Performance of variance estimators in the analysis of longitudinal data with a large cluster size

Generalized estimating equations (GEE) is a widely used method for analysing longitudinal data, and the sandwich method is often used to estimate the variance–covariance matrix of the regression coefficient estimators. However, the sandwich method relies on the residual products as an estimator for the true covariance of the responses, and the estimator becomes singular and sparse when the cluster size (n) becomes larger. We carry out a large set of simulation studies to address the question, when the cluster size becomes large, whether the sandwich estimator and their modified versions are still valid when a sparse or singular matrix is used as an estimate of the true covariance of the responses. The performance of smooth bootstrap which involves perturbing the estimating functions is also worth to be investigated when the cluster size is large. Two datasets are analysed to illustrate these findings.