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Evaluating Model Fit in Bayesian Confirmatory Factor Analysis With Large Samples: Simulation Study Introducing the

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A new Bayesian Root Mean Square Error of Approximation (BRMSEA) statistic is introduced for evaluating model fit in large samples. This Bayesian confirmatory factor analysis (CFA) tool enhances the assessment of reliability and validity in psychological and educational measures.

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Bayesian proceduresfactor analysismodel fitsimulationvalidity

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Area of Science:

  • Psychometrics
  • Statistical Modeling

Background:

  • Frequentist confirmatory factor analysis (CFA) is widely used for assessing psychometric properties.
  • Current fit statistics in Bayesian CFA have limitations with increasing sample sizes.
  • There is a need for robust model fit evaluation in large-sample Bayesian analyses.

Purpose of the Study:

  • To propose and validate a Bayesian variant of the Root Mean Square Error of Approximation (RMSEA), termed BRMSEA.
  • To assess the performance of BRMSEA in evaluating model fit across various conditions in large samples.
  • To provide a reliable tool for model fit assessment in Bayesian CFA.

Main Methods:

  • A simulation study was conducted manipulating model misspecification, factor loading magnitude, number of indicators, number of factors, and sample size.
  • The 90% posterior probability interval of the proposed BRMSEA was analyzed.
  • An empirical illustration was used to demonstrate the practical application of BRMSEA.

Main Results:

  • The 90% posterior probability interval of the BRMSEA demonstrates validity for model fit evaluation in large samples (N≥1,000).
  • Recommended cutoff values for the BRMSEA interval are <.05 for the lower limit and <.08 for the upper limit.
  • The BRMSEA effectively accounts for sample size and model complexity in large-sample Bayesian CFA.

Conclusions:

  • The BRMSEA is a suitable statistic for evaluating model fit in large-sample Bayesian CFA.
  • This new metric enhances the assessment of reliability and validity for educational and psychological measures.
  • BRMSEA addresses the limitations of existing fit statistics in large-scale Bayesian analyses.