Empirical Bayes Meta-Analysis

As interest in quantitative research synthesis grows, investigators increasingly seek to use information about study features—study contexts, designs, treatments, and subjects—to account for variation in study outcomes. To facilitate analysis of diverse study findings, a mixed linear model with fixed and random effects is presented and illustrated with data from teacher expectancy experiments. This strategy enables the analyst to (a) estimate the variance of the effect size parameters by means of maximum likelihood; (b) pose a series of linear models to explain the effect parameter variance; (c) use information about study characteristics to derive improved empirical Bayes estimates of individual study effect sizes; and (d) examine the sensitivity of all substantive inferences to likely errors in the estimation of variance components.