Some Symmetry Models for the Analysis of Collapsed Square Contingency Tables with Ordered Categories

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  • Kouji Yamamoto
    Department of Medical Innovation, Osaka University Hospital, Japan
  • Kouji Tahata
    Department of Information Sciences, Faculty of Science and Technology, Tokyo University of Science, Japan
  • Sadao Tomizawa
    Department of Information Sciences, Faculty of Science and Technology, Tokyo University of Science, Japan

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<jats:p> Abtsrcat </jats:p><jats:p> For the square contingency tables with ordered categories, there may be some cases that one wants to analyze them by considering collapsed tables with some adjacent categories combined in the original table. This paper considers some symmetry models for collapsed square contingency tables and proposes two new models which have the structure of global symmetry and that of quasi-symmetry for the collapsed square tables. Also this paper gives two kinds of decompositions of the symmetry model for collapsed square tables. The new models and decompositions are useful for analyzing the collapsed square tables. Examples are given. </jats:p>

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