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

doi:10.3390/e10040776

This article is

freely available
re-usable

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

Kouji Yamamoto , Yohei Ban and Sadao Tomizawa *

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 Entropy and Information)

Download PDF Full-Text [181 KB, uploaded 20 December 2008 20:34 CET]

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

Article Statistics

Click here to load and display the download statistics.

Cite This Article

MDPI and ACS Style

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.

AMA Style

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(4):776-785.

Chicago/Turabian Style

Yamamoto, Kouji; Ban, Yohei; Tomizawa, Sadao. 2008. "Generalized Measure of Departure from No Three-Factor Interaction Model for 2 x 2 x K Contingency Tables." Entropy 10, no. 4: 776-785.

Entropy EISSN 1099-4300 Published by MDPI Publishing, Basel, Switzerland RSS E-Mail Table of Contents Alert