Bayesian factor selection in a hybrid approach to confirmatory factor analysis.

Area of Science:

• Psychometrics
• Statistical Modeling
• Health Services Research

Background:

• Confirmatory factor analysis (CFA) utilizes various factor structures like higher-order and bifactor models to investigate latent variables.
• Measured variables can exhibit cross-loadings, small or moderate non-zero loadings on multiple group factors, complicating structural identification.
• Accurate and identifiable latent structures are crucial for evaluating the impact of constructs in CFA models.

Purpose of the Study:

• To discuss identifiability conditions for bifactor models with cross-loadings.
• To implement Bayesian variable selection for bifactor structures incorporating cross-loadings using spike and slab priors.
• To evaluate the performance of the proposed methods in accurately identifying latent structures.

Main Methods:

• Bayesian variable selection with spike and slab priors was employed to allow cross-loadings on bifactor structures.
• Inclusion probabilities for all group factor loadings were assessed, leveraging known structural information.
• A Monte Carlo simulation study was conducted to compare the proposed methods with existing techniques.

Main Results:

• The proposed Bayesian approach demonstrated more accurate identification of latent structures compared to other available methods.
• Application to the SF-12 version 2 scale resulted in a more parsimonious model with superior fit indices.
• The selected model outperformed models using ridge prior selection and strict bifactor models.

Conclusions:

• The developed Bayesian variable selection method effectively handles cross-loadings in bifactor models, enhancing structural identification.
• This approach offers a more parsimonious and better-fitting model for analyzing complex latent variables, as shown with the SF-12 scale.
• The methods provide a robust tool for researchers needing to evaluate constructs within complex measurement structures.