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Measure of deviancy from marginal mean equality based on cumulative marginal probabilities in square contingency tables

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  • Shuji Ando

    (Tokyo University of Science)

Abstract

This study proposes a measure that can concurrently evaluate the degree and direction of deviancy from the marginal mean equality (ME) model in square contingency tables with ordered categories. The proposed measure is constructed as the function of the row and column cumulative marginal probabilities. When the ME model does not fit data, we are interested in measuring the degree of deviancy from the ME model, because the model having weaker restrictions than the ME model is only the saturated model. This existing measure, which represents the degree of deviancy from the ME model, does not depend on the probabilities that observations will fall in the main diagonal cells of the table. For the data in which observations are concentrated in the main diagonal cells, the existing measure may overestimate the degree of deviancy from the ME model. The proposed measure can address this issue. This study derives an estimator and an approximate confidence interval for the proposed measure using the delta method. The proposed measure would be utility for comparing degrees of deviancy from the ME model in two datasets. The proposed measure is evaluated the usefulness with the application to real data of clinical trials.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metrik:v:87:y:2024:i:8:d:10.1007_s00184-023-00945-x
    DOI: 10.1007/s00184-023-00945-x
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    References listed on IDEAS

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    1. 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.
    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. 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.
    4. Shuji Ando, 2022. "Directional Measure for Analyzing the Degree of Deviance from Generalized Marginal Mean Equality Model in Square Contingency Tables," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 708-721, November.
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