When researchers want to analyze results from multiple studies, they use meta-analysis to combine results and estimate an overall effect size. The existing meta suite is used to perform standard and multivariate meta-analysis.
Sometimes the reported effect sizes are nested within higher-level groupings, such as geographical locations (states or countries) or administrative units (school districts). Effect sizes within the same groups (for example, districts) are likely to be similar and thus dependent. In this case, you can use multilevel meta-analysis. The goal of multilevel meta-analysis is to not only synthesize an overall effect size but also account for this dependence and assess the variability among the effect sizes at different hierarchical levels. The new estimation commands meta meregress and meta multilevel are used to perform multilevel meta-analysis.
Say that we have studies reporting effects (mean differences) of two teaching methods on math test scores, y, and sampling standard errors of y in se. The effect sizes are nested within schools, and schools are nested in districts. We can fit a three-level random intercepts model with (. meta meregress y || district: || school:, essevariable(se)) or (. meta multilevel y, relevels(district school) essevariable(se)) .
If we have covariates and want to include random slopes, we can use meta meregress: (meta meregress y x1 x2 || district: x1 x2 || school:, essevariable(se))
After fitting the model, postestimation commands are available for computing multilevel heterogeneity statistics, displaying estimated random-effects covariance matrices, and more.
The syntax is the simplest of any package available. meta meregress is also the most flexible in terms of the constraints that can be applied to the random effects.