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Non-linear Information Inequalities
Entropy 2008, 10(4), 776-785; doi:10.3390/e10040776

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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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 which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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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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