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Marginal inhomogeneity models for square contingency tables with nominal categories

Author

Listed:
  • Nobuko Miyamoto
  • Kouji Tahata
  • Hirokazu Ebie
  • Sadao Tomizawa

Abstract

For the analysis of square contingency tables with nominal categories, this paper proposes two kinds of models that indicate the structure of marginal inhomogeneity. One model states that the absolute values of log odds of the row marginal probability to the corresponding column marginal probability for each category i are constant for every i. The other model states that, on the condition that an observation falls in one of the off-diagonal cells in the square table, the absolute values of log odds of the conditional row marginal probability to the corresponding conditional column marginal probability for each category i are constant for every i. These models are used when the marginal homogeneity model does not hold, and the values of parameters in the models are useful for seeing the degree of departure from marginal homogeneity for the data on a nominal scale. Examples are given.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:japsta:v:33:y:2006:i:2:p:203-215
    DOI: 10.1080/02664760500251576
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    Citations

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    Cited by:

    1. Kouji Tahata, 2012. "Quasi-asymmetry model for square tables with nominal categories," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(4), pages 723-729, August.
    2. Kouji Tahata & Takuya Yoshimoto, 2015. "Marginal asymmetry model for square contingency tables with ordered categories," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(2), pages 371-379, February.
    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.

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