Journal ArticleDOI
On Extending the Bradley-Terry Model to Accommodate Ties in Paired Comparison Experiments
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In this article, a new model is developed and its performance compared with a model proposed by Rao and Kupper, and the likelihood ratio test of the hypothesis of equal preferences is shown to have the same asymptotic efficiency as that for the Rao-Kupper model.Abstract:
This study is concerned with the extension of the Bradley-Terry model for paired comparisons to situations which allow an expression of no preference. A new model is developed and its performance compared with a model proposed by Rao and Kupper. The maximum likelihood estimates of the parameters are found using an iterative procedure which, under a weak assumption, converges monotonically to the solution of the likelihood equations. It is noted that for a balanced paired comparison experiment the ranking obtained from the maximum likelihood estimates agrees with that obtained from a scoring system which allots two points for a win, one for a tie and zero for a loss. The likelihood ratio test of the hypothesis of equal preferences is shown to have the same asymptotic efficiency as that for the Rao-Kupper model. Two examples are presented, one of which introduces a set of data for an unbalanced paired comparison experiment. Initial applications of the test of goodness of fit suggest that the propos...read more
Citations
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Journal ArticleDOI
MM algorithms for generalized Bradley-Terry models
TL;DR: In this paper, the authors present a technique for producing iterative maximum likelihood estimation algorithms for a wide class of generalizations of the Bradley-Terry model for paired comparisons, which is a simple and muchstudied means to describe the probabilities of the possible outcomes when individuals are judged against one another in pairs.
Journal ArticleDOI
Parameter estimation in large dynamic paired comparison experiments
TL;DR: In this paper, a non-iterative algorithm for fitting a particular dynamic paired comparison model was proposed, which improves over the commonly used algorithm of Elo by incorporating the variability in parameter estimates, can be performed regularly even for large populations of competitors.
Book
Regression for Categorical Data
TL;DR: This paper presents a meta-modelling architecture for binary regression that combines log-linear and graphical models, and some basic tools for random effects modeling are presented.
Journal ArticleDOI
Bradley-Terry Models in R: The BradleyTerry2 Package
Heather Turner,David Firth +1 more
TL;DR: This is a short overview of the R add-on package BradleyTerry2, which facilitates the specification and fitting of Bradley-Terry logit, probit or cauchit models to paircomparison data.
Journal ArticleDOI
Group decision making using the analytic hierarchy process
Indrani Basak,Thomas L. Saaty +1 more
TL;DR: Two different approaches to synthesize the judgments of a group are discussed, one deterministic and the other stochastic, which address the issues of obtaining priority weights for a group of individuals.
References
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Journal ArticleDOI
Tests of statistical hypotheses concerning several parameters when the number of observations is large
Journal ArticleDOI
Rank Analysis of Incomplete Block Designs: I. The Method of Paired Comparisons
Ralph A. Bradley,Milton E. Terry +1 more
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Rank Analysis of Incomplete Block Designs: I. The Method of Paired Comparisons
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