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Area of Science:

  • Psychometrics
  • Statistical Modeling
  • Quantitative Psychology

Background:

  • Frequentist model fit indices (MFIs) and Bayesian model selection criteria (MCC) are used for cross-loading selection in factor analysis.
  • Performance varies under different sample sizes, cross-loading magnitudes, and distributional assumption violations.

Purpose of the Study:

  • To compare the performance of frequentist MFIs and Bayesian MCC for cross-loading selection in factor analysis.
  • To evaluate their effectiveness under various simulation conditions.

Main Methods:

  • Simulations were conducted comparing Bayes factor (BF), Bayesian Information Criterion (BIC), Deviance Information Criterion (DIC), leave-one-out with Pareto smoothed importance sampling (LOO-PSIS), and spike-and-slab prior (SSP) methods.
  • Frequentist methods included likelihood ratio tests (LRTs), root mean squared error of approximation (RMSEA), and Tucker-Lewis index (TLI).

Main Results:

  • BF and BIC demonstrated the best balance of true and false positive rates among Bayesian criteria, followed by SSP.
  • LOO-PSIS and DIC had the highest true positive rates but also elevated false positive rates.
  • LRTs were preferred frequentist tools, but BF, BIC, and SSP showed lower false positive rates under distributional assumption violations.

Conclusions:

  • Bayesian criteria, particularly BF and BIC, offer a robust approach to cross-loading selection in factor analysis, especially when distributional assumptions are violated.
  • Frequentist indices like RMSEA and TLI impose stricter penalties on model complexity, offering an alternative when models are not nested.