Multinomial Processing Tree Models for Discrete Choice

This paper shows how to develop new multinomial processing tree (MPT) models for discrete choice, and in particular binary choice. First it reviews the history of discrete choice with special attention to Duncan Luce’s book Individual Choice Behavior. Luce’s choice axiom leads to the Bradley-Terry-Luce (BTL) paired-comparison model which is the basis of logit models of discrete choice used throughout the social and behavioral sciences. It is shown that a reparameterization of the BTL model is represented by choice probabilities generated from a finite state Markov chain, and this representation is closely related to the rooted tree structure of MPT models. New MPT models of binary choice can be obtained by placing restrictions on this representation of the BTL model. Several of these new MPT models for paired comparisons are described, compared to the BTL model, and applied to data from a replicated round-robin data structure.