When fixed and random effects mismatch: Another case of inflation of evidence in non-maximal models

Mixed-effects models that include both fixed and random effects are widely used in the cognitive sciences because they are particularly suited to the analysis of clustered data. However, testing hypotheses about fixed effects in the presence of random effects is far from straightforward and a set of best practices is still lacking. In the target article, van Doorn et al. (2021) examined how Bayesian hypothesis testing with mixed-effects models is impacted by particular model specifications. Here, I extend their work to the more complex case of multiple correlated predictors, such as a predictor of interest and a covariate. I show how non-maximal models can display 'mismatches' between fixed and random effects, which occur when a model includes random slopes for the effect of interest, but fails to include them for those predictors that correlate with the effect of interest. Bayesian model comparisons with synthetic data revealed that such mismatches can lead to an underestimation of random variance and to inflated Bayes factors. I provide specific recommendations for resolving mismatches of this type: fitting maximal models, eliminating correlations between predictors, and residualising the random effects. Data and code are publicly available in an OSF repository at https://osf.io/njaup.