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Directional Measure for Analyzing the Degree of Deviance from Generalized Marginal Mean Equality Model in Square Contingency Tables

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Abstract

When the concerned model does not fit the data, we may be interested in measuring the degree of deviance from the concerned model. This study proposes a measure for simultaneously analyzing the degree and direction of deviance from the generalized marginal mean equality model based on the ordered scores for each category. Previous study proposed a measure for analyzing both the degree and direction of deviance from the marginal mean equality model based on only the equally spaced scores. When it is appropriate to assign the ordered scores to categories, we are interested in analyzing whether the row marginal mean based on the known ordered scores is equal to the column marginal mean. It is necessary to analyze both the degree and direction of deviance from the generalized marginal mean equality model because there are two kinds of direction. We derive a confidence interval for the proposed measure using the delta method. The proposed measure is also helpful for comparing degrees of deviance from the generalized marginal mean equality model for several datasets. We show the utility of the proposed measure by applied it to real data.

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Acknowledgements

The author would like to thank the anonymous reviewers and the editors for careful reading and comments to improve this paper.

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The authors have solely funded the research by themselves.

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  1. Department of Information Sciences, Tokyo University of Science, 2641 Yamazaki, Noda City, 2788510, Chiba, Japan

    Shuji Ando

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  1. Shuji Ando
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Correspondence to Shuji Ando.

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Ando, S. Directional Measure for Analyzing the Degree of Deviance from Generalized Marginal Mean Equality Model in Square Contingency Tables. Sankhya B 84, 708–721 (2022). https://doi.org/10.1007/s13571-022-00283-4

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  • DOI: https://doi.org/10.1007/s13571-022-00283-4

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