One common question about multivariate/multi-level meta-analysis is how such models assign weight to individual effect size estimates. When a version of the question came up recently on the R-sig-meta-analysis listserv, Dr. Wolfgang Viechtbauer offered a whole blog post in reply, demonstrating how weights work in simpler fixed effect and random effects meta-analysis and then how things get more complicated in multivariate models. In this post, I'll try to add some further intuition on how weights work in certain multivariate meta-analysis models. Most of the discussion will apply to models that include multiple level of random effects, but no predictors. I'll also comment briefly on meta-regression models with only study-level predictor variables, and finally give some pointers to work on more complicated models.
I’m just back from the Society for Research on Educational Effectiveness meetings, where I presented work on small-sample corrections for cluster-robust variance estimators in two-stage least squares models, which I’ve implemented in the clubSandwich R package.
In settings with independent observations, sample size is one way to quickly characterize the precision of an estimate. But what if your estimate is based on weighted data, where each observation doesn’t necessarily contribute to equally to the estimate?