The linear mixed model (LMM) is a popular statistical model for the analysis of longitudinal data. However, the robust estimation of and inferential conclusions for the LMM in the presence of outliers (i.e., observations with very low probability of occurrence under Normality) is not part of mainstream longitudinal data analysis. In this work, we compared the coverage rates of confidence intervals (CIs) based on two bootstrap methods, applied to three robust estimation methods. We carried out a simulation experiment to compare CIs under three different conditions: data 1) without contamination, 2) contaminated by within-, or 3) between-participant outliers. Results showed that the semi-parametric bootstrap associated to the composite tau-estimator leads to valid inferential decisions with both uncontaminated and contaminated data. This being the most comprehensive study of CIs applied to robust estimators of the LMM, we provide fully commented R code for all methods applied to a popular example.

中文翻译：

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稳健线性混合模型的基于参数和半参数自举的置信区间

线性混合模型 (LMM) 是一种流行的用于分析纵向数据的统计模型。然而，在存在异常值（即，在正态性下发生概率非常低的观察）的情况下，LMM 的稳健估计和推断结论并不是主流纵向数据分析的一部分。在这项工作中，我们比较了基于两种自举方法的置信区间 (CI) 的覆盖率，并将其应用于三种稳健的估计方法。我们进行了一个模拟实验来比较三种不同条件下的 CI：数据 1) 没有污染，2) 被内部污染，或 3) 参与者之间的异常值。结果表明，与复合 tau 估计器相关的半参数引导程序可以对未受污染和受污染的数据进行有效的推理决策。