  Using instruments comprising ordered responses to items are 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
non-existing 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 on the
probability of each response category. A metric that is easier to manipulate
while maintaining the necessary ordering constraints on the thresholds. The
resulting induced-prior is more communicable, and we demonstrate comparable
statistical efficiency that existing threshold priors. Evidence is provided
using a simulated data set, a Monte Carlo simulation study, and an example
multi-group 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.
