A Probabilistic Model for the Multidimensional Scaling of Proximity and Preference Data/Commentaries/Reply: Considerations in the Use of Probabilistic Multidimensional Scaling Models

A probabilistic multidimensional scaling model that estimates both location and variance parameters for proximity and preference data is presented and compared to a deterministic scaling model. Simulated and empirical choice data are employed to compare the models. Variance estimates from the probabilistic model are applied to test a hypothesis about the homogeneity of stimulus perception under alternative modes of stimulus presentation. McMennamin comments that the mathematical analysis systems in MacKay and Zinnes (M-Z) are superb, but the input material too often is not. Windal regards M-Z's work as a useful extension of deterministic multidimensional scaling models, and M-Z reply that the probabilistic model they present is only a start, not the ultimate solution.