Semiparametric Stochastic Mixed Models for Longitudinal Data
提出一种半参数随机混合模型，用参数固定效应和光滑函数分别处理协变量和时间效应，通过随机效应和随机过程刻画个体内相关性，并给出估计和推断方法。
We consider inference for a semiparametric stochastic mixed model for longitudinal data. This model uses parametric fixed effects to represent the covariate effects and an arbitrary smooth function to model the time effect and accounts for the within-subject correlation using random effects and a stationary or nonstationary stochastic process. We derive maximum penalized likelihood estimators of the regression coefficients and the nonparametric function. The resulting estimator of the nonparametric function is a smoothing spline. We propose and compare frequentist inference and Bayesian inference on these model components. We use restricted maximum likelihood to estimate the smoothing parameter and the variance components simultaneously. We show that estimation of all model components of interest can proceed by fitting a modified linear mixed model. We illustrate the proposed method by analyzing a hormone dataset and evaluate its performance through simulations.