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

Dan Wei1,2, Peida Zhan3

  • 1Faculty of Psychology, Beijing Normal University, Beijing, China.

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|July 19, 2023
PubMed
Summary

Bayesian estimation offers a more accurate and reliable method for the random moderation model (RMM) compared to traditional maximum likelihood estimations. This approach provides better effect size accuracy and controlled error rates in moderation analysis.

Keywords:
Bayesian estimationheteroscedasticitymoderation analysisrandom moderation modeltwo-level regression model

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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.