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A Note on Comparing the Bifactor and Second-Order Factor Models: Is the Bayesian Information Criterion a Routinely

Tenko Raykov1, Christine DiStefano2, Lisa Calvocoressi3

  • 1Michigan State University, East Lansing, USA.

Educational and Psychological Measurement
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Summary
This summary is machine-generated.

The Bayesian Information Criterion (BIC) may not reliably select between bifactor and second-order factor models. Researchers should exercise caution, as BIC may incorrectly favor the second-order model even when data fits the bifactor model.

Keywords:
Bayesian information criterionbifactor modelconfirmatory factor analysismodel selectionsecond-order factor model

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Area of Science:

  • Psychometrics
  • Statistical Modeling

Background:

  • The Bayesian Information Criterion (BIC) is commonly used for model selection in statistical analysis.
  • Bifactor and second-order factor models are frequently employed to explain the structure of multidimensional data.

Purpose of the Study:

  • To evaluate the dependability of the BIC for distinguishing between bifactor and second-order factor models.
  • To investigate potential discrepancies in BIC-based model selection when data is generated from a bifactor structure.

Main Methods:

  • Simulated data generation following a bifactor model across various sample sizes.
  • Comparison of model fit indices, specifically BIC, for both bifactor and second-order factor models.

Main Results:

  • The bifactor model was consistently found to be inferior to the second-order model based on BIC values.
  • This occurred despite the data being generated from the bifactor model in numerous replications.

Conclusions:

  • Routine reliance on BIC for model selection between bifactor and second-order models can be misleading.
  • Researchers should be aware of BIC's limitations in accurately identifying the data-generating model in these specific contexts.