Opaque prior distributions in Bayesian latent variable models

We review common situations in Bayesian latent variable models where the prior distribution that a researcher specifies does not match the prior distribution that the estimation method uses. These situations can arise from the positive definite requirement on correlation matrices, from the 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 these issues sometimes involves use of informative prior distributions. We explore other solutions and make recommendations for practice.