Assessing robustness of generalised estimating equations and quadratic inference functions

In the presence of data contamination or outliers, some empirical studies have indicated that the two methods of generalised estimating equations and quadratic inference functions appear to have rather different robustness behaviour. This paper presents a theoretical investigation from the perspective of the influence function to identify the causes for the difference. We show that quadratic inference functions lead to bounded influence functions and the corresponding M-estimator has a redescending property, but the generalised estimating equation approach does not. We also illustrate that, unlike generalised estimating equations, quadratic inference functions can still provide consistent estimators even if part of the data is contaminated. We conclude that the quadratic inference function is a preferable method to the generalised estimating equation as far as robustness is concerned. This conclusion is supported by simulations and real-data examples.