Selection criterion of work matrix as a function of limiting estimates of the covariance matrix of correlated data in GEE

The modeling of generalized estimating equations used in the analysis of longitudinal data whether in continuous or discrete variables, necessarily requires the prior specification of a correlation matrix in its iterative process in order to obtain the estimates of the regression parameters. Such a matrix is called working correlation matrix and its incorrect specification produces less efficient estimates for the model parameters. Due to this fact, this study aims to propose a selection criterion of working correlation matrix based on the covariance matrix estimates of correlated responses resulting from the limiting values of the association parameter estimates. For validation of the criterion, we used simulation studies considering normal and binary correlated responses. Compared to some criteria in the literature, it was concluded that the proposed criterion resulted in a better performance when the correlation structure for exchangeable working correlation matrix was considered as true structure in the simulated samples and for large samples, the proposed criterion showed similar behavior to the other criteria, resulting in higher success rates.