Statistica Sinica 17(2007), 691-711

AN EXTENDED CLASS OF MARGINAL LINK FUNCTIONS

FOR MODELLING CONTINGENCY TABLES BY

EQUALITY AND INEQUALITY CONSTRAINTS

Francesco Bartolucci$^1$, Roberto Colombi$^2$ and Antonio Forcina$^1$

$^1$Università di Perugia and $^2$Università di Bergamo

Abstract: We extend Bergsma and Rudas (2002)'s hierarchical complete marginal parameterization to allow for logits and higher order effects of global and continuation 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.

Key words and phrases: Chi-bar-squared distribution, likelihood inference, marginal models, one-sided linear hypothesis.