Using information-theoretic approaches for model selection in meta-analysis

Meta-regression can be used to examine the association between effect size estimates and the characteristics of the studies included in a meta-analysis using regression-type methods. By searching for those characteristics (i.e., moderators) that are related to the effect sizes, we seek to identify a model that represents the best approximation to the underlying data generating mechanism. Model selection via testing, either through a series of univariate models or a model including all moderators, is the most commonly used approach for this purpose. Here, we describe alternative model selection methods based on information criteria, multimodel inference, and relative variable importance. We demonstrate their application using an illustrative example and present results from a simulation study to compare the performance of the various model selection methods for identifying the true model across a wide variety of conditions. Whether information-theoretic approaches can also be used not only in combination with maximum likelihood (ML) but also restricted maximum likelihood (REML) estimation was also examined. The results indicate that the conventional methods for model selection may be outperformed by information-theoretic approaches. The latter are more often among the set of best methods across all of the conditions simulated and can have higher probabilities for identifying the true model under particular scenarios. Moreover, their performance based on REML estimation was either very similar to that from ML estimation or at times even better depending on how exactly the REML likelihood was computed. These results suggest that alternative model selection methods should be more widely applied in meta-regression.