Bradley–Terry Model

1
Peter B. Imrey

Peter B. Imrey

Cleveland Clinic, Cleveland, OH, USA

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First published: 15 July 2005

Abstract

Bradley–Terry models parsimoniously summarize preferences expressed in paired comparisons of objects through a set of latent “merit” or “preference” parameters linked to the individual objects rather than to the pairs. When comparisons of all pairs of k objects are observed, the resulting k(k - 1)/2 linearly independent proportions are reduced to k - 1 latent parameters, or potentially fewer if these are further modeled using characteristics of the objects. This entry introduces the basic model, discusses its relationship with the probit, logit, and loglinear models developed in other contexts, and describes some extensions that allow for data with ties, varying degrees of preference, or simultaneous expressions of preferences along multiple dimensions of assessment.

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