Improving generalized estimating equations using quadratic inference functions

Abstract


The generalized estimating equations (GEE) (Liang & Zeger, 1986) are popular in longitudinal data analysis. It enables one to estimate regression parameters consistently even when the correlation structure is misspecified. However, under such misspecification, the estimator of the regression parameter can be inefficient. We introduce a new approach based on the quadratic inference functions (QIF) that arise in the generalized method of moments (Hansen, 1982). This approach does not require correlation parameter estimation except indirectly. A key assumption in the construction of the quadratic inference function is that the working correlation matrix can be represented by a linear combination of basis matrices, which is true of the working correlations most commonly used. Both asymptotic theory and simulation results show that under misspecified working assumptions these estimators are more efficient than those of the GEE. A second advantage of the quadratic inference function approach is that it can be used to construct a chi-squared decomposition for testing of nested models. We establish some new inferential testing properties that add to testing results from Hansen (1982) and Lee (1996). It is particularly important that the test statistics follow a chi-square distribution asymptotically whether or not the working correlation structure is correctly specified.

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