Asymptotic comparison of identifying constraints for Bradley-Terry models
Wei‐Chen Wu, Brian W. Junker, Nynke M. D. Niezink · arXiv (Cornell University) · 2022
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.