Empirical evidence has established the existence of a phenomenon known as the decoy effect, which suggests that including irrelevant alternatives into a choice-set may affect the way in which the original alternatives are evaluated. In this paper we explore different ways to characterize the decoy effect and offer an in-depth discussion on the theoretical and empirical implications of the different modeling approaches. We also consider a stated preference experiment for which we model the phenomenon according to the assumptions of regret theory, emergent value, and prospect theory. Based on theoretical and empirical considerations, our results suggest that models based on prospect theory seem to outperform alternative behavioral paradigms to model the decoy effect. • This study examines different modelling approached to consider the decoy effect from theoretical and empirical perspectives. • This study considers different specifications based on random regret, emergent value, and prospect theory models. • This study finds support for relying on prospect theory models to consider the decoy effect.