Generalized varying coefficient models for longitudinal data

We propose a generalization of the varying coefficient model for longitudinal data to cases where not only current but also recent past values of the predictor process affect current response. More precisely, the targeted regression coefficient functions of the proposed model have sliding window supports around current time t. A variant of a recently proposed two-step estimation method for varying coefficient models is proposed for estimation in the context of these generalized varying coefficient models, and is found to lead to improvements, especially for the case of additive measurement errors in both response and predictors. Asymptotic distributions of the proposed estimators are derived, and the model is applied to the problem of predicting protein concentrations in a longitudinal study. Simulation studies demonstrate the efficacy of the proposed estimation procedure.