Multivariate dispersion models generated from Gaussian copula

In this paper a class of multivariate dispersion models generated from the multivariate Gaussian copula is presented. Being a multivariate extension o f Jergensen's (1987a) dispersion models, this class of multivariate models is parametrized by marginal position, dispersion and dependence parameters, producing a large variety of multivariate discrete and continuous models i ncluding the multivariate normal as a special case. Properties of the multi variate distributions are investigated, some of which are similar to those of the multivariate normal distribution, which makes these models potential ly useful for the analysis of correlated non-normal data in a way analogous to that of multivariate normal data. As an example, we illustrate an appli cation of the models to the regression analysis of longitudinal data, and e stablish an asymptotic relationship between the likelihood equation and the generalized estimating equation of Liang gr Zeger (1986).