> The existence of maximum likelihood estimates in the Bradley-Terry model and its extensions (with Kenneth Butler)

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This project concerns the Bradley-Terry method of modelling paired comparison experiments, in which the relative strengths of a set of objects (such as foods to be taste-tested or participants in a competition) are to be determined by comparing them two at a time. Assuming that the odds of one object being preferred over another in a given comparison are given by the ratio of their ratings, the "correct" ratings are defined to be those which maximize the probability for the set of paired comparisons performed to produce the observed results. The ratios of ratings defined by this procedure are not guaranteed to be finite or unique, which poses problems for the maximization procedure; we have found an efficient method to determine which pairs of objects will have ratings whose ratios are zero, infinite, or unconstrained by the maximum likelihood equations, and calculate only the ratios of ratings which are finite and well-defined.

This work is available as Technical Report No. DALTR-00-1, Dept. of Mathematics and Statistics, Dalhousie University

Last Modified: 2011 April 6

Dr. John T. Whelan / john.whelan@astro.rit.edu / Professor, School of Mathematical Sciences & Center for Computational Relativity and Gravitation, Rochester Institute of TechnologyThe contents of this communication are the sole responsibility of Prof. John T. Whelan and do not necessarily represent the opinions or policies of RIT, SMS, or CCRG.