On repeated measures analysis with misspecified covariance structure

In recent years various sophisticated methods have been developed for the analysis of repeated measures, or longitudinal data. The more traditional approach, based on a normal likelihood function, has been shown to be unsatisfactory, in the sense of yielding asymptotically biased estimates when the covariance structure is misspecified. More recent methodology, based on generalized linear models and quasi-likelihood estimation, has gained widespread acceptance as 'generalized estimating equations'. However, this also has theoretical problems. In this paper a suggestion is made for improving the asymptotic behaviour of estimators by using the older approach, implemented via Gaussian estimation. The resulting estimating equations include the quasi-score function as one component, so the methodology proposed can be viewed as a combination of Gaussian estimation and generalized estimating equations which has a firmer asymptotic basis than either alone has.