Research On Nonparametric Varying Coefficient Mixed Effects Model And Its Estimation Procedures

Longitudinal data such as repeated measurements taken on each of a number of subjects over time arise frequently from many biomedical and clinical studies as well as from other scientific areas.However,for many applications,parametric models may be too restrictive or limited,and sometimes unavailable at least for preliminary data analyses.To overcome this difficulty,nonparametric regression techniques have been developed for longitudinal data analysis in recent years.In this paper,we provide a survey of a new estimation of nonparametric varying-coefficient mixed effects model that combine mixed effects modeling ideas,time varying coefficient models and nonparametric regression techniques for longitudinal data analysis,then a profile likelihood based estimation procedure with a fully iterated two step local estimation method is proposed for the varying coefficients and random effects.Simulation studies are carried out to demonstrate the efficiency of the proposed estimator in the finite sample.The simulation results show that fully iterated two step estimation method works very well and surpasses naive method,one step method and two step method.The proposed methods are illustrated via an application to a real longitudinal data set collected in health care expenditure of 28 provinces from 1995-2006 in China's urban and rural areas.Comparison of the estimated coefficients shows that nonparametric varying-coefficient mixed effects model surpasses the parametric one,confirming that the estimated coefficients are time-varying which can better describe the time-varying relationship between health care expenditure inequality in China,income inequality and provincial government budget deficit in the long run.