Bayesian estimation for the random moderation model: effect size, coverage, power of test, and type І error

The random moderation model (RMM) was developed based on a two-level regression to cope with heteroscedasticity in analysis, and normal-distributed-based maximum likelihood (NML) estimation estimate the RMM. To present an alternative NML, this article discusses effectiveness of Bayesian for RMM, aiming explore more practical method using popular software Mplus. Through simulation study, RMM investigated compared (ML) estimations, including NML default ML results indicated that approach outperformed two estimations. It showed (a) higher accuracy effect size effect; (b) 95% credibility interval coverage true value (c) well-controlled stable type I error rates, while powers comparable estimations were provided.