A Bayesian solution to non-convergence of crossed random effects models

Crossed random effects models can simultaneously take into account both fixed effects and random effects of the subjects and stimuli when observations are nested within combinations of subjects and stimuli. Unfortunately, maximum likelihood estimation (MLE) and restricted maximum likelihood (REML) estimation often encounter convergence problems, which in turn lead researchers to fit simpler models that yield invalid statistical inferences. On the other hand, if the random effects structure is too simple, tests of fixed effects are not valid; if the random effect structure is too complex, tests of fixed effects are inefficient. This study examines non-convergence issues inherent with MLE and REML as well as whether using Bayesian estimation can solve estimation problems when using crossed random effects models.