Extending the Bradley–Terry model for paired comparisons to accommodate weights

Abstract

In the method of paired comparisons (PCs), treatments are compared on the basis of qualitative characteristics they possess, in the light of their sensory evaluations made by judges. However, there may emerge the situations where in addition to qualitative merits/worths, judges may assign quantitative weights to reflect/specify the relative importance of the treatments. In this study, an attempt is made to reconcile the qualitative and the quantitative PCs through assigning quantitative weights to treatments having qualitative merits using/extending the Bradley–Terry (BT) model. Behaviors of the existing BT model and the proposed weighted BT model are studied through the test of goodness-of-fit. Experimental and simulated data sets are used for illustration.