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The existence of maximum likelihood estimates in the Bradley-Terry model and its extensions

Kenneth Butler·John T. Whelan
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Abstract

In the Bradley-Terry model for paired comparisons, and its extensions to include order effects and ties, the maximum likelihood estimates of probabilities of certain outcomes can be 0 or 1 under certain data configurations. This poses problems for standard estimation methods. In this paper, we give algorithms for identifying the outcomes with estimated probability 0 or 1, and indicate how the remaining probabilities may be estimated and summarized.

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Kenneth Butler, John T. Whelan. 2004-12-12. The existence of maximum likelihood estimates in the Bradley-Terry model and its extensions. https://arxiv.org/abs/math/0412232

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