Institute for Employment Research, Regensburger Strasse 104, 90478, Nuremberg, Germany.
The University of Manchester, Oxford Road, M13 9PL, Manchester, UK.
Behav Res Methods. 2018 Oct;50(5):1824-1840. doi: 10.3758/s13428-017-0951-1.
When datasets are affected by nonresponse, imputation of the missing values is a viable solution. However, most imputation routines implemented in commonly used statistical software packages do not accommodate multilevel models that are popular in education research and other settings involving clustering of units. A common strategy to take the hierarchical structure of the data into account is to include cluster-specific fixed effects in the imputation model. Still, this ad hoc approach has never been compared analytically to the congenial multilevel imputation in a random slopes setting. In this paper, we evaluate the impact of the cluster-specific fixed-effects imputation model on multilevel inference. We show analytically that the cluster-specific fixed-effects imputation strategy will generally bias inferences obtained from random coefficient models. The bias of random-effects variances and global fixed-effects confidence intervals depends on the cluster size, the relation of within- and between-cluster variance, and the missing data mechanism. We illustrate the negative implications of cluster-specific fixed-effects imputation using simulation studies and an application based on data from the National Educational Panel Study (NEPS) in Germany.
当数据集受到无应答影响时，缺失值的插补是一种可行的解决方案。然而，在教育研究和其他涉及单位聚类的环境中流行的多层次模型中，常用统计软件包中实施的大多数插补例程并不适用。一种常见的策略是在插补模型中包含特定于群集的固定效应，以考虑数据的层次结构。尽管如此，这种特定于群集的固定效应插补方法从未在分析上与随机斜率设置中的同源多层次插补进行比较。在本文中，我们评估了特定于群集的固定效应插补模型对多层次推理的影响。我们从分析上表明，特定于群集的固定效应插补策略通常会偏倚从随机系数模型中获得的推断。随机效应方差和全局固定效应置信区间的偏差取决于群集大小、群内和群间方差的关系以及缺失数据机制。我们使用模拟研究和基于德国国家教育面板研究 (NEPS) 数据的应用程序说明了特定于群集的固定效应插补的负面影响。
