The Influence of Using Inaccurate Priors on Bayesian Multilevel Estimation

Researchers in psychology, education, and organizational behavior often encounter multilevel data with hierarchical structures. Bayesian approach is usually more advantageous than traditional frequentist-based approach in small sample sizes, but it is also more susceptible to the subjective specification of priors. To investigate the potentially detrimental effects of inaccurate prior information on Bayesian approach and compare its performance with that of traditional method, a series of simulations was conducted under a multilevel model framework with different settings. The results reveal the devastating impacts of inaccurate prior information on Bayesian estimation, especially in the cases of larger intraclass correlation coefficient, smaller level 2 sample size, and smaller prior variance. When the dependent variable is non-normal or binary, these negative effects are more noticeable. The present study investigated the impacts of inaccurate prior information and provides advice on the specification of priors.