Modelling covariance structure in bivariate marginal models for longitudinal data

It can be more challenging and demanding to efficiently model the covariance matrices for multivariate longitudinal data than for univariate case because of the correlations between responses arising from multiple variables and repeated measurements over time. In addition to the more complicated covariance structures, the positive-definiteness constraint is still the major obstacle in modelling covariance matrices as in univariate case. In this paper, we develop a data-based method to model the covariance structures. Using this method, the constrained and hard-to-model parameters of ∑i are traded in for uncon- strained and interpretable parameters. Estimates of these parameters, together with the parameters in the mean, are obtained by maximum likelihood approach, and the large- sample asymptotic properties are derived when the observations are normally distributed. A simulation is carried out to illustrate the asymptotics. Application to a set of bivariate visual data shows that our method performs very well even when modelling bivariate nonstationary dependence structures.