Evaluating the Bayes Factor under Model Misspecification in Repeated-Measures Designs

We evaluate the performance of the Bayes factor under model misspecification, with a focus on violations of compound symmetry and deviations from the normality assumption in repeated-measures designs. Simulation studies reveal that a paradox—discrepancies between inferences drawn from classical repeated-measures analysis of variance (rANOVA) and Bayesian analyses using Bayes factors with random intercept-only models—can arise under certain model misspecifications. We argue that the underlying misspecifications are best viewed as manifestations of covariance heterogeneity, rather than the existence of individual differences (random slopes) in the effects of independent variables. Our results demonstrate that models with both random intercepts and slopes effectively mitigate such discrepancies. We elucidate the rationale for adopting random-slope models as a means of accommodating a more complex marginal covariance structure than is assumed by a random intercept-only model. This study supports recent recommendations advocating the use of random intercept and slope models in analyzing repeated-measures data and explains the theoretical foundations of their effectiveness. We additionally substantiate that Bayes factors are generally robust to misspecifications in the distributions of random effects and residuals in linear mixed-effects models. We present a theorem demonstrating model selection consistency of the Bayes factor under model misspecification for the simple case of a one-sample t-test.