Three-level clustered data commonly occur in social and behavioral research and are prominently analyzed using multilevel modeling. The influence of the clustering on estimation results is assessed with the intraclass correlation coefficients (ICCs), which indicate the fraction of variance in the outcome located at each higher level. However, ICCs are prone to bias due to high requirements regarding the overall sample size and the sample size at each data level. In Monte Carlo simulations, we investigate how these sample characteristics influence the bias of the ICCs and statistical power of the variance components using robust ML-estimation. Results reveal considerable underestimation on Level-3 and the importance of the Level-3 sample size in combination with the ICC sizes. Based on our results, we derive concise sampling recommendations and discuss limits to our inferences.

中文翻译：

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在三级模型中获得良好的类内相关性和方差估计：抽样策略的作用

三级聚类数据通常出现在社会和行为研究中，并使用多级建模进行突出分析。聚类对估计结果的影响使用组内相关系数 (ICC) 进行评估，ICC 表示位于每个更高级别的结果中的方差分数。然而，由于对总体样本量和每个数据级别的样本量要求较高，ICC 容易出现偏差。在蒙特卡罗模拟中，我们使用稳健的 ML 估计研究这些样本特征如何影响 ICC 的偏差和方差分量的统计能力。结果显示对 Level-3 的严重低估以及 Level-3 样本量与 ICC 大小相结合的重要性。根据我们的结果，