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Marginal Continuation odds Ratio Model and Decomposition of Marginal Homogeneity Model for Multi-way Contingency Tables

Author

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  • Satoru Shinoda

    (Taisho Pharmaceutical Co., Ltd.
    Tokyo University of Science)

  • Kouji Tahata

    (Tokyo University of Science)

  • Kouji Yamamoto

    (Yokohama City University)

  • Sadao Tomizawa

    (Tokyo University of Science)

Abstract

For square contingency tables with ordered categories, the marginal homogeneity model is represented by various expressions, and some extensions of the marginal homogeneity model were proposed. Herein we consider the marginal continuation-ratio to examine a new expression of the marginal homogeneity model. We also propose an extension of the marginal homogeneity model using the ratio of marginal continuation-ratios; namely, the marginal continuation odds ratio. The proposed model can be interpreted in various ways. Additionally, we propose a generalization of it, and decompose the marginal homogeneity model using the generalized model. Furthermore, we extend the models and decompositions into multi-way contingency tables.

Suggested Citation

  • Satoru Shinoda & Kouji Tahata & Kouji Yamamoto & Sadao Tomizawa, 2021. "Marginal Continuation odds Ratio Model and Decomposition of Marginal Homogeneity Model for Multi-way Contingency Tables," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 304-324, November.
    • Handle: RePEc:spr:sankhb:v:83:y:2021:i:2:d:10.1007_s13571-020-00228-9
    DOI: 10.1007/s13571-020-00228-9
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    References listed on IDEAS

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    1. Bhapkar, V. P. & Darroch, J. N., 1990. "Marginal symmetry and quasi symmetry of general order," Journal of Multivariate Analysis, Elsevier, vol. 34(2), pages 173-184, August.
    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. Tutz, Gerhard, 1991. "Sequential models in categorical regression," Computational Statistics & Data Analysis, Elsevier, vol. 11(3), pages 275-295, May.
    4. Nobuko Miyamoto & Kouji Tahata & Hirokazu Ebie & Sadao Tomizawa, 2006. "Marginal inhomogeneity models for square contingency tables with nominal categories," Journal of Applied Statistics, Taylor & Francis Journals, vol. 33(2), pages 203-215.
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    Cited by:

    1. Kiyotaka Iki & Sadao Tomizawa, 2022. "Parsimonious Bivariate T-distribution Type Symmetry Models for Square Contingency Tables," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 11(5), pages 1-44, November.
    2. 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.
    3. Shuji Ando & Kei Fujimoto & Sadao Tomizawa, 2024. "A Measure of Departure from Marginal Homogeneity using Continuation Odds for Square Contingency Tables with Ordered Categories," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 86(2), pages 311-332, November.

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