A measure of linear diagonals-parameter symmetry for square contingency tables with ordered categories

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  • Kouji Yamamoto
    Department of Information Sciences, Faculty of Science and Technology, Tokyo University of Science, Noda City, Chiba, Japan. E-mail: yamamoto_kouji@ymail.plala.or.jp; tomizawa@is.noda.tus.ac.jp
  • Sadao Tomizawa
    Department of Information Sciences, Faculty of Science and Technology, Tokyo University of Science, Noda City, Chiba, Japan. E-mail: yamamoto_kouji@ymail.plala.or.jp; tomizawa@is.noda.tus.ac.jp

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For square contingency tables with ordered categories, Agresti (1) considered the linear diagonals-parameter symmetry (LDPS) model being an extension of the symmetry model. This paper proposes a measure which represents the degree of departure from the LDPS model. The measure proposed is expressed using the Cressie-Read power-divergence or Patil-Taillie diversity index. The measure is useful for comparing the degree of departure from LDPS in several tables, and it may be appropriate for comparing the degrees of departure from the equality of the marginal variances for several square ordinal tables if it is reasonable to assume underlying bivariate normal distributions. Examples are also given.

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