Statistical Modelling 6 (2006), 43–57
Regression models for covariance structures in longitudinal studies
Jianxin Pan
School of Mathematics,
University of Manchester
Gilbert MacKenzie
Centre for Biostatistics,
University of Limerick,
Limerick
Ireland
eMail: gilbert.mackenzie@ul.ie
Abstract:
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.
Keywords:
Cholesky decomposition; covariate dependent covariance matrix;
joint mean-covariance models; longitudinal trials;
unbalanced observations; unconstrained parameterization
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