What can go wrong when ignoring correlation bounds in the use of generalized estimating equations

The analysis of repeated measure or clustered data is often complicated by the presence of correlation. Further complications arise for discrete responses, where the marginal probability-dependent Frechet bounds impose feasibility limits on the correlation that are often more restrictive than the positive definite range. Some popular statistical methods, such as generalized estimating equations (GEE), ignore these bounds, and as such can generate erroneous estimates and lead to incorrect inferential results. In this paper, we discuss two alternative strategies: (i) using QIC to select a data-driven correlation value within the Frechet bounds, and (ii) the use of likelihood-based latent variable modeling, such as multivariate probit, to get around the problem all together. We provide two examples of the repercussions of incorrectly using existing GEE software in the presence of correlated binary responses. Copyright (C) 2010 John Wiley & Sons, Ltd.