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Biometrika 2000 87(4):823-836; doi:10.1093/biomet/87.4.823
© 2000 by Biometrika Trust
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Improving generalised estimating equations using quadratic inference functions

Annie Qu, Bruce G. Lindsay and Bing Li

Department of Statistics, Oregon State University, Corvallis, Oregon 97331, U.S.A. qu@stat.orst.edu Department of Statistics, 326 Thomas Building, The Pennsylvania State University, University Park, Pennsylvania 16802, U.S.A. bgl@psu.edu bing@stat.psu.edu

Generalised estimating equations enable one to estimate regression parameters consistently in longitudinal data analysis even when the correlation structure 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 estimation 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 basis matrices, a representation that is valid for the working correlations most commonly used. Both asymptotic theory and simulation show that under misspecified working assumptions these estimators are more efficient than estimators 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 correlation structure is correctly specified.

Key Words: Generalised estimating equation; Generalised method of moments; Linear approximate inverse; Longitudinal data; Quadratic inference function; Quasilikelihood.


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