Meta-Analysis of Single-Case Design Research: Application of Multilevel Modeling

This study describes the benefits and challenges of meta-analyses of single-case design research using multilevel modeling. The researchers illustrate procedures for conducting meta-analyses using four-level multilevel modeling through open-source R code. The demonstration uses data from multiple-baseline or multiple-probe across-participant single-case design studies (n = 21) on word problem instruction for students with learning disabilities published between 1975 and 2023. Researchers explore changes in levels and trends between adjacent phases (baseline vs. intervention and intervention vs. maintenance) using the sample data. The researchers conclude that word problem solving of students with learning disabilities varies based on the complexity of the word problem measures involving single-word problem, mixed-word problem, and generalization questions. These moderating effects differed across adjacent phases. These findings extend previous literature on meta-analyses methodology by describing how multilevel modeling can be used to compare the impacts of time-varying predictors within and across cases when analyzing single-case design studies. Future researchers may want to use this methodology to explore the roles of time-varying predictors as well as case or study-level moderators.