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

Asymptotic comparison of identifying constraints for Bradley-Terry models