A Model-Based Imputation Procedure for Multilevel Regression Models With Random Coefficients, Interaction Effects, and Nonlinear 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 article is to extend model-based imputation to multilevel models with up to 3 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 article includes a data analysis example illustrating its use. Translational Abstract Multiple imputation is a missing data handling technique that creates several copies of the incomplete data, each with different estimates of the missing values. The researcher analyzes each data set, and the resulting estimates and standard errors are averaged into a single set of results. The primary goal of this paper was to outline a novel multiple imputation approach to multilevel analyses with interactive effects. Multilevel data are exceedingly common throughout psychology and the behavioral sciences, examples of such nested data structures include children within classrooms, individuals within families, employees within workgroups, and repeated measurements within individuals, to name a few. Interactive effects are equally common and occur when the magnitude of an association between two variables is modified by a third variable. Most popular current approaches to handling multilevel missing data produced biased estimates of interactive effects, and our approach addresses this important practical problem. The study used computer simulation to create many artificial data sets with missing values, after which it imputed each data s