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A Measure of Departure from Marginal Homogeneity using Continuation Odds for Square Contingency Tables with Ordered Categories

Author

Listed:
  • Shuji Ando

    (Tokyo University of Science)

  • Kei Fujimoto

    (Tokyo University of Science)

  • Sadao Tomizawa

    (Meisei University)

Abstract

For the analysis of square contingency tables with ordinal classifications, the marginal homogeneity (MH) model is the one of important models. Some measures for analyzing the degree of departure from the MH model have been proposed. This study proposes a new measure using the continuation odds. Continuation odds may be considered as discrete time hazard. The proposed measure is expressed in the form of Cressie-Read’s power-divergence (including the Kullback-Leibler divergence) or Patil and Taillie’s diversity index (including Shannon entropy). This study derives a plug-in estimator of the proposed measure and an approximate confidence interval for the proposed measure. Through numerical examples, we evaluate the performances of them. Additionally. the usefulness of the proposed measure is demonstrated by applying it to real data that the row and column variables are the discrete survival time variables.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sankhb:v:86:y:2024:i:2:d:10.1007_s13571-024-00343-x
    DOI: 10.1007/s13571-024-00343-x
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    References listed on IDEAS

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    1. 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.
    2. 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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