Reliability of Bayesian mixed-effects estimates when frequentist models fail to converge

Ascertain whether Bayesian mixed-effects models implemented via brms/Stan provide reliable estimates of random effects in scenarios where frequentist mixed-effects methods, such as lme4, fail to converge, by establishing theoretical guarantees and/or conducting systematic simulation studies.

Background

Within acoustic phonetics and sociophonetics, linear mixed-effects models are widely used. Bayesian approaches (e.g., brms/Stan) have grown in popularity, partly due to their flexibility and the practical advantage that they can return parameter estimates even when frequentist software (e.g., lme4) reports non-convergence.

The authors explicitly note that, despite this practical convenience, it is not clearly established whether such Bayesian estimates are reliable in these non-convergent cases, highlighting a gap in current theoretical and empirical understanding.