Varying Coefficient Models and Basis Function Approximations
for the Analysis of Longitudinal data

Longitudinal data occur frequently in medical and epidemiological studies where both the outcome and the covariates of a set of randomly selected subjects are repeatedly recorded on the same individual over time. While the observations obtained from different subjects can be thought of as independent, those obtained at different time points within the same subject are possibly correlated. We develop a global smoothing method using basis function approximations for nonparametric estimation and inference for a varying coefficient model with longitudinal data. Inference procedures based a resampling subject bootstrap and asymptotic distribution are proposed. Application of the proposed method will be demonstrated through analyzing some epidemiological data sets. In contrast to the existing methods in the literature, the proposed approach applies without regard to the covariates being time-invariant or not and is directly applicable when observation times are irregularly placed and observations are sparse at distinct observation times.