Methods for diagnosing multiplicative-interaction models for two-way contingency tables

An expanded class of multiplicative-interaction (M-I) models is proposed for two-way contingency tables. These models a generalization of Goodman's association models, fill in the gap between the independence and the saturated models. Diagnostic rules based on a transformation of the data are proposed for the detection of such models. These rules, utilizing the singular value decomposition of the transformed data, are very easy to use. Maximum likelihood estimation is considered and the computational algorithms discussed. A data set from Goodman (1981) and another from Gabriel and Zamir (1979) are used to demostrate the diagnostic rules.