The uniform difference association-multivariate Logit model

Abstract

The Goodman Association Model and its generalization called Uniform Difference Association Model are well known for their flexibility in modelling the association between two categorical variables and for the graphical displays that can be obtained from the estimates of their parameters, but these models are not appropriate if the focus of the investigation is in modelling the marginal probabilities. This is so because these models imply complicate parametric expressions for the marginal probabilities. Having in mind that a simple parameterization of the marginal probabilities is often desirable a modification of the Uniform Difference Association Model is proposed, in order to obtain a model, that allows a simple parameterization of the marginal probabilities, and models the association between categorical variables in the same way followed by the Goodman Association Model and the Uniform Difference Association Model. For the proposed model, it shown how the maximum likelihood estimates of the parameters can be computed. The properties of the maximum likelihood estimators are discussed as well. Finally a generalization to the case of more than two categorical variables is discussed.