Model evaluation is crucial in psychological methodology, particularly in the context of Bayesian latent variable models. Bayesian evaluation methods require integrating out latent variables to compute marginal likelihoods for information criteria and integrating both latent variables and model parameters to compute fully marginal likelihoods for Bayes factors. These processes can be computationally demanding, as likelihoods in many latent variable models are intractable. Moreover, the role of latent variables in model evaluation has been insufficiently addressed in applied research, likely due to a lack of practical guidance and user-friendly software. This tutorial fills these gaps by (a) offering step-by-step instructions for approximating marginal likelihoods using an efficient numerical method (i.e., adaptive Gauss-Hermite quadrature), (b) developing an R package, bleval, designed specifically for computing information criteria and fully marginal likelihoods in Bayesian latent variable models, and (c) demonstrating the application of this package to various empirical scenarios, including structural equation models, item response theory models, and multilevel models. The empirical examples also investigate practical issues such as the sensitivity of model evaluation results to the number of quadrature nodes, the performance of the numerical quadrature method in high-dimensional latent variable models, and the handling of latent class variables in Bayesian mixture models. (PsycInfo Database Record (c) 2026 APA, all rights reserved).
Luo et al. (Mon,) studied this question.