Bayesian longitudinal paired comparison model and its application to sports data using weighted likelihood bootstrap

This article describes a procedure for Bayesian longitudinal paired comparison data analysis to rank stimuli. The proposed model is developed by combining the Bradley–Terry model and a nonlinear model that utilizes an exponential distribution to describe longitudinal changes in scale values. The weighted likelihood bootstrap method (WLB) is used to obtain samples from posterior distributions of parameters. WLB is an effective tool because neither diagnosing parameter convergence nor specifying proposal distributions is required, which decreases both the preparation necessary and the time involved. The proposed model is a simple one with few parameters, so WLB can be effectively accommodated. An actual example using sports data from sumo wrestling is presented to verify the efficacy of the proposed method.