Contour Method and Collapsibility Criteria for $2{\times}3{\times}K$ Contingency Tables

  • Hong, C.S. (Department of Statistics, Sungkyunkwan University) ;
  • Son, B.U. (Department of Information Statistics, Korea National Open University) ;
  • Park, J.Y. (Department of Information Statistics, Korea National Open University)
  • Published : 2004.11.30

Abstract

The contour method which was originally designed for $2{\times}2{\times}2$ contingency table is studied for $2{\times}2{\times}K$ and $2{\times}3{\times}K$ tables. Whereas a contour plot for a $2{\times}2{\times}K$ table is represented on unit squared two dimensional plane, a contour plot of a $2{\times}3{\times}K$ table can be expressed with a regular hexahedron on three dimensional space. Based on contour plots for categorical data fitted to all possible three dimensional log-linear models, one might identify whether $2{\times}2{\times}k$ or $2{\times}3{\times}K$ tables are collapsible over the third variable.

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