Backfitting Random Varying‐Coefficient Models with Time‐Dependent Smoothing Covariates

In this paper, we propose a random varying‐coefficient model for longitudinal data. This model is different from the standard varying‐coefficient model in the sense that the time‐varying coefficients are assumed to be subject‐specific, and can be considered as realizations of stochastic processes. This modelling strategy allows us to employ powerful mixed‐effects modelling techniques to efficiently incorporate the within‐subject and between‐subject variations in the estimators of time‐varying coefficients. Thus, the subject‐specific feature of longitudinal data is effectively considered in the proposed model. A backfitting algorithm is proposed to estimate the coefficient functions. Simulation studies show that the proposed estimation methods are more efficient in finite‐sample performance compared with the standard local least squares method. An application to an AIDS clinical study is presented to illustrate the proposed methodologies.