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Research on multilevel models using Bayesian analysis is lacking, even though the Bayesian approach offers more benefits than the frequentist approach. In this study, a 2-1-1 multilevel structural equation modeling (MSEM) was analyzed via the Bayesian method. Based on a simulation study, the performance of nine different priors was analyzed depending on intraclass correlation (ICC) values. It was found that, as the ICC value increased, the performance of all priors tended to improve. However, it was not possible to conclude that certain priors performed better than other priors or the robust maximum likelihood estimator.