Often, primary studies that are pooled in a meta-analysis provide information on several outcomes of interest. Multivariate meta-analysis allows to analyze these outcomes simultaneously and model their relationship, and in addition can be more efficient than separate, univariate meta-analyses. However, standard multivariate meta-analysis models typically assume that the between-study variances and correlations are constant across studies. While it is possible to relax this assumption of constant heterogeneity by using location-scale models in univariate meta-analysis, extensions to the multivariate case have not yet been proposed. Here, we fill this gap by describing a location-scale model for the multivariate setting where both the between-study variances of the different outcomes and the correlations between them can depend on covariates. We examine its performance in a simulation study, where we compare univariate and bivariate location-scale models and different estimation methods. In addition, we show how to apply this model to data from a meta-analysis on the effects of motivational reading instruction on reading achievement and motivation. We discuss the implications of our findings for further research on meta-analysis of multiple outcomes and provide recommendations for the use of multivariate location-scale meta-analysis in applications.
Jansen et al. (Thu,) studied this question.