Criterion for the simultaneous selection of a working correlation structure and either generalized estimating equations or the quadratic inference function approach

Generalized estimating equations (GEE) are commonly used for the marginal analysis of correlated data, although the quadratic inference function (QIF) approach is an alternative that is increasing in popularity. This method optimally combines distinct sets of unbiased estimating equations that are based upon a working correlation structure, therefore asymptotically increasing or maintaining estimation efficiency relative to GEE. However, in finite samples, additional estimation variability arises when combining these sets of estimating equations, and therefore the QIF approach is not guaranteed to work as well as GEE. Furthermore, estimation efficiency can be improved for both analysis methods by accurate modeling of the correlation structure. Our goal is to improve parameter estimation, relative to existing methods, by simultaneously selecting a working correlation structure and choosing between GEE and two versions of the QIF approach. To do this, we propose the use of a criterion based upon the trace of the empirical covariance matrix (TECM). To make GEE and both QIF versions directly comparable for any given working correlation structure, the proposed TECM utilizes a penalty to account for the finite-sample variance inflation that can occur with either version of the QIF approach. Via a simulation study and in application to a longitudinal study, we show that penalizing the variance inflation that occurs with the QIF approach is necessary and that the proposed criterion works very well.