Regularizing threshold priors with sparse response patterns in Bayesian factor analysis with categorical indicators

Using instruments comprising ordered responses to items is ubiquitous for studying many constructs of interest. However, using such an item response format may lead to items with response categories infrequently endorsed or unendorsed completely. In maximum likelihood estimation, this results in nonexisting estimates for thresholds. This work focuses on a Bayesian estimation approach to counter this issue. The issue changes from the existence of an estimate to how to effectively construct threshold priors. The proposed prior specification reconceptualizes the threshold prior as prior to the probability of each response category, which is an easier metric to manipulate while maintaining the necessary ordering constraints on the thresholds. The resulting induced-prior is more communicable, and we demonstrate comparable statistical efficiency with existing threshold priors. Evidence is provided using a simulated data set, a Monte Carlo simulation study, and an example multigroup item-factor model analysis. All analyses demonstrate how at least a relatively informative threshold prior is necessary to avoid inefficient posterior sampling and increase confidence in the coverage rates of posterior credible intervals. (PsycInfo Database Record (c) 2025 APA, all rights reserved).