Stochastic tree unfolding (STUN) models.

In this paper we propose two versions of stochastic choice models based on tree structure models - called "tree unfolding models". Probably a better and more informative name for this class of models is "ideal point models", since they generally assume preference is related to distance from an "ideal" stimulus point by a non-increasing monotonic function. From this point of view, the current class of models would be termed "tree ideal point" rather than "tree unfolding" models. However, in keeping with the historical use of the term "unfolding", particularly in mathematical psychology and psychometrics, we shall continue to use the (perhaps) less informative but more "colorful" name "tree unfolding". Thus we call these models, generically, Stochastic Tree UNfolding (or STUN) models. They can be viewed as discrete (tree structure) analogues of a recently proposed class of continuous (spatial) random utility models for paired comparisons choice data called the "wandering vector" and "wandering ideal point" models.