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Power-divergence-type measure of departure from diagonals-parameter symmetry for square contingency tables with ordered categories |
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| Authors: | Sadao Tomizawa Nobuko Miyamoto Shunsuke Yamane |
| Affiliation: | 1. Department of Information Sciences, Faculty of Science and Technology , Tokyo University of Science , Noda City, Chiba, 278-8510, Japan tomizawa@is.noda.tus.ac.jp;3. Department of Information Sciences, Faculty of Science and Technology , Tokyo University of Science , Noda City, Chiba, 278-8510, Japan |
| Abstract: | For the analysis of square contingency tables with ordered categories, Goodman considered the diagonals-parameter symmetry (DPS) model. This paper proposes a measure to represent the degree of departure from the DPS model. The proposed measure is expressed by applying Read and Cressie’s power-divergence or Patil and Taillie’s diversity index. The measure would be useful for comparing the degree of departure from the DPS model in several tables. Examples are given. |
| Keywords: | Diversity index Kullback–Leibler information Measure Power-divergence Shannon entropy Symmetry |