Statistical ranking with dynamic covariates

Abstract

We introduce a general covariate-assisted statistical ranking model within the Plackett-Luce framework. Unlike previous studies that focus on individual effects with fixed covariates, our model allows covariates to vary across comparisons. This added flexibility enhances model fitting but also brings significant challenges in analysis. This article addresses these challenges in the context of maximum likelihood estimation (MLE). We first provide necessary and sufficient conditions for both model identifiability and the unique existence of the MLE. Then, we develop an efficient alternating maximization algorithm to compute the MLE. Under suitable assumptions on the design of comparison graphs and covariates, we establish a uniform consistency result for the MLE, with convergence rates determined by the asymptotic connectivity of the graph sequence. We also construct random designs under which the proposed assumptions hold almost surely. Numerical studies are conducted to support our findings and demonstrate the model's application to real-world datasets, including horse racing and tennis competitions.