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

Huub Hoofs*, Rens van de Schoot, Nicole W. H. Jansen, IJmert Kant

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

31 Citations (Web of Science)

Abstract

Bayesian confirmatory factor analysis (CFA) offers an alternative to frequentist CFA based on, for example, maximum likelihood estimation for the assessment of reliability and validity of educational and psychological measures. For increasing sample sizes, however, the applicability of current fit statistics evaluating model fit within Bayesian CFA is limited. We propose, therefore, a Bayesian variant of the root mean square error of approximation (RMSEA), the BRMSEA. A simulation study was performed with variations in model misspecification, factor loading magnitude, number of indicators, number of factors, and sample size. This showed that the 90% posterior probability interval of the BRMSEA is valid for evaluating model fit in large samples (N 1,000), using cutoff values for the lower (<.05) and upper limit (<.08) as guideline. An empirical illustration further shows the advantage of the BRMSEA in large sample Bayesian CFA models. In conclusion, it can be stated that the BRMSEA is well suited to evaluate model fit in large sample Bayesian CFA models by taking sample size and model complexity into account.
Original languageEnglish
Pages (from-to)537-568
Number of pages32
JournalEducational and Psychological Measurement
Volume78
Issue number4
DOIs
Publication statusPublished - 1 Aug 2018

Keywords

  • Bayesian procedures
  • factor analysis
  • model fit
  • validity
  • simulation
  • STRUCTURAL EQUATION MODELS
  • JOB CONTENT QUESTIONNAIRE
  • GOODNESS-OF-FIT
  • INDEXES
  • RMSEA
  • SIZE
  • MISSPECIFICATION
  • RELIABILITY
  • SENSITIVITY
  • VALIDITY

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