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Area of Science:

  • Statistics
  • Psychometrics
  • Computational Statistics

Background:

  • Frequentist structural equation modeling (SEM) uses chi-square tests and approximate fit indices for model evaluation.
  • Current Bayesian SEM (BSEM) primarily relies on posterior predictive p-values (PPP χ2) or model comparison criteria, with limitations in PPP χ2.
  • Existing fit indices developed for frequentist methods are not readily available in BSEM software.

Purpose of the Study:

  • To adapt seven chi-square-based approximate fit indices for use in Bayesian SEM.
  • To provide a Bayesian analog of the chi-square model-fit statistic for evaluating overall model fit.
  • To enable the use of familiar fit metrics within the BSEM framework.

Main Methods:

  • Adapted seven frequentist chi-square-based approximate fit indices for BSEM.
  • Developed a Bayesian analog of the chi-square model-fit statistic.
  • Evaluated the performance of the adapted indices using simulation studies across various sample sizes, model types, and misspecification levels.

Main Results:

  • The sampling distributions of the posterior means of the adapted fit indices closely resemble their frequentist counterparts when using noninformative priors.
  • The proposed indices provide a means for overall model-fit evaluation in BSEM using established metrics.
  • An accompanying interval quantifies the uncertainty associated with the proposed fit indices.
  • Application to models with informative priors may yield different results compared to frequentist methods.

Conclusions:

  • Adapted chi-square-based fit indices are viable for evaluating overall model fit in BSEM, particularly with noninformative priors.
  • These indices offer a familiar metric for Bayesian model assessment, complementing existing methods.
  • Caution is advised when applying these indices to models with informative priors due to potential discrepancies with frequentist approaches.