Human interaction and communication has become one of the essential features of social life. Individuals’ preference may be influenced by those of their peers or friends in a social network. In the literature, individuals’ rank-order preferences and their social network are often modeled separately. In this article, we propose a new joint probabilistic model for ranking data and social network. With a latent space for all the individuals and items, the proposed model assume that the social network and rankings of items are governed by the locations of individuals and items. Based on an efficient MCMC algorithm, we develop a set of Bayesian inference approaches for the proposed model, including procedures of model selection, criteria to evaluate model fitness and a test for conditional independence between individuals’ rankings and their social network given their positions in the latent space. Simulation studies reveal the usefulness of our proposed methods for parameter estimation, model fitness evaluation, model selection and conditional independence testing. Finally, we apply our model to the CiaoDVD dataset which consists of users’ trust relations and their implicit preferences on DVD categories.

人际交往和交流已成为社会生活的基本特征之一。个人的偏好可能会受到社交网络中的同龄人或朋友的影响。在文献中，个人的排序偏好和他们的社交网络通常是分开建模的。在本文中，我们提出了一种用于排名数据和社交网络的新联合概率模型。由于所有个人和项目的潜在空间，所提出的模型假设社交网络和项目的排名由个人和项目的位置控制。基于高效的 MCMC 算法，我们为所提出的模型开发了一套贝叶斯推理方法，包括模型选择过程，评估模型适合度的标准，以及在给定个人在潜在空间中的位置的情况下，对个人排名与其社交网络之间的条件独立性进行测试。仿真研究揭示了我们提出的参数估计、模型适应度评估、模型选择和条件独立性测试方法的有用性。最后，我们将我们的模型应用于 CiaoDVD 数据集，该数据集由用户的信任关系和他们对 DVD 类别的隐含偏好组成。