Modelling marginal covariance structures in linear mixed models

Pourahmadi (1999) provided a convenient reparameterisation of the marginal covariance matrix arising in longitudinal studies. We exploit his work to model the dependence of this covariance structure on baseline covariates, time and their interaction. The rationale for this approach is the realisation that in linear mixed models (LMMs) the assumption of a homogeneous covariance structure with respect to the covariate space is a testable model choice. Accordingly, we provide methods for testing this assumption and re-analyse Kenward’s (1987) cattle data set using our new model.