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A convenient reparametrization of the marginal covariance matrix arising in
longitudinal studies is discussed. The new parameters have transparent statistical
interpretations, are unconstrained and may be modelled parsimoniously in terms of
polynomials of time. We exploit this framework to model the dependence of the
covariance structure on baseline covariates, time and their interaction. The
rationale is based on the assumption that a homogeneous covariance structure with
respect to the covariate space is a testable model choice. Accordingly, we
provide methods for testing this assumption by incorporating covariates along with
time into the model for the covariance structure. We also present new computational
algorithms which can handle unbalanced longitudinal data, thereby extending existing
methods. The new model is used to analyse Kenward’s (1987) cattle data,
and the findings are compared with published analyses of the same data set.
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