A note on identification constraints and information criteria in Bayesian latent variable models.

Area of Science:

• Psychometrics
• Statistical Modeling
• Quantitative Psychology

Background:

• Traditional structural equation modeling (SEM) requires setting a scale for latent variables, typically by fixing latent variance or a factor loading.
• This identification constraint can impact Bayesian model comparison metrics, unlike in Maximum Likelihood (ML) estimation.
• Varying constraints can lead to different results, potentially allowing researchers to artificially favor specific models.

Purpose of the Study:

• To demonstrate how different identification constraints in SEM affect Bayesian model comparison metrics.
• To propose and evaluate principled methods for setting latent variable scales that stabilize these metrics.
• To ensure the reliability and replicability of Bayesian model comparisons in SEM.

Main Methods:

• Utilized a single-factor confirmatory factor analysis (CFA) model as a motivating example.
• Investigated the impact of fixing latent variance versus fixing a factor loading on Bayesian model comparison.
• Proposed and tested two methods: placing priors on ratios of factor loadings and employing effect coding.

Main Results:

• Showed that Bayesian model comparison metrics systematically change based on the identification constraint used.
• Demonstrated that priors on factor loading ratios and effect coding stabilize model comparison metrics.
• Validated the proposed methods through simulation studies and a practical application.

Conclusions:

• The choice of identification constraint in SEM significantly influences Bayesian model comparison outcomes.
• Priors on factor loading ratios and effect coding offer robust solutions for stable latent variable scaling.
• These methods enhance the validity of Bayesian model comparison in SEM, preventing artificial model preference.