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

Area of Science:

• Statistics
• Psychometrics
• Quantitative Psychology

Background:

• The random moderation model (RMM) addresses heteroscedasticity in moderation analysis using two-level regression.
• Normal-distributed-based maximum likelihood (NML) estimation was previously developed for the RMM.

Purpose of the Study:

• To evaluate the effectiveness of Bayesian estimation as an alternative to NML for the RMM.
• To explore a more practical RMM estimation method using Mplus software.

Main Methods:

• A simulation study was conducted to investigate the RMM.
• Bayesian estimation for RMM was compared against NML and default maximum likelihood (ML) estimations in Mplus.

Main Results:

• Bayesian estimation demonstrated higher accuracy in estimating the moderation effect size.
• The Bayesian approach provided higher 95% credibility interval coverage for the true moderation effect.
• Type I error rates were well-controlled and more stable with Bayesian estimation, while statistical power remained comparable to ML methods.

Conclusions:

• Bayesian estimation is a superior and more practical alternative for estimating the RMM compared to NML and default ML.
• The findings support the use of Bayesian methods for more robust moderation analysis in complex statistical modeling.