Fitting three-level meta-analytic models in R: A step-by-step tutorial

Applying a multilevel approach to meta-analysis is a strong method for dealing with dependency of effect sizes. However, this method is relatively unknown among researchers and, to date, has not been widely used in meta-analytic research. Therefore, the purpose of this tutorial was to show how a three-level random effects model can be applied to meta-analytic models in R using the rma.mv function of the metafor package. This application is illustrated by taking the reader through a step-by-step guide to the multilevel analyses comprising the steps of (1) organizing a data file; (2) setting up the R environment; (3) calculating an overall effect; (4) examining heterogeneity of within-study variance and between-study variance; (5) performing categorical and continuous moderator analyses; and (6) examining a multiple moderator model. By example, the authors demonstrate how the multilevel approach can be applied to meta-analytically examining the association between mental health disorders of juveniles and juvenile offender recidivism. In our opinion, the rma.mv function of the metafor package provides an easy and 2 exible way of applying a multi-level structure to meta-analytic models in R. Further, the multilevel meta-analytic models can be easily extended so that the potential moderating influence of variables can be examined.