A probabilistic multidimensional scaling vector model

Abstract

This article presents the development of a new stochastic multidimensional scaling (MDS) method, which operates on paired comparisons data and renders a spatial representation of subjects and stimuli. 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 respective information as to the utility (or whatever latent construct is under investigation) of the stimuli to the subjects. The psychometric literature concerning related MDS methods that also operate on paired comparisons data is reviewed, and a technical description of the new method is provided. A small monte carlo analysis performed on synthetic data with the new method is also presented. To illustrate the versatility of the model, an application measuring consumer satisfaction and investigating the impact of hypothesized determinants, using one of the optional reparameterized models, is described. Future areas of further research are identified.