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Entropy 2008, 10(4), 776-785; doi:10.3390/e10040776
Article

Generalized Measure of Departure from No Three-Factor Interaction Model for 2 x 2 x K Contingency Tables

,
 and *
Department of Information Sciences, Faculty of Science and Technology, Tokyo University of Science, Noda City, Chiba, 278-8510, Japan
* Author to whom correspondence should be addressed.
Received: 31 October 2008 / Accepted: 16 December 2008 / Published: 22 December 2008
(This article belongs to the Special Issue Information and Entropy)
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Abstract

For 2 x 2 x K contingency tables, Tomizawa considered a Shannon entropy type measure to represent the degree of departure from a log-linear model of no three-factor interaction (the NOTFI model). This paper proposes a generalization of Tomizawa's measure for 2 x 2 x K tables. The measure proposed is expressed by using Patil-Taillie diversity index or Cressie-Read power-divergence. A special case of the proposed measure includes Tomizawa's measure. The proposed measure would be useful for comparing the degrees of departure from the NOTFI model in several tables.
Keywords: Diversity index; odds-ratio; power-divergence Diversity index; odds-ratio; power-divergence
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Yamamoto, K.; Ban, Y.; Tomizawa, S. Generalized Measure of Departure from No Three-Factor Interaction Model for 2 x 2 x K Contingency Tables. Entropy 2008, 10, 776-785.

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