The linear mixed model (LMM) and latent growth model (LGM) are frequently applied to within-subject two-group comparison studies to investigate group differences in the time effect, supposedly due to differential group treatments. Yet, research about LMM and LGM in the presence of outliers (defined as observations with a very low probability of occurrence if assumed from a given distribution) is scarce. Moreover, when such research exists, it focuses on estimation properties (bias and efficiency), neglecting inferential characteristics (e.g., power and type-I error). We study power and type-I error rates of Wald-type and bootstrap confidence intervals (CIs), as well as coverage and length of CIs and mean absolute error (MAE) of estimates, associated with classical and robust estimations of LMM and LGM, applied to a within-subject two-group comparison design. We conduct a Monte Carlo simulation experiment to compare CIs and MAEs under different conditions: data (a) without contamination, (b) contaminated by within-subject outliers, (c) contaminated by between-subject outliers, and (d) both contaminated by within- and between-subject outliers. Results show that without contamination, methods perform similarly, except CIs based on S, a robust LMM estimator, which are slightly less close to nominal values in their coverage. However, in the presence of both within- and between-subject outliers, CIs based on robust estimators, especially S, performed better than those of classical methods. In particular, the percentile CI with the wild bootstrap applied to the robust LMM estimators outperformed all other methods, especially with between-subject outliers, when we found the classical Wald-type CI based on the t statistic with Satterthwaite approximation for LMM to be highly misleading. We provide R code to compute all methods presented here. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

中文翻译：

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线性混合模型和潜在生长曲线模型，用于受异常值污染的组比较研究。


线性混合模型 （LMM） 和潜在生长模型 （LGM） 经常应用于受试者内两组比较研究，以研究时间效应的组差异，这可能是由于差异组处理造成的。然而，关于存在异常值（定义为如果从给定分布假设，则发生概率非常低的观测值）的 LMM 和 LGM 的研究很少。此外，当存在此类研究时，它侧重于估计特性（偏差和效率），而忽略了推理特性（例如，功效和 I 类误差）。我们研究了 Wald 型和自举置信区间 （CI） 的功效和 I 型误差率，以及 CI 的覆盖率和长度以及估计的平均绝对误差 （MAE），与 LMM 和 LGM 的经典和稳健估计相关，应用于受试者内两组比较设计。我们进行了蒙特卡洛模拟实验，以比较不同条件下的 CI 和 MAE：数据 （a） 无污染，（b） 被受试者内异常值污染，（c） 被受试者间异常值污染，以及 （d） 都被受试者内和受试者间异常值污染。结果表明，在没有污染的情况下，方法的性能相似，但基于 S（一种稳健的 LMM 估计器）的 CI 除外，其覆盖率与标称值的接近程度略低。然而，在存在受试者内和受试者间异常值的情况下，基于稳健估计量的 CI，尤其是 S，比经典方法的 CI 表现更好。 特别是，当我们发现基于 LMM 的 t 统计量和 Satterthwaite 近似值的经典 Wald 型 CI 具有高度误导性时，将野生 bootstrap 应用于稳健 LMM 估计量的百分位 CI 优于所有其他方法，尤其是对于受试者间异常值。我们提供 R 代码来计算此处提供的所有方法。（PsycInfo 数据库记录 （c） 2024 APA，保留所有权利）。