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Biometrika 2003 90(1):239-244; doi:10.1093/biomet/90.1.239
© 2003 by Biometrika Trust
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On modelling mean-covariance structures in longitudinal studies

Jianxin Pan1 and Gilbert Mackenzie2

1 Department of Mathematics, The University of Manchester, Manchester M13 9PL, U.Kjpan{at}maths.man.ac.uk 2 The Centre for Medical Statistics, Department of Mathematics, Keele University, Staffordshire ST5 5BG, U.K.g.mackenzie{at}keele.ac.uk

We exploit a reparameterisation of the marginal covariance matrix arising in longitudinal studies (Pourahmadi, 1999, 2000) to model, jointly, the mean and covariance structures in terms of three polynomial functions of time.By reanalysing Kenward's (1987) cattle data, we compare model selection procedures based on regressogram estimation with these based on a global search of the model space. Using a BIC-based model selection criterion to identify the optimum degree triple of the three polynomials, we show that the use of a saturated mean model is not optimal and explain why regressogram-based model estimation may be misleading. We also suggest a new computational method for finding the global optimum based on a criterion involving three pairwise saturated profile likelihoods.

Key Words: Cholesky decomposition; Global optimisation; Joint mean-covariance model; Longitudinal data analysis

Received January 2002. Revised May 2002


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