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Statistical Modelling
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Regression models for covariance structures in longitudinal studies

Jianxin Pan

School of Mathematics, University of Manchester, England

Gilbert MacKenzie

Centre of Biostatistics, University of Limerick, Ireland, gilbert.mackenzie{at}ul.ie

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.

Key Words: Cholesky decomposition • covariate dependent covariance matrix • joint mean-covariance models • longitudinal trials • unbalanced observations • unconstrained parametrization

Statistical Modelling, Vol. 6, No. 1, 43-57 (2006)
DOI: 10.1191/1471082X06st105oa
Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us   Add to Digg Digg   Add to Reddit Reddit   Add to Technorati Technorati    What's this?