Data in the form of rankings, ratings, pair comparisons or clicks are frequently collected in diverse fields, from marketing to politics, to understand assessors' individual preferences. Combining such preference data with features associated with the assessors can lead to a better understanding of the assessors' behaviors and choices. The Mallows model is a popular model for rankings, as it flexibly adapts to different types of preference data, and the previously proposed Bayesian Mallows Model (BMM) offers a computationally efficient framework for Bayesian inference, also allowing capturing the users' heterogeneity via a finite mixture. We develop a Bayesian Mallows-based finite mixture model that performs clustering while also accounting for assessor-related features, called the Bayesian Mallows model with covariates (BMMx). BMMx is based on a similarity function that a priori favours the aggregation of assessors into a cluster when their covariates are similar, using the Product Partition models (PPMx) proposal. We present two approaches to measure the covariate similarity: one based on a novel deterministic function measuring the covariates' goodness-of-fit to the cluster, and one based on an augmented model as in PPMx. We investigate the performance of BMMx in both simulation experiments and real-data examples, showing the method's potential for advancing the understanding of assessor preferences and behaviors in different applications.

翻译：排序、评分、成对比较或点击形式的数据在从市场营销到政治学的多个领域中频繁收集，用于理解评估者的个体偏好。将此类偏好数据与评估者的特征相结合，有助于更深入地理解评估者的行为和选择。马洛斯模型是排序分析中常用的模型，因其能灵活适应不同类型的偏好数据；此前提出的贝叶斯马洛斯模型（BMM）为贝叶斯推断提供了高效的计算框架，并可通过有限混合模型捕捉用户的异质性。我们开发了一种基于贝叶斯马洛斯的有限混合模型，该模型在执行聚类的同时纳入评估者相关特征，称为带协变量的贝叶斯马洛斯模型（BMMx）。BMMx基于相似性函数，该函数先验地倾向于将协变量相似的评估者聚合到同一聚类中，并采用了产品分区模型（PPMx）的扩展框架。我们提出两种测量协变量相似性的方法：一种基于新颖的确定性函数，用于评估协变量对聚类的拟合优度；另一种基于PPMx中的增广模型。通过模拟实验和真实数据案例，我们研究了BMMx的性能，展示了该方法在促进不同应用场景中理解评估者偏好与行为方面的潜力。