An extended class of marginal link functions for modelling contingency tables by equality and inequality constraints

Abstract

We extend Bergsma and Rudas (2002)'s hierarchical complete marginal parameterization to allow for logits and higher order effects of global and continu- ation type which may be more suitable with ordinal data. We introduce a general definition of marginal interaction parameters and show that this parameterization constitutes a link function so that linear models defined by equality and inequality constraints may be fitted and tested by extending the methods of Colombi and Forcina (2001). Computation and asymptotic properties of maximum likelihood estimators are discussed, and the asymptotic distribution of the likelihood ratio test is derived.