Double-smoothing for varying coefficient models

Abstract

Moderation analyses are widely used in biomedical and psychosocial research to investigate differential treatment effects, with moderators frequently identified through testing the significance of the interaction between the predictor and the potential moderator under strong parametric assumptions. Without imposing any parametric forms on how the moderators may affect the relationship between predictors and responses, varying coefficient models address this fundamental problem of strong parametric assumptions with the current practice of moderation analysis and provide a much broader class of models for complex moderation relationships. Local polynomial, especially local linear (LL), methods are commonly used in estimating the varying coefficient models. Recently, a double-smoothing (DS) LL method has been proposed for nonparametric regression models, with nice properties compared to LL and local cubic (LC) methods. In this paper, we generalise DS to varying coefficient models, and show that it holds similar advantages over LL and LC methods.