Location-scale models for meta-analysis

Heterogeneity is commonplace in meta-analysis. When heterogeneity is found, researchers often aim to identify predictors that account for at least part of such heterogeneity by using mixed-effects meta-regression models. Another potentially relevant goal is to focus on the amount of heterogeneity as a function of one or more predictors, but this cannot be examined with standard random- and mixed-effects models, which assume a constant (i.e., homoscedastic) value for the heterogeneity variance component across studies. In this paper, we describe a location-scale model for meta-analysis as an extension of the standard random- and mixed-effects models that not only allows an examination of whether predictors are related to the size of the outcomes (i.e., their location), but also the amount of heterogeneity (i.e., their scale). We present estimation methods for such a location-scale model through maximum and restricted maximum likelihood approaches, as well as methods for inference and suggestions for visualization. We also provide an implementation via the metafor package for R that makes this model readily available to researchers. Location-scale models can provide a useful tool to researchers interested in heterogeneity in meta-analysis, with the potential to enhance the scope of research questions in the field of evidence synthesis.