Random effects in longitudinal multilevel models represent individuals' deviations from population means and are indicators of individual differences. Researchers are often interested in examining how these random effects predict outcome variables that vary across individuals. This can be done via a two-step approach in which empirical Bayes (EB) estimates of the random effects are extracted and then treated as observed predictor variables in follow-up regression analyses. This approach ignores the unreliability of EB estimates, leading to underestimation of regression coefficients. As such, previous studies have recommended a multilevel structural equation modeling (ML-SEM) approach that treats random effects as latent variables. The current study uses simulation and empirical data to show that a bias-variance tradeoff exists when selecting between the two approaches. ML-SEM produces generally unbiased regression coefficient estimates but also larger standard errors, which can lead to lower power than the two-step approach. Implications of the results for model selection and alternative solutions are discussed.

中文翻译：

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将随机效应视为观察到的与潜在的预测变量：小样本中的偏差-方差权衡。

纵向多水平模型中的随机效应代表个体与总体均值的偏差，是个体差异的指标。研究人员通常对研究这些随机效应如何预测因人而异的结果变量感兴趣。这可以通过两步方法完成，其中提取随机效应的经验贝叶斯 (EB) 估计，然后在后续回归分析中将其视为观察到的预测变量。这种方法忽略了 EB 估计的不可靠性，导致低估了回归系数。因此，以前的研究推荐了一种将随机效应视为潜在变量的多级结构方程建模 (ML-SEM) 方法。目前的研究使用模拟和经验数据来表明在两种方法之间进行选择时存在偏差 - 方差权衡。ML-SEM 产生通常无偏的回归系数估计，但也产生较大的标准误差，这可能导致比两步法更低的功效。讨论了模型选择和替代解决方案的结果的含义。