A Model-Based Imputation Procedure for Multilevel Regression Models with Random Coefficients, Interaction Effects, and Non-Linear Terms

Despite the broad appeal of missing data handling approaches that assume a missing at random (MAR) mechanism (e.g., multiple imputation and maximum likelihood estimation), some very common analysis models in the behavioral science literature are known to cause bias-inducing problems for these approaches. Regression models with incomplete interactive or polynomial effects are a particularly important example because they are among the most common analyses in behavioral science research applications. In the context of single-level regression, fully Bayesian (model-based) imputation approaches have shown great promise with these popular analysis models. The purpose of this paper is to extend model-based imputation to multilevel models with up to three levels, including functionality for mixtures of categorical and continuous variables. Computer simulation results suggest that this new approach can be quite effective when applied to multilevel models with random coefficients and interaction effects. In most scenarios that we examined, imputation-based parameter estimates were quite accurate and tracked closely with those of the complete data. The new procedure is available in the Blimp software application for macOS, Windows, and Linux, and the paper includes a data analysis example illustrating its use. [This is the online version of an article published in "Psychological Methods."]