We consider a covariate-assisted ranking model grounded in the Plackett--Luce framework. Unlike existing works focusing on pure covariates or individual effects with fixed covariates, our approach integrates individual effects with dynamic covariates. This added flexibility enhances realistic ranking yet poses significant challenges for analyzing the associated estimation procedures. This paper makes an initial attempt to address these challenges. We begin by discussing the sufficient and necessary condition for the model's identifiability. We then introduce an efficient alternating maximization algorithm to compute the maximum likelihood estimator (MLE). Under suitable assumptions on the topology of comparison graphs and dynamic covariates, we establish a quantitative uniform consistency result for the MLE with convergence rates characterized by the asymptotic graph connectivity. The proposed graph topology assumption holds for several popular random graph models under optimal leading-order sparsity conditions. A comprehensive numerical study is conducted to corroborate our theoretical findings and demonstrate the application of the proposed model to real-world datasets, including horse racing and tennis competitions.

翻译：我们提出了一种基于Plackett-Luce框架的协变量辅助排序模型。与现有聚焦于纯协变量或固定协变量下个体效应的研究不同，我们的方法将个体效应与动态协变量相结合。这种增强的灵活性提升了排序的现实性，但也给相关估计过程的分析带来了重大挑战。本文首次尝试解决这些挑战。我们首先讨论了模型可识别性的充分必要条件，随后提出一种高效的交替最大化算法来计算最大似然估计量（MLE）。在比较图拓扑结构和动态协变量的适当假设下，我们建立了MLE的定量一致收敛结果，其收敛速率由渐近图连通性决定。所提出的图拓扑假设在最优主阶稀疏条件下适用于多种流行的随机图模型。我们通过系统的数值研究验证了理论结果，并展示了所提模型在赛马和网球比赛等实际数据集中的应用。