Multiple imputation of multilevel data with single-level models: A fully conditional specification approach using adjusted group means.

Missing data are a common challenge in multilevel designs, and multiple imputation (MI) is often used for handling them. Past research has shown that multilevel MI provides an effective treatment of missing data, so long as the imputation model takes the multilevel structure and the intended analyses into account, and modern methods have been developed that can accommodate even complex types of analyses. However, multilevel MI can be difficult to apply in practice, where the multilevel structure is often not very pronounced or not of immediate interest in the analysis. In these applications, existing methods can become unstable and often struggle to provide reliable results. In this article, we introduce a fully conditional specification (FCS) approach to multilevel MI that combines single-level imputation methods with group means (GM) or adjusted group means (AGM) to accommodate the multilevel structure. Based on theoretical investigations and multiple simulation studies, we evaluated the performance of these methods across balanced and unbalanced designs and with larger numbers of variables. Our findings suggest that the AGM approach - though not the GM approach - performs well across most scenarios we investigated and can even outperform conventional multilevel MI approaches in challenging applications. We also provide an illustrative example of implementing these methods in a simulated setting and discuss the implications of our findings for practice.