Bayesian Analysis of Log-Linear Form of the Bradley-Terry Model

Abstract

Bayesian analysis of log-linear model is rather difficult and performed by Leonard (1975), who considered log-linear models in his thesis work. For computational convenience, he estimated parameters by joint posterior modes rather than posterior means. Dittrich et al (1998) considered the log-linear representation of the basic paired comparison model. Their study focuses on the development of log-linear models. They generalized the model for allowing of ties and order effects and their estimation procedure is based on generalized linear models framework in generalized linear interactive modeling software. We modify their loglinear model into the Bayesian analysis and compare with their model parameters' estimates. Their technique aliases one parameter value, while as, we estimate that value under Bayesian inference. We also predict the posterior probabilities for future single comparison between pair of European Universities. Finally we apply Bayesian testing of hypotheses about the parameters each of fifteen pairs which maintain the ranking of Universities as '1ttai'1ed through the Bayes estimators.