Inference in Varying-Coefficient Mixed Models\\by Using Smoothing Spline

Varying-coefficients mixed model (VCMM) is proposed for longitudinal data and the other correlated data. This model allows flexible functional dependence of the response variable on the covariates by using varying-coefficients linear part to present the covariates effects, while accounting the within-subject correlation by using random effect. In this article, the coefficient functions are estimated by using smoothing spline and restricted maximum likelihood is used to estimate the smoothing parameters and the variance components simultaneously. The performance of the proposed method is evaluated though some simulation studies, which show that both the coefficient functions and variance components could be estimated well for the VCMMs with all kinds of covariance structures.