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.

中文翻译：

---

混合效果包络模型

当随着时间的推移重复收集多个度量时，响应之间通常存在冗余。最近提出了包络法，以减小响应的维度，而不会因多元响应而使信息回归。与标准最小二乘估计器相比，它可以获得更高的效率。在本文中，我们将包络方法推广到具有可能不平衡的设计和时变预测变量的纵向数据的混合效应模型。我们表明，与混合效果模型中的标准估算器相比，我们的模型提供了更有效的估算器。在模拟和控制糖尿病风险的心血管行为（ACCORD）研究中均观察到，与标准的混合效应模型估计量相比，该方法的准确性和效率有所提高。