Statistical ranking with dynamic covariates

TL;DR

This paper develops a flexible covariate-assisted ranking model within the Plackett--Luce framework, addressing estimation challenges and demonstrating its effectiveness on real-world sports data.

Contribution

It introduces a novel dynamic covariate model, provides conditions for identifiability and MLE existence, and proposes an efficient algorithm with theoretical guarantees.

Findings

MLE is consistent under certain graph and covariate conditions

The model effectively ranks horses and tennis players in real datasets

An efficient alternating maximization algorithm is developed

Abstract

We introduce a general covariate-assisted statistical ranking model within the Plackett--Luce framework. Unlike previous studies focusing on individual effects with fixed covariates, our model allows covariates to vary across comparisons. This added flexibility enhances model fitting yet brings significant challenges in analysis. This paper addresses these challenges in the context of maximum likelihood estimation (MLE). We first provide sufficient and necessary 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 graph connectivity. We also construct random designs where 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.