Opaque prior distributions in Bayesian latent variable models

Abstract

We review common situations in Bayesian latent variable models where the prior distribution that a researcher specifies differs from the prior distribution used during estimation. These situations can arise from the positive definite requirement on correlation matrices, from sign indeterminacy of factor loadings, and from order constraints on threshold parameters. The issue is especially problematic for reproducibility and for model checks that involve prior distributions, including prior predictive assessment and Bayes factors. In these cases, one might be assessing the wrong model, casting doubt on the relevance of the results. The most straightforward solution to the issue sometimes involves use of informative prior distributions. We explore other solutions and make recommendations for practice.

arXiv comment25 pages, 8 figures

References in corpus (7)

• The prior can generally only be understood in the context of the likelihood
• blavaan: Bayesian structural equation models via parameter expansion
• Validating Bayesian Inference Algorithms with Simulation-Based Calibration
• Bayesian comparison of latent variable models: Conditional vs marginal likelihoods
• Efficient Bayesian Structural Equation Modeling in Stan
• Rotational Uniqueness Conditions Under Oblique Factor Correlation Metric
• Regularizing threshold priors with sparse response patterns in Bayesian factor analysis with categorical indicators

Cited by in corpus (1)

• Gaussian distributional structural equation models: A framework for modeling latent heteroscedasticity