Asymptotic comparison of identifying constraints for Bradley-Terry models

2022/05/09 by Wei‐Chen Wu, Wu, Weichen, Brian W. Junker +3 · 1 citation
Computer Science · #Data Mining Algorithms and Applications #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2205.04341

openalex publication_date 2022/05/09 · openalex created_date 2023/02/12 · openalex updated_date 2026/07/28

Abstract

The Bradley-Terry model is widely used for pairwise comparison data analysis. In this paper, we analyze the asymptotic behavior of the maximum likelihood estimator of the Bradley-Terry model in its logistic parameterization, under a general class of linear identifiability constraints. We show that the constraint requiring the Bradley-Terry scores for all compared objects to sum to zero minimizes the sum of the variances of the estimated scores, and recommend using this constraint in practice.

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