Multiplicative-interaction logit models for i×j×2 three-way tables

Abstract

Multiplicative-interaction (M-I) logit models are proposed for three-way IxJx2 contingency tables where the third variable constitutes a binary response. Models are derived by assigning unknown scores to the categories and forming product interactions from them. Asymptotic results under special sampling constraints are derived for maximum likelihood estimates and the goodness-of-fit statistics. The class of models proposed in this paper are found to be useful when no obvious scores are available. An example is included.

Keywords:

• goodness-of-fit statistic
• logit model
• maximum likelihood estimate
• multinomial model
• produat-multinomial sampling