Modelling covariance structure in bivariate marginal models for longitudinal data

Abstract

SUMMARY It can be more challenging to efficiently model the covariance matrices for multivariate longitudinal data than for the univariate case, due to the correlations arising between multiple responses. The positive-definiteness constraint and the high dimensionality are further obstacles in covariance modelling. In this paper, we develop a data-based method by which the parametersinthecovariancematricesarereplacedbyunconstrainedandinterpretableparameterswith reduced dimensions. The maximum likelihood estimators for the mean and covariance parameters are shown to be consistent and asymptotically normally distributed. Simulations and real data analysis show that the new approach performs very well even when modelling bivariate nonstationary dependence structures.