotaka Momozaki Tomoyuki Nakagawa Aki Ishii Yusuke Saigusa Sadao Tomizawa
author_sort	Tomotaka Momozaki
title	Two-Dimensional Index of Departure from the Symmetry Model for Square Contingency Tables with Nominal Categories
title_short	Two-Dimensional Index of Departure from the Symmetry Model for Square Contingency Tables with Nominal Categories
title_full	Two-Dimensional Index of Departure from the Symmetry Model for Square Contingency Tables with Nominal Categories
title_fullStr	Two-Dimensional Index of Departure from the Symmetry Model for Square Contingency Tables with Nominal Categories
title_full_unstemmed	Two-Dimensional Index of Departure from the Symmetry Model for Square Contingency Tables with Nominal Categories
title_sort	two-dimensional index of departure from the symmetry model for square contingency tables with nominal categories
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/e7191fe9aed142cf8f1ae88dcc1e129b
work_keys_str_mv	AT tomotakamomozaki twodimensionalindexofdeparturefromthesymmetrymodelforsquarecontingencytableswithnominalcategories AT tomoyukinakagawa twodimensionalindexofdeparturefromthesymmetrymodelforsquarecontingencytableswithnominalcategories AT akiishii twodimensionalindexofdeparturefromthesymmetrymodelforsquarecontingencytableswithnominalcategories AT yusukesaigusa twodimensionalindexofdeparturefromthesymmetrymodelforsquarecontingencytableswithnominalcategories AT sadaotomizawa twodimensionalindexofdeparturefromthesymmetrymodelforsquarecontingencytableswithnominalcategories
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Two-Dimensional Index of Departure from the Symmetry Model for Square Contingency Tables with Nominal Categories

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