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A Bivariate Index for Visually Measuring Marginal Inhomogeneity in Square Tables

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  • Shuji Ando

Abstract

For square tables, the marginal homogeneity model which has a structure that the row marginal distribution is equal to the column marginal distribution was proposed. Thereafter, various extended models of marginal homogeneity have been proposed, these models can be classified into two types marginal inhomogeneity. On the other hand, various indexes which measure the degree of deviation from marginal homogeneity have been proposed. However these indexes cannot concurrently define degrees of deviation from marginal homogeneity with respect to two types marginal inhomogeneity. This paper proposes a bivariate index that can concurrently define degrees of deviation from those. The proposed bivariate index would also be utility for visually comparing degrees of deviation from marginal homogeneity in several tables using confidence regions.

Suggested Citation

  • Shuji Ando, 2019. "A Bivariate Index for Visually Measuring Marginal Inhomogeneity in Square Tables," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 8(5), pages 58-65, September.
    • Handle: RePEc:ibn:ijspjl:v:8:y:2019:i:5:p:58
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    References listed on IDEAS

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    1. Shuji Ando & Kouji Tahata & Sadao Tomizawa, 2019. "A bivariate index vector for measuring departure from double symmetry in square contingency tables," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(2), pages 519-529, June.
    2. Kouji Tahata & Sadao Tomizawa, 2008. "Generalized marginal homogeneity model and its relation to marginal equimoments for square contingency tables with ordered categories," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 2(3), pages 295-311, December.
    3. Kiyotaka Iki & Kouji Tahata & Sadao Tomizawa, 2012. "Measure of departure from marginal homogeneity using marginal odds for multi-way tables with ordered categories," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(2), pages 279-295, April.
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    Cited by:

    1. Shuji Ando, 2024. "Measure of deviancy from marginal mean equality based on cumulative marginal probabilities in square contingency tables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 87(8), pages 1037-1048, November.

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    More about this item

    Keywords

    confidence region; power divergence; marginal homogeneity; ordered category; visualization;
    All these keywords.

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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