In a traditional analysis of ordinal comparison data, the goal is to infer an overall ranking of objects from best to worst with each object having a unique rank. However, the ranks of some objects may not be statistically distinguishable. This could happen due to insufficient data or to the true underlying abilities or qualities being equal for some objects. In such cases, practitioners may prefer an overall ranking where groups of objects are allowed to have equal ranks or to be $\textit{rank-clustered}$. Existing models related to rank-clustering are limited by their inability to handle a variety of ordinal data types, to quantify uncertainty, or by the need to pre-specify the number and size of potential rank-clusters. We solve these limitations through the proposed Bayesian $\textit{Rank-Clustered Bradley-Terry-Luce}$ model. We allow for rank-clustering via parameter fusion by imposing a novel spike-and-slab prior on object-specific worth parameters in Bradley-Terry-Luce family of distributions for ordinal comparisons. We demonstrate the model on simulated and real datasets in survey analysis, elections, and sports.

翻译：在传统的序数比较数据分析中，目标是从最佳到最差推断出对象的整体排序，其中每个对象具有唯一的秩。然而，某些对象的秩可能在统计上无法区分。这可能由于数据不足，或某些对象的真实潜在能力或品质相等所致。在这种情况下，实践者可能更倾向于一种允许对象组具有相等秩或进行$\textit{排序聚类}$的整体排序。现有的与排序聚类相关的模型存在局限性：无法处理多种序数数据类型、无法量化不确定性，或需要预先指定潜在排序聚类的数量和大小。我们通过提出的贝叶斯$\textit{排序聚类布拉德利-特里-卢斯}$模型解决了这些限制。我们通过对布拉德利-特里-卢斯分布族中对象特定价值参数施加一种新颖的尖峰-平板先验，实现参数融合，从而允许排序聚类。我们在调查分析、选举和体育领域的模拟和真实数据集上验证了该模型。