Model Robust Regression Based on Generalized Estimating Equations

One form of model robust regression (MRR) predicts mean response as a convexcombination of a parametric and a nonparametric prediction. MRR is a semiparametricmethod by which an incompletely or an incorrectly specified parametric model can beimproved through adding an appropriate amount of a nonparametric fit. The combinedpredictor can have less bias than the parametric model estimate alone and lessvariance than the nonparametric estimate alone. Additionally, as shown in previouswork for uncorrelated data with linear mean function, MRR can converge faster than thenonparametric predictor alone. We extend the MRR technique to the problem ofpredicting mean response for clustered non-normal data. We combine a nonparametricmethod based on local estimation with a global, parametric generalized estimatingequations (GEE) estimate through a mixing parameter on both the mean scale and thelinear predictor scale. As a special case, when data are uncorrelated, this amounts tomixing a local likelihood estimate with predictions from a global generalized linearmodel. Cross-validation bandwidth and optimal mixing parameter selectors aredeveloped. The global fits and the optimal and data-driven local and mixed fits arestudied under no/some/substantial model misspecification via simulation. The methodsare then illustrated through application to data from a longitudinal study.