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