Test for link misspecification in dependent binary regression using generalized estimating equations

The generalized estimating equations (GEE) method has become quite useful in modeling correlated binary data such as, for example, in clinical trials designed to evaluate the efficacy of new drugs. It is well known that the GEE yield consistent estimators of the regression parameters and of their variances provided the model for the marginal mean is correctly specified. Thus, a crucial step in GEE regression is to check whether the link function used in the mean model is adequate. In this paper, we develop a goodness-of link test on the basis of a generalized score statistic and a parametric link family. By using two link families that have been proposed in the literature, two different tests are generated. These tests are illustrated using data from a longitudinal study designed to compare treatments for mental depression and their small-sample behaviors are assessed through Monte Carlo simulation.