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Bayesian Multilevel Mediation: Evaluation of Inaccurate Priors in Latent 1-1-1 Designs

Abstract When latent constructs are measured by observed indicators from individuals nested within groups, multilevel structural equation modeling (MSEM) for 1-1-1 mediation designs allows researchers to simultaneously test indirect effects at each level of the data structure. However, with small samples (i.e., few clusters and/or small cluster sizes), such complex mediation models often run into estimation problems like nonconvergence, biased estimates, and insufficient power. Although Bayesian estimation with accurate informative priors can help alleviate these problems, it is unrealistic in practice to assume priors are correctly specified at the true population value. This study evaluates the performance of inaccurate (informative) priors in 1-1-1 MSEM mediation under varying sample sizes, ICCs, and effect sizes. Results indicate that while within-level indirect effect estimates are somewhat robust to inaccurate priors, between-level estimates are severely impacted, especially at small sample sizes. Implications and recommendations for conducting 1-1-1 MSEM mediation with Bayesian methods are discussed.