Modelling Mean-Covariance Structures in the Growth Curve Models

The growth curve model (GCM) has been widely used in longitudinal studies and repeated measures. Most existing spproaches for statistical inference in the GCM assume a specific structure on the within-subject covariances e.g., compound symmetry, AR(1) and unstructured covariances. This specification, however, may select a suboptimal or even wrong model, which in turn may affect the estimates of regression co-efficients and/or bias standard errors of the estimates. Accordingly, statistical inferences of the GCM may be severely affected by misspecification of covariance structures. Within the framework of the GCM in this paper we propose a data-driven approach for modelling the within-subject covariance structures, investigate the effects of misspecification of covariance structures on statistical inferences and study the possible heterogeneity of covariances between different treatment groups