Fixed effects and variance components estimation in three-level meta-analysis

Meta-analytic methods have been widely applied to education, medicine, and the social sciences. Much of meta-analytic data are hierarchically structured since effect size estimates are nested within studies, and in turn studies can be nested within level-3 units such as laboratories or investigators, and so forth. Thus, multilevel models are a natural framework for analyzing meta-analytic data. This paper discusses the application of a Fisher scoring method in two- and three-level meta-analysis that takes into account random variation at the second and at the third levels. The usefulness of the model is demonstrated using data that provide information about school calendar types. SAS proc mixed and HLM can be used to compute the estimates of fixed effects and variance components.