SEMIPARAMETRIC STOCHASTIC MIXED MODELS FOR LONGITUDINAL DATA

We consider inference for a semiparametric stochastic mixed model for longitudinal data. This model uses parametric fixed effects to represe nt the covariate effects and an arbitrary smooth function to model the time effect and accounts for the within-subject correlation using ran dom effects and a stationary or nonstationary stochastic process. We d erive maximum penalized likelihood estimators of the regression coeffi cients and the nonparametric function. The resulting estimator of the nonparametric function is a smoothing spline. We propose and compare f requentist inference and Bayesian inference on these model components. We use restricted maximum likelihood to estimate the smoothing parame ter and the variance components simultaneously. We show that estimatio n of all model components of interest can proceed by fitting a modifie d linear mixed model. We illustrate the proposed method by analyzing a hormone dataset and evaluate its performance through simulations.