Opaque prior distributions in Bayesian latent variable models

TL;DR

This paper discusses how discrepancies between specified priors and those used during estimation in Bayesian latent variable models can affect reproducibility and model assessment, and explores solutions including informative priors.

Contribution

It highlights common situations causing prior discrepancies in Bayesian latent variable models and provides practical recommendations to address these issues.

Findings

Discrepancies can lead to incorrect model assessment.

Using informative priors can mitigate prior discrepancies.

Recommendations improve reproducibility and model validity.

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.