The application of meta-analytic (multi-level) models with multiple random effects: A systematic review
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The application of meta-analytic (multi-level) models with multiple random effects: A systematic review Belén Fernández-Castilla 1,2 Wim Van den Noortgate 1,2
&
Laleh Jamshidi 1,2 & Lies Declercq 1,2 & S. Natasha Beretvas 3 & Patrick Onghena 1 &
# The Psychonomic Society, Inc. 2020
Abstract In meta-analysis, study participants are nested within studies, leading to a multilevel data structure. The traditional random effects model can be considered as a model with a random study effect, but additional random effects can be added in order to account for dependent effects sizes within or across studies. The goal of this systematic review is three-fold. First, we will describe how multilevel models with multiple random effects (i.e., hierarchical three-, four-, five-level models and cross-classified random effects models) are applied in meta-analysis. Second, we will illustrate how in some specific three-level meta-analyses, a more sophisticated model could have been used to deal with additional dependencies in the data. Third and last, we will describe the distribution of the characteristics of multilevel meta-analyses (e.g., distribution of the number of outcomes across studies or which dependencies are typically modeled) so that future simulation studies can simulate more realistic conditions. Results showed that four- or five-level or cross-classified random effects models are not often used although they might account better for the meta-analytic data structure of the analyzed datasets. Also, we found that the simulation studies done on multilevel metaanalysis with multiple random factors could have used more realistic simulation factor conditions. The implications of these results are discussed, and further suggestions are given. Keywords Systematic review . meta-analysis . multiple effect sizes . multilevel models In any scientific discipline, it is common to find units that are nested in higher-level clusters. An example in educational research is the nesting of children in classrooms. Children from the same classroom are exposed to common stimuli that might make their behavior in general more alike than the behavior of children from different classrooms. Examples of clustered data structures in biology or medicine are animals clustered in phylogenetic families, or patients nested within hospitals. This nesting of observations within higher-level clusters involves the possible existence of dependency among Electronic supplementary material The online version of this article (https://doi.org/10.3758/s13428-020-01373-9) contains supplementary material, which is available to authorized users. * Belén Fernández-Castilla [email protected] 1
Faculty of Psychology and Educational Sciences, KU Leuven, University of Leuven, Etienne Sabbelaan 51, 8500 Kortrijk, Belgium
2
ITEC, imec research group at KU Leuven, University of Leuven, Leuven, Belgium
3
University of Texas at Austin, Austin, TX, USA
observations. That is, each observation does not give unique information, and not taking this interd
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