Multiple imputation of missing data in multilevel research
Multilevel models are one of the most frequently used methods for analyzing multilevel data. These types of data occur when observations (Level 1) are clustered within higher-level collectives (Level 2), for example, students nested in schools or employees nested in work teams. Unfortunately, multilevel data often contain missing data, for example, when participants omit certain items in a questionnaire or they drop out before the end of a study. If treated improperly, missing data can distort parameter estimates and compromise statistical decision making. For this reason, it is often recommended to use principled methods for dealing with missing data such as multiple imputation (MI) or maximum likelihood estimation (ML). In the present dissertation, I consider the treatment of missing data with an emphasis on multilevel MI. In multilevel research, it is important that the imputation model takes the multilevel structure into account. However, many open questions remain about how this can be achieved in practice. In multiple studies, I considered different implementations of multilevel MI and examined how missing data can be treated in multilevel models with random intercepts, random slopes, interaction effects, continuous and categorical data, and missing data at Level 2. In addition, I considered the analysis of multiply imputed data sets and examined different procedures for pooling the results of multiparameter tests (e.g., model comparisons), including applications in the analysis of variance (ANOVA) and multilevel models with tests about fixed effects and variance components. Finally, I present the R package mitml, which provides a set of practical tools for conducting multilevel MI. This includes tools for the specification of the imputation model, convergence diagnostics, analyzing multiply imputed data sets, and various pooling methods along with a tutorial article that illustrates its features and provides a nontechnical introduction to multilevel MI.