Advances in meta-analysis: A unifying modelling framework with measurement error correction

In psychological studies, multivariate outcomes measured on the same individuals are often encountered. Effects originating from these outcomes are consequently dependent. Multivariate meta-analysis examines the relationships of multivariate outcomes by estimating the mean effects and their variance-covariance matrices from series of primary studies. In this paper we discuss a unified modelling framework for multivariate meta-analysis that also incorporates measurement error corrections. We focus on two types of effect sizes, standardized mean differences (d) and correlations (r), that are common in psychological studies. Using generalized least squares estimation, we outline estimated mean vectors and variance-covariance matrices for d and r that are corrected for measurement error. Given the burgeoning research involving multivariate outcomes, and the largely overlooked ramifications of measurement error, we advocate addressing measurement error while conducting multivariate meta-analysis to enhance the replicability of psychological research.