1. Asymptotic comparison of identifying constraints for Bradley-Terry models
- Author
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Wu, Weichen, Junker, Brian W., and Niezink, Nynke M. D.
- Subjects
Methodology (stat.ME) ,FOS: Computer and information sciences ,Mathematics::History and Overview ,FOS: Mathematics ,Statistics::Methodology ,Mathematics - Statistics Theory ,Statistics Theory (math.ST) ,Statistics - Methodology - 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.
- Published
- 2022