Ridit Score Type Quasi-Symmetry and Decomposition of Symmetry for Square Contingency Tables with Ordered Categories

Authors

  • Kiyotaka Iki Department of Information Sciences, Tokyo University of Science, Japan
  • Kouji Tahata Department of Information Sciences, Tokyo University of Science, Japan
  • Sadao Tomizawa Department of Information Sciences, Tokyo University of Science, Japan

DOI:

https://doi.org/10.17713/ajs.v38i3.271

Abstract

For square contingency tables with the same row and column ordinal classifications, this paper proposes the quasi-symmetry model based on the marginal ridits. The model indicates that the log-odds that an observation will fall in the (i; j) cell instead of in the (j; i) cell, i < j, is proportional to the difference between the average ridit score of row and column marginal distributions for category j and that for category i. This paper also gives a
theorem such that the symmetry model holds if and only if both the proposed model and the marginal mean equality model hold. Examples are given.

References

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Published

2016-04-03

How to Cite

Iki, K., Tahata, K., & Tomizawa, S. (2016). Ridit Score Type Quasi-Symmetry and Decomposition of Symmetry for Square Contingency Tables with Ordered Categories. Austrian Journal of Statistics, 38(3), 183–192. https://doi.org/10.17713/ajs.v38i3.271

Issue

Section

Articles