A Sensitivity Analysis of two Multivariate Response Models

Abstract

Using extensive Monte Carlo simulations, the sensitivity of two multivariate response models with respect to their underlying assumptions is investigated: the Multivariate Probit Model, already suggested in 1970 by Ashford and Sowden [4] and the Multivariate Global Cross Ratio Model, a generalization of Dale's model (see [7]). Both types of models are designed to regress a multivariate, ordered, categorical response vector on discrete and/or continuous measurements. This paper focuses on the behaviour of the maximum likelihood estimate of the association parameters mainly under misspecification of the marginal distributions. The investigation will be restricted to 2- and 3-dimensional response models. The use of the two models is illustrated on a medical and a biological data set.