Benefits of Bayesian Model Averaging for Mixed-Effects Modeling

Abstract

Bayes factors allow researchers to test the effects of experimental manipulations in within-subjects designs using mixed-effects models. van Doorn et al. (2021) showed that such hypothesis tests can be performed by comparing different pairs of models which vary in the specification of the fixed- and random-effect structure for the within-subjects factor. To discuss the question of which model comparison is most appropriate, van Doorn et al. compared three corresponding Bayes factors using a case study. We argue that researchers should not only focus on pairwise comparisons of two nested models but rather use Bayesian model selection for the direct comparison of a larger set of mixed models reflecting different auxiliary assumptions regarding the heterogeneity of effect sizes across individuals. In a standard one-factorial, repeated measures design, the comparison should include four mixed-effects models: fixed-effects H0, fixed-effects H1, random-effects H0, and random-effects H1. Thereby, one can test both the average effect of condition and the heterogeneity of effect sizes across individuals. Bayesian model averaging provides an inclusion Bayes factor which quantifies the evidence for or against the presence of an average effect of condition while taking model selection uncertainty about the heterogeneity of individual effects into account. We present a simulation study showing that model averaging among a larger set of mixed models performs well in recovering the true, data-generating model.