Subject-specific Bradley–Terry–Luce models with implicit variable selection

Abstract

The Bradley–Terry–Luce (BTL) model for paired comparison data is able to obtain a ranking of the objects that are compared pairwise by subjects. The task of each subject is to make preference decisions in favour of one of the objects. This decision is binary when subjects prefer either the first object or the second object, but can also be ordinal when subjects make their decisions on more than two preference categories. Since subject-specific covariates, which reflect characteristics of the subject, may affect the preference decision, it is essential to incorporate subject-specific covariates into the model. However, the inclusion of subject-specific covariates yields a model that contains many parameters and thus estimation becomes challenging. To overcome this problem, we propose a procedure that is able to select and estimate only relevant variables.