Ecological momentary assessment and other modern data collection technologies facilitate research on both within-subject and between-subject variability of health outcomes and behaviors. For such intensively measured longitudinal data, Hedeker et al extended the usual two-level mixed-effects model to a two-level mixed-effects location scale (MELS) model to accommodate covariates' influence as well as random subject effects on both mean (location) and variability (scale) of the outcome. However, there is a lack of existing standardized effect size measures for the MELS model. To fill this gap, our study extends Rights and Sterba's framework of $R^2$ measures for multilevel models, which is based on model-implied variances, to MELS models. Our proposed framework applies to two different specifications of the random location effects, namely, through covariate-influenced random intercepts and through random intercepts combined with random slopes of observation-level covariates. We also provide an R function, R2MELS, that outputs summary tables and visualization for values of our $R^2$ measures. This framework is validated through a simulation study, and data from a health behaviors study and a depression study are used as examples to demonstrate this framework. These $R^2$ measures can help researchers provide greater interpretation of their findings using MELS models.

中文翻译：

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为混合效应位置尺度模型定义 R 方度量

生态瞬时评估和其他现代数据收集技术促进了对健康结果和行为的受试者内和受试者间变异性的研究。对于这种密集测量的纵向数据，Hedeker 等人将通常的两级混合效应模型扩展到两级混合效应位置量表 (MELS) 模型，以适应协变量的影响以及对均值（位置) 和结果的可变性（规模）。然而，MELS 模型缺乏现有的标准化效应量测量。为了填补这一空白，我们的研究扩展了 Rights 和 Sterba 的框架$R^2$基于模型隐含方差的多级模型对 MELS 模型的度量。我们提出的框架适用于随机位置效应的两种不同规范，即通过受协变量影响的随机截距和通过随机截距与观察水平协变量的随机斜率相结合。我们还提供了一个 R 函数R2MELS，它输出汇总表和可视化我们的值$R^2$措施。该框架通过模拟研究得到验证，并以健康行为研究和抑郁症研究的数据为例来展示该框架。这些$R^2$措施可以帮助研究人员使用 MELS 模型更好地解释他们的发现。