Prediction and Creation of Smooth Curves for Temporally Correlated Longitudinal Data
提出一种为每个个体生成平滑曲线的方法，适用于观测次数少或无法设定参数随机效应的情况，通过假设总体均值曲线和重复测量相关性结构，用最大似然估计参数并利用克里金法预测个体未来值。
Abstract This article presents a method of obtaining smoothed curves for a sample of individuals that permits an arbitrary number and spacing of observations for each individual. We consider the case where each individual's curve cannot be separately estimated because either the n i 's are too small or no suitable parametric forms for the random effects are available. The model assumes a parametric form for the population mean curve and the correlation of the repeated measures. The assumed correlation structure is evaluated using the empirical semivariogram, a function of the sum of the squared differences of within-individual residuals. A method is proposed to validate the form and stationarity of the correlation structure. Maximum likelihood estimates for the population mean parameters and variance components are obtained simultaneously. These estimates may be used to create a semiparametric differentiable curve and to predict future values for each individual using a method called kriging. This method also yields instantaneous estimates of growth velocity. An example of this method is presented, and connections to kriging are discussed.