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Dealing with Reflection Invariance in Bayesian Factor Analysis.

Elena A Erosheva1, S McKay Curtis2

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Summary
This summary is machine-generated.

This study addresses reflection unidentifiability in Bayesian confirmatory factor analysis (CFA). A novel relabeling algorithm is proposed to resolve multimodality issues in Bayesian factor analysis models.

Keywords:
Markov chain Monte Carloidentifiability constraintslabel-switchingrelabelingrotationrotational invariance

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Area of Science:

  • Psychometrics
  • Statistical Modeling
  • Bayesian Inference

Background:

  • Confirmatory Factor Analysis (CFA) models can suffer from reflection unidentifiability.
  • This issue leads to multimodality in Bayesian estimation, complicating interpretation.
  • Existing methods may not fully resolve this problem in complex models.

Purpose of the Study:

  • To introduce a simple and generalizable approach for handling reflection unidentifiability in Bayesian factor analysis.
  • To provide a method that leverages the analogy with finite mixture models.
  • To facilitate accurate Bayesian estimation and interpretation of CFA models.

Main Methods:

  • Drawing an analogy between CFA sign changes and finite mixture model relabeling.
  • Developing a relabeling algorithm to address posterior multimodality.
  • Fitting Bayesian factor analysis models without rotational constraints on loadings.
  • Utilizing Markov chain Monte Carlo (MCMC) to explore the full posterior distribution.

Main Results:

  • A straightforward algorithm is presented for resolving reflection unidentifiability in Bayesian factor analysis.
  • The method effectively handles multimodality arising from sign invariance.
  • Demonstrated effectiveness on a bifactor model, with potential for generalization.

Conclusions:

  • The proposed relabeling algorithm offers a practical solution for reflection unidentifiability in Bayesian CFA.
  • This approach enhances the reliability of Bayesian factor analysis estimation.
  • The method is adaptable to various factor analysis models with similar identifiability issues.