On the use of working correlation matrices in the GEE approach for longitudinal data

Liang and Zeger (1986) proposed a generalized estimating equations (GEE) approach to the analysis of longitudinal data. One of the advantages of the GEE modelling approach is its robustness on the structure of the working correlation matrix. The parameter estimator and its covariance matrix can be consistently estimated even if an incorrect working correlation matrix is used. Recently, however, Crowder (1995) pointed out that the use of an incorrect correlation matrix can cause an inconsistency problem in estimation. His results are based on the asymptotic theory. For the practioners, it is more important to know whether Crowder's results hold for moderate sample size data. In this paper, we investigate the effect of correlation structures on estimating regression parameters and variance parameters for the case of moderate sample sizes through Monte-Carlo simulation studies. We focus on binary responses and Poisson responses. On the contrary to Crowder's findings, the simulation results show that there are no differences between the cases when the correct correlation matrix is used and when the incorrect one is used. Thus, for moderate sample sizes the GEE approach is robust to the choice of the working correlation structure.