Multiple Imputation of Multilevel Missing Data-Rigor versus Simplicity

Multiple imputation is widely accepted as the method of choice to address item-nonresponse in surveys. However, research on imputation strategies for the hierarchical structures that are typically found in the data in educational contexts is still limited. While a multilevel imputation model should be preferred from a theoretical point of view if the analysis model of interest is also a multilevel model, many practitioners prefer a fixed effects imputation model with dummies for the clusters since these models are easy to set up with standard imputation software. In this article, we theoretically and empirically evaluate the impacts of this simplified approach. We illustrate that the cluster effects that are often of central interest in educational research can be biased if a fixed effects imputation model is used. We show that the potential bias depends on three quantities: the amount of missingness, the intraclass correlation, and the cluster size. We argue that the bias for the random effects can be substantial while the bias for the fixed effects will be negligible in most real-data situations. We further illustrate this with an application using data from the German National Educational Panel Survey.