Bias reduction and robustness for Gaussian longitudinal data analysis

In the analysis of clustered or longitudinal data structures, such as those coming from surveys or trials, it is desirable to accurately estimate the dependence parameters within repeated measurements. Marginal models together with the generalized estimating equation allow to consistently estimate regression coefficients. Inference may be problematic for small and moderate sample sizes, or with models involving many covariates. Moreover, the correlation structure may be misspecified leading to a substantial bias in the sandwich covariance matrix estimator. The paper focuses on Gaussian with exchangeable correlation matrix model and proposes to use adjustments of the score function aiming at mean and median bias reduction of maximum likelihood estimates. Extensive simulation studies show a remarkable performance of the proposed methods. In addition, we show that the bias reduction methods maintain an appreciable robustness with respect to the maximum likelihood under misspecification of the correlation matrix.