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Prior Sensitivity in Bayesian Structural Equation Modeling for Sparse Factor Loading Structures.

Xinya Liang1

  • 1University of Arkansas, Fayetteville, AR, USA.

Educational and Psychological Measurement
|October 29, 2020
PubMed
Summary
This summary is machine-generated.

Bayesian structural equation modeling with normal priors (BSEM-N) effectively identifies sparse factor loadings. Optimal prior settings balance variable selection accuracy and parameter estimation, especially with minimal cross-loadings.

Keywords:
Bayesian model fitBayesian structural equation modelingprior sensitivitysparse factor loading structurevariable selection

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Area of Science:

  • Statistics
  • Psychometrics
  • Quantitative Psychology

Background:

  • Bayesian structural equation modeling (BSEM) is a powerful technique for analyzing complex data structures.
  • Estimating sparse factor loading structures, where most cross-loadings are zero, is crucial for accurate model interpretation.
  • The performance of BSEM with normal priors (BSEM-N) for variable selection and parameter estimation requires careful examination.

Purpose of the Study:

  • To investigate the prior sensitivity of Bayesian structural equation modeling with normal priors (BSEM-N).
  • To evaluate BSEM-N's effectiveness in variable selection and parameter estimation for sparse factor loading structures.
  • To determine optimal prior settings for balancing model fit, parameter recovery, and selection accuracy.

Main Methods:

  • A simulation study (Study 1) assessed prior sensitivity using various shrinkage and noninformative priors on cross-loadings and other parameters.
  • Model fit, population model recovery, true/false positive rates, and parameter estimation were key evaluation metrics.
  • An empirical example (Study 2) illustrated the impact of different priors on real-world data.

Main Results:

  • Shrinkage priors with 95% credible intervals that narrowly encompassed population cross-loading values yielded the best true and false positive rates.
  • Variable selection is most effective with sparse cross-loading structures, minimal nontrivial cross-loadings, and high primary loadings.
  • Larger prior variances improve parameter estimates, but BSEM-N with zero-mean priors is not recommended for large cross-loadings.

Conclusions:

  • BSEM-N offers a flexible approach for exploring and estimating sparse factor loading structures.
  • Careful selection of shrinkage priors is essential for optimizing variable selection and parameter estimation.
  • The study provides guidance on choosing priors to enhance the reliability and accuracy of BSEM analyses.