Modelling of covariance structures in generalised estimating equations for longitudinal data

• Published in: Biometrika Vol. 93; no. 4; pp. 927 - 941
• Main Authors: Ye, Huajun, Pan, Jianxin
• Format: Journal Article
• Language: English
• Published: Oxford Oxford University Press 01.12.2006; Biometrika Trust, University College London; Oxford University Press for Biometrika Trust; Oxford Publishing Limited (England)
• Series: Biometrika
• Subjects: Applications; Asymptotic methods; Biology, psychology, social sciences; Cellular communications; Cholesky decomposition; Correlations; Covariance; Covariance matrices; Decomposition; Efficiency; Estimating techniques; Estimators; Estimators for the mean; Exact sciences and technology; Generalised estimating equation; Linear models; Longitudinal data; Mathematical models; Mathematics; Misspecification of covariance structure; Modelling of mean and covariance structures; Multivariate analysis; Parameter estimation; Parametric models; Probability and statistics; Proposals; Sciences and techniques of general use; Statistical discrepancies; Statistics; Studies; Biometrics; Bad specification; Efficiency loss; Generalised estimating equation; Gaussian distribution; Longitudinal data; Statistical simulation; Asymptotic convergence; Cholesky decomposition; Modelling of mean and covariance structures; Estimator efficiency; Cholesky method; Efficiency; Generalized equation; Estimating equation; Misspecification of covariance structure; Data covariances
• ISSN: 0006-3444; 1464-3510
• DOI: 10.1093/biomet/93.4.927

When used for modelling longitudinal data generalised estimating equations specify a working structure for the within-subject covariance matrices, aiming to produce efficient parameter estimators. However, misspecification of the working covariance structure may lead to a large loss of efficiency of the estimators of the mean parameters. In this paper we propose an approach for joint modelling of the mean and covariance structures of longitudinal data within the framework of generalised estimating equations. The resulting estimators for the mean and covariance parameters are shown to be consistent and asymptotically Normally distributed. Real data analysis and simulation studies show that the proposed approach yields e?cient estimators for both the mean and covariance parameters.