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.

翻译：采用有序反应类别的量表工具在众多感兴趣的构念研究中普遍存在。然而，这种项目响应格式可能导致某些项目的响应类别出现低频率选择或完全未被选择的情况。在最大似然估计中，这会引发阈值估计值不存在的问题。本研究聚焦于解决该问题的贝叶斯估计方法：核心问题从估计的存在性转变为如何有效构建阈值先验。本文提出的先验规范将阈值先验重新概念化为每个响应类别概率的先验——这一度量指标更易操控，同时能维持阈值必要的排序约束。由此推导出的诱导先验具有更强的可传递性，且我们证明其统计效率与现有阈值先验相当。通过模拟数据集、蒙特卡洛模拟研究及多群组项目-因子模型实例分析，研究证据表明：至少需要采用相对信息性的阈值先验，才能避免低效的后验抽样，并提升后验可信区间覆盖率的可靠性。