Probabilistic Multidimensional Scaling Models for Analyzing Consumer Choice Behavior

We review the development of two new stochastic multidimensional scaling (MDS) methodologies that operate on paired comparisons choice data and render a spatial representation of subjects and stimuli. In the probabilistic vector MDS model, subjects are represented as vectors and stimuli as points in a T-dimensional space, where the scalar products or projections of the stimulus points onto the subject vectors provide information about the utility of the stimuli to the subjects. In the probabilistic unfolding MDS model, subjects are represented as ideal points and stimuli as points in a T-dimensional space, where the Euclidean distance between the stimulus points and the subject ideal points provides information as to the respective utility of the stimuli to the subjects. To illustrate the versatility of the two models, a marketing application measuring consumer choice for fourteen actual brands of over-the-counter analgesics, utilizing optional reparameterizations, is described. Finally, other applications are identified.