Multilevel meta-analysis of multiple regression coefficients from single-case experimental studies
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Multilevel meta-analysis of multiple regression coefficients from single-case experimental studies Laleh Jamshidi 1,2 & Lies Declercq 1 & Belén Fernández-Castilla 1 & John M. Ferron 3 & Mariola Moeyaert 4 & S. Natasha Beretvas 5 & Wim Van den Noortgate 1
# The Psychonomic Society, Inc. 2020
Abstract The focus of the current study is on handling the dependence among multiple regression coefficients representing the treatment effects when meta-analyzing data from single-case experimental studies. We compare the results when applying three different multilevel meta-analytic models (i.e., a univariate multilevel model avoiding the dependence, a multivariate multilevel model ignoring covariance at higher levels, and a multivariate multilevel model modeling the existing covariance) to deal with the dependent effect sizes. The results indicate better estimates of the overall treatment effects and variance components when a multivariate multilevel model is applied, independent of modeling or ignoring the existing covariance. These findings confirm the robustness of multilevel modeling to misspecifying the existing covariance at the case and study level in terms of estimating the overall treatment effects and variance components. The results also show that the overall treatment effect estimates are unbiased regardless of the underlying model, but the between-case and between-study variance components are biased in certain conditions. In addition, the between-study variance estimates are particularly biased when the number of studies is smaller than 40 (i.e., 10 or 20) and the true value of the between-case variance is relatively large (i.e., 8). The observed bias is larger for the between-case variance estimates compared to the between-study variance estimates when the true between-case variance is relatively small (i.e., 0.5). Keywords Single-case experimental design . Multilevel meta-analysis . Multivariate multilevel model . Robust variance estimator
Introduction Single-case experimental designs (SCEDs) have been frequently used in many different fields such as psychology, education, social sciences, and medical sciences to establish evidence-based practices. In this kind of design, the outcome * Laleh Jamshidi [email protected] 1
Faculty of Psychology and Educational Sciences & ITEC, imec research group at KU Leuven, KU Leuven, University of Leuven, Leuven, Belgium
2
Canadian Institute for Public Safety Research and Treatment (CIPSRT), University of Regina, Regina, Canada
3
Department of Educational Measurement and Research, University of South Florida, Tampa, FL, USA
4
Department of Educational and Counseling Psychology, University at Albany (State University of New York), Albany, NY, USA
5
Department of Educational Psychology, University of Texas at Austin, Austin, TX, USA
of interest is measured repeatedly over time prior to and during or after the treatment. Afterwards, scores under these conditions (pre and post treatment) can be compared to evaluate treatment effectiveness (Horner et al., 2005
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