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

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