Sensitivity analysis of prior distributions in Bayesian graphical modeling: Guiding informed prior choices for conditional independence testing

Abstract

Bayesian analysis methods provide a significant advancement in network psychometrics, allowing researchers to use the edge inclusion Bayes factor for testing conditional independence between pairs of variables in the network. Using this methodology requires setting prior distributions on the network parameters and on the network’s structure. However, the impact of both prior distributions on the inclusion Bayes factor is underexplored. In this paper, we focus on a specific class of Markov Random Field models for ordinal and binary data. We first discuss the different choices of prior distributions for the network parameters and the network structure, and then perform an extensive simulation study to assess the sensitivity of the inclusion Bayes factor to these distributions. We pay particular attention to the effect of the scale of the prior on the inclusion Bayes factor. To improve the accessibility of the results, we also provide an interactive Shiny app. Finally, we present the R package simBgms, which provides researchers with a user-friendly tool to perform their own simulation studies for Bayesian Markov Random Field models. All of this should help researchers make more informed, evidence-based decisions when preparing to analyze empirical data using network psychometric models.