Models for Longitudinal Data with Random Effects and AR(1) Errors
研究了同时包含个体间随机效应和个体内误差自相关的线性模型，提出了自相关的得分检验、极大似然估计方法，并考虑了经验贝叶斯估计和预测。
Abstract For longitudinal data on several individuals, linear models that contain both random effects across individuals and autocorrelation in the within-individual errors are studied. A score test for autocorrelation in the within-individual errors for the “conditional independence” random effects model is first developed. An explicit maximum likelihood estimation procedure using the scoring method for the model with random effects and (autoregressive) AR(1) errors is then derived. Empirical Bayes estimation of the random effects and prediction of future responses of an individual based on this random effects with AR(1) errors model are also considered. A numerical example is presented to illustrate these methods.