Using Markov chain Monte Carlo (MCMC) to visualize and test the linearity assumption of the Bradley-Terry class of models

► We present a method for testing whether the linearity of paired comparison data has been met. ► Our method uses the geometry of a posterior distribution of possible rankings given the data. ► This method is intuitive, efficient for large samples and takes into account linear and nonlinear information. ► The method determines the relevancy and validity of results of analyses based on assumptions of linearity. ► If the assumption of linearity is not met, other ranking methods (e.g. beta random field) should be considered.