Abstract
The Bradley-Terry model has been widely and effectively used to rank stimuli from paired comparison data. Existing approaches for paired comparison data analysis, however, have a number of limitations. First, among applied Bradley-Terry models in which multidimensionality is assumed, the effects of individual differences are not considered. Second, in these multidimensional Bradley-Terry models, the number of dimensions is generally evaluated only after analyzing several models with different dimensions separately, thus causing computational inconvenience.
In this study, a multidimensional Bradley-Terry model that considers the effects of individual differences is proposed. The proposed model allows estimation of parameters for both scale values of stimuli and individual differences in multidimensional space. A procedure of parameter estimation is presented that uses a reversible jump Markov chain Monte Carlo (RJMCMC) algorithm to estimate the optimal number of dimensions as well as associated parameters simultaneously. Simulation studies for examining the utility of the RJMCMC algorithm are performed, and real sports data from sumo are used in a representative example, where the time periods of tournaments are used as parameters for individual differences, in order to verify the validity of the proposed model.
