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：使用包含有序响应项目的测量工具在研究中广泛用于探讨许多感兴趣的构念。然而，采用这种项目响应格式可能导致项目出现某些响应类别被低频选择或完全未选择的情况。在最大似然估计中，这会导致阈值估计不存在。本研究聚焦于贝叶斯估计方法以应对该问题，该问题从估计的存在性转变为如何有效构建阈值先验。所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，这是一种更易操作且能维持阈值必要排序约束的度量。由此推导出的诱导先验更具可沟通性，我们证明其与现有阈值先验具有相当的统计效率。通过模拟数据集、蒙特卡洛模拟研究以及一个多群组项目因子模型分析实例提供了证据。所有分析均表明，至少需要相对信息性的阈值先验以避免低效的后验采样，并提高后验置信区间覆盖率。