Paired Comparison Models with Time-Varying Parameters

Abstract : Paired comparison experiments involve comparisons among a set of objects, treatments, or competitors in blocks of size two to determine relative merits among the objects. Applications to tournament chess competition or team sports differ from the usual paired comparison framework in that competitors' abilities may change over time. A dynamic model is developed for the usual paired comparison experiment in which only a binary indicator of the preferred object is available (or trinary, if ties are allowed), and for alternative paired comparison experiments in which more information (perhaps the score) is available. Posterior distributions of the rating parameters and posterior prediction intervals for the results of future comparisons axe obtained using methods that are closely related to the Kalman filter. The methodology is applied to the analysis of professional football game outcomes and to chess tournament results from the 1988-1989 World Cup.