Grund Simon, Lüdtke Oliver, Robitzsch Alexander
Centre for International Student Assessment, Leibniz Institute for Science and Mathematics Education, Kiel, Germany.
Innovation and Development of the Austrian School System, Federal Institute for Education Research, Salzburg, Austria.
Behav Res Methods. 2016 Jun;48(2):640-9. doi: 10.3758/s13428-015-0590-3.
Multiple imputation (MI) has become one of the main procedures used to treat missing data, but the guidelines from the methodological literature are not easily transferred to multilevel research. For models including random slopes, proper MI can be difficult, especially when the covariate values are partially missing. In the present article, we discuss applications of MI in multilevel random-coefficient models, theoretical challenges posed by slope variation, and the current limitations of standard MI software. Our findings from three simulation studies suggest that (a) MI is able to recover most parameters, but is currently not well suited to capture slope variation entirely when covariate values are missing; (b) MI offers reasonable estimates for most parameters, even in smaller samples or when its assumptions are not met; and
多重填补（MI）已成为处理缺失数据的主要方法之一，但方法学文献中的指南不易应用于多层次研究。对于包含随机斜率的模型，恰当的多重填补可能会很困难，尤其是当协变量值部分缺失时。在本文中，我们讨论了多重填补在多层次随机系数模型中的应用、斜率变化带来的理论挑战以及标准多重填补软件目前的局限性。我们三项模拟研究的结果表明：（a）多重填补能够恢复大多数参数，但当协变量值缺失时，目前还不太适合完全捕捉斜率变化；（b）即使在较小样本或假设不成立的情况下，多重填补对大多数参数也能提供合理的估计；并且
