When multiple measures are collected repeatedly over time, redundancy typically exists among responses. The envelope method was recently proposed to reduce the dimension of responses without loss of information in regression with multivariate responses. It can gain substantial efficiency over the standard least squares estimator. In this paper, we generalize the envelope method to mixed effects models for longitudinal data with possibly unbalanced design and time-varying predictors. We show that our model provides more efficient estimators than the standard estimators in mixed effects models. Improved accuracy and efficiency of the proposed method over the standard mixed effects model estimator are observed in both the simulations and the Action to Control Cardiovascular Risk in Diabetes (ACCORD) study.

翻译：当反复收集多种措施时,答复中通常会存在冗余,最近建议采用封套方法,以减少反应的层面,而不会因多变反应而失去信息,在回归时会大大超过标准的最小方形估计值。在本文中,我们将封套方法推广到纵向数据的混合效果模型,可能的设计不平衡和时间分布预测器。我们显示,我们的模型比混合效应模型的标准估计器提供更有效的估计器。在模拟和糖尿病中都观察到了比标准混合效应模型估计器更准确、效率更高的拟议方法。