Bayesian evaluation for latent variable models: A tutorial on computing information criteria and bayes factors with...

Area of Science:

• Psychological methodology
• Computational statistics
• Bayesian inference

Background:

• Bayesian model evaluation is vital for latent variable models.
• Computing marginal likelihoods for information criteria and Bayes factors is computationally intensive.
• Applied research lacks practical guidance and software for these evaluations.

Purpose of the Study:

• To provide practical guidance for approximating marginal likelihoods in Bayesian latent variable models.
• To develop user-friendly software (R package bleval) for Bayesian model evaluation.
• To demonstrate the application of bleval in diverse empirical scenarios.

Main Methods:

• Utilizing adaptive Gauss-Hermite quadrature for efficient marginal likelihood approximation.
• Developing the R package 'bleval' for computing information criteria and fully marginal likelihoods.
• Applying bleval to structural equation, item response theory, and multilevel models.

Main Results:

• The bleval package effectively computes information criteria and Bayes factors for Bayesian latent variable models.
• Adaptive Gauss-Hermite quadrature provides an efficient method for marginal likelihood approximation.
• Empirical examples highlight practical considerations for using bleval, including sensitivity analyses.

Conclusions:

• The bleval package offers a practical solution for Bayesian model evaluation in psychology.
• Efficient numerical methods enhance the feasibility of complex model comparisons.
• This work facilitates more rigorous application of Bayesian methods in psychological research.