BTLLasso: A Common Framework and Software Package for the Inclusion and Selection of Covariates in Bradley-Terry Models

In paired comparison models, the inclusion of covariates is a tool to account for the heterogeneity of preferences and to investigate which characteristics determine the preferences. Although methods for the selection of variables have been proposed no coherent framework that combines all possible types of covariates is available. There are three different types of covariates that can occur in paired comparisons, the covariates can either vary over the subjects, the objects or both the subjects and the objects of the paired comparisons. This paper gives an overview over all possible types of covariates in paired comparisons and introduces a general framework to include covariate effects into Bradley-Terry models. For each type of covariate, appropriate penalty terms that allow for sparser models and, therefore, easier interpretation are proposed. The whole framework is implemented in the R package BTLLasso. The main functionality and the visualization tools of the package are introduced and illustrated by real data sets.