McNeish Daniel, Wentzel Kathryn R
a Department of Methodology and Statistics , Utrecht University.
b Department of Human Development and Quantitative Methodology , University of Maryland.
Multivariate Behav Res. 2017 Mar-Apr;52(2):200-215. doi: 10.1080/00273171.2016.1262236. Epub 2016 Dec 23.
Small samples sizes are a pervasive problem when modeling clustered data. In two-level models, this problem has been well studied, and several resources provide guidance for modeling such data. However, a recent review of small-sample clustered data methods has noted that no studies have investigated methods for modeling three-level data with small sample sizes. Furthermore, strategies for two-level models do not necessarily translate to the three-level context. Moreover, three-level models are prone to small samples because the "small sample" designation is primarily based on the sample size of the highest level, and large samples are increasingly difficult to amass as one progresses up a hierarchy. In this study, we focus on the case when the third level is incidental, meaning that the third level is important to consider but there are no explicit research questions at the third level. This study performs a simulation study to examine the performance of seven methods for modeling three-level data with a small sample at the third level. A motivating educational psychology example is also provided to demonstrate how the choice of method can greatly affect results.
在对聚类数据进行建模时，小样本量是一个普遍存在的问题。在二级模型中，这个问题已经得到了充分研究，并且有多种资源为这类数据的建模提供指导。然而，最近一项关于小样本聚类数据方法的综述指出，尚无研究探讨过小样本量的三级数据建模方法。此外，二级模型的策略不一定能直接应用于三级模型的情况。而且，三级模型容易出现小样本问题，因为“小样本”的定义主要基于最高层级的样本量，随着层级上升，获取大样本越来越困难。在本研究中，我们关注第三层级为附带层级的情况，即第三层级虽需考虑但没有明确的研究问题。本研究进行了一项模拟研究，以检验七种用于对第三层级为小样本的三级数据进行建模的方法的性能。还提供了一个具有启发性的教育心理学实例，以说明方法的选择如何能极大地影响结果。
