Multidimensional Models of Perception and Cognition

By F. Gregory Ashby | Go to book overview
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2
A Probabilistic
Multidimensional Scaling
Approach: Properties
and Procedures

Joseph L. Zinnes Temple University

David B. MacKay Indiana University

Multidimensional Scaling has had a relatively long history, starting perhaps with the foundational paper by Young and Householder ( 1938), but, as evidenced by this book, only recently does it seem to be making contact with other areas of psychology. We like to think that this has resulted from probabilistic, multidimensional approaches gaining wider acceptance.

Our aim in this chapter is to review some of the main features of the probabilistic model that we have been working with for some time, covering some technical details, but mainly focusing on some of its properties and empirical applications. Our hope is that this introduction will make the probabilistic Multidimensional Scaling approaches more amenable and interesting to the reader, and even, perhaps, to encourage the reader to explore further their potentialities as explanatory theories.


FOUNDATIONS

This section shows how the general model has been applied to different experimental tasks involving similarity or preference judgments. In the following two sections some of the more important properties of the model are highlighted, as indicated by various simulations and empirical findings.


The General Model

As do many other authors in this volume, we assume that the perceptual aspects of each stimulus can be represented by a random vector having a multivariate

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