Improving generalised estimating equations using quadratic inference functions

Q. U. Annie, Bruce G. Lindsay, L. I. Bing

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)823-836
Number of pages14
Issue number4
StatePublished - Dec 1 2000


  • Generalised estimating equation
  • Generalised method of moments
  • Linear approximate inverse
  • Longitudinal data
  • Quadratic inference function
  • Quasilikelihood

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Agricultural and Biological Sciences(all)
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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