Issues and solutions in meta-analysis of single-case design with multiple dependent variables using multilevel modeling

Abstract

It is common to include multiple dependent variables (DVs) in single-case experimental design (SCED) meta-analyses. However, statistical issues associated with multiple DVs in the multilevel modeling approach (i.e., possible dependency of error, heterogeneous treatment effects, and heterogeneous error structures) have not been fully investigated. In this study, we first addressed various issues caused by multiple DVs and examined current modeling practice, then proposed several modeling options for handling multiple DVs and compared their impact on parameter estimates and statistical inferences by conducting both empirical and simulation studies. The results indicated that different modeling options can lead to very different conclusions about the treatment effects, variance components, and model fit. Among the presented modeling options, modeling heterogeneity in the level-1 error structure and adding DV type as moderators had a noticeably large and consistent impact on both fixed and random effects as well as model fit. Although including DV types as an additional level had a relatively small impact compared to the other options, it was still able to alter the conclusion of the statistical inferences on the treatment effects.