Reformulating the Meta-analytical Random Effects Model as a Mixture Model

Abstract

The “traditional” random-effects model (REM) in meta-analysis was formulated as a variance-components model, based on the work of Cochrane and Hedges. It has been accepted routinely although it is known that has several defects, because it is conventionally accepted that the impact of those flaws is negligible. It is especially important in effect size indices whose conditional sampling variance is a function of the effect size itself. We describe an alternative formulation of the REM, as a mixture model. We have derive formulas for the expected value, the variance, and the skewness of the marginal distribution of g. They can be used to improve meta analytical techniques, as they provide very accurate predictions. Our main conclusion is that the mixture model is a more correct, flexible, and elegant way to formulate the REM