Using multiple group modeling to test moderators in meta-analysis.

Meta-analysis is a popular and flexible analysis that can be fit in many modeling frameworks. Two methods of fitting meta-analyses that are growing in popularity are structural equation modeling (SEM) and multilevel modeling (MLM). By using SEM or MLM to fit a meta-analysis researchers have access to powerful techniques associated with SEM and MLM. This paper details how to use one such technique, multiple group analysis, to test categorical moderators in meta-analysis. In a multiple group meta-analysis a model is fit to each level of the moderator simultaneously. By constraining parameters across groups any model parameter can be tested for equality. Using multiple groups to test for moderators is especially relevant in random-effects meta-analysis where both the mean and the between studies variance of the effect size may be compared across groups. A simulation study and the analysis of a real data set are used to illustrate multiple group modeling with both SEM and MLM. Issues related to multiple group meta-analysis and future directions for research are discussed.