Opaque Prior Distributions in Bayesian Latent Variable Models

Authors

  • Edgar C. Merkle Orcid
    Department of Psychological Sciences, University of Missouri, Columbia, MO, USA
  • Oludare Ariyo Orcid
    School of Mathematics, Statistics and Actuarial Science, University of Essex, United Kingdom
  • Sonja D. Winter Orcid
    College of Education & Human Development. University of Missouri, Columbia, MO, USA
  • Mauricio Garnier-Villarreal Orcid
    Department of Sociology, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands

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.