Bayesian paired comparison with the bpcs package

This article introduces the bpcs R package (Bayesian Paired Comparison in Stan) and the statistical models implemented in the package. This package aims to facilitate the use of Bayesian models for paired comparison data in behavioral research. Bayesian analysis of paired comparison data allows parameter estimation even in conditions where the maximum likelihood does not exist, allows easy extension of paired comparison models, provides straightforward interpretation of the results with credible intervals, has better control of type I error, has more robust evidence towards the null hypothesis, allows propagation of uncertainties, includes prior information, and performs well when handling models with many parameters and latent variables. The bpcs package provides a consistent interface for R users and several functions to evaluate the posterior distribution of all parameters to estimate the posterior distribution of any contest between items and to obtain the posterior distribution of the ranks. Three reanalyses of recent studies that used the frequentist Bradley-Terry model are presented. These reanalyses are conducted with the Bayesian models of the bpcs package, and all the code used to fit the models, generate the figures, and the tables are available in the online appendix.