Improving generalised estimating equations using quadratic inference functions

Generalised estimating equations enable one to estimate regression paramete rs consistently in longitudinal data analysis even when the correlation str ucture is misspecified. However, under such misspecification, the estimator of the regression parameter can be inefficient. In this paper we introduce a method of quadratic inference functions that does not involve direct est imation of the correlation parameter, and that remains,optimal even if the working correlation structure is misspecified. The idea is to represent the inverse of the working correlation matrix by the linear combination of bas is matrices, a representation that is valid for the working correlations mo st commonly used. Both asymptotic theory and simulation show that under mis specified working assumptions these estimators are more efficient than esti mators from generalised estimating equations. This approach also provides a chi-squared inference function for testing nested models and a chi-squared regression misspecification test. Furthermore, the test statistic follows a chi-squared distribution asymptotically whether or not the working correl ation structure is correctly specified.