A comparison of methods for specifying optimal random effects structures

Using Monte Carlo simulations, this study compared the performance of various approaches to the specification of random effects structures in linear mixed effects models (LMMs), including the minimal approach, the maximal approach, the forward search, the backward search, and the all-possible structures approach. The results showed that if the predictor of interest is at the within-cluster level or involves a cross-level interaction, the maximal approach, the best-path forward search, and the best-path backward search are all desirable methods. If the predictor of interest is at the cluster level, it is not essential to specify random slopes of Level-1 predictors. In addition, it is important to specify random slopes of within-cluster control variables, as they can increase the statistical power for testing the main within-cluster variables, especially when the sample size is small and the variance of the random slope of the control variable is large. peerReviewed publishedVersion

本研究借助蒙特卡洛（Monte Carlo）模拟，对比了线性混合效应模型（Linear Mixed Effects Models, LMMs）下随机效应结构（random effects structures）设定的多种方法的表现，包括最小化法（minimal approach）、最大化法（maximal approach）、向前筛选法（forward search）、向后筛选法（backward search）以及全可能结构法（all-possible structures approach）。研究结果显示，当关注的预测变量处于组内水平（within-cluster level），或涉及跨水平交互作用（cross-level interaction）时，最大化法、最优路径向前筛选法（best-path forward search）以及最优路径向后筛选法（best-path backward search）均为优选方法。若关注的预测变量处于组水平（cluster level），则无需设定一阶预测变量（Level-1 predictors）的随机斜率。此外，对组内控制变量设定随机斜率至关重要，此举可提升检验核心组内变量的统计效力（statistical power），尤其在样本量较小且控制变量的随机斜率方差较大时效果更为显著。经同行评议的已发表版本。