School of Education, University of Cincinnati.
Department of Educational Psychology, Texas A&M University.
Psychol Methods. 2018 Mar;23(1):94-112. doi: 10.1037/met0000137. Epub 2017 Mar 16.
The research literature has paid little attention to the issue of finite population at a higher level in hierarchical linear modeling. In this article, we propose a method to obtain finite-population-adjusted standard errors of Level-1 and Level-2 fixed effects in 2-level hierarchical linear models. When the finite population at Level-2 is incorrectly assumed as being infinite, the standard errors of the fixed effects are overestimated, resulting in lower statistical power and wider confidence intervals. The impact of ignoring finite population correction is illustrated by using both a real data example and a simulation study with a random intercept model and a random slope model. Simulation results indicated that the bias in the unadjusted fixed-effect standard errors was substantial when the Level-2 sample size exceeded 10% of the Level-2 population size; the bias increased with a larger intraclass correlation, a larger number of clusters, and a larger average cluster size. We also found that the proposed adjustment produced unbiased standard errors, particularly when the number of clusters was at least 30 and the average cluster size was at least 10. We encourage researchers to consider the characteristics of the target population for their studies and adjust for finite population when appropriate. (PsycINFO Database Record
研究文献在层次线性模型中对更高层次的有限总体问题关注较少。在本文中，我们提出了一种在 2 水平层次线性模型中获得 1 水平和 2 水平固定效应有限总体调整标准误差的方法。当错误地假设 2 水平的有限总体为无限时，固定效应的标准误差会被高估，从而导致统计功效降低和置信区间变宽。通过使用真实数据示例和具有随机截距模型和随机斜率模型的模拟研究来说明忽略有限总体校正的影响。模拟结果表明，当 2 水平样本量超过 2 水平总体大小的 10%时，未调整的固定效应标准误差的偏差很大；随着组内相关系数、聚类数和平均聚类大小的增加，偏差也会增加。我们还发现，所提出的调整方法产生了无偏的标准误差，特别是当聚类数至少为 30 且平均聚类大小至少为 10 时。我们鼓励研究人员在进行研究时考虑目标人群的特征，并在适当的情况下对有限总体进行调整。
