Multidimensional Scaling


NETWORK: Newsletter of the Society for Psychotherapy Research U.K. Volume 6(1):6-7 March 1995. ISSN 1359-3706

Mounted by Chris Evans in July 1995, as part of NETWORK 6(1) {3kb} mounted as individual file to help people with slow connections 8.ii.96

Cox, Trevor F. & Cox, Michael A.A. (1994) Multidimensional Scaling. (Monographs on Statistics and Applied Probability 59.) Chapman & Hall:London ISBN 0-412-49120-6 (hdbk.), 213pp. with 3½" diskette of DOS MDS programs and data £32.50

This is latest book in the authoritative series from Chapman & Hall. These books are at the approachable end of the definitive statements on stats. and I think Multidimensional Scaling (MDS) has much to offer psychotherapy research. MDS includes a number of related techniques for mapping data onto a single dimension (the origin of the "scaling" in the name) or into a multidimensional space (hence the "MD"). Some methods take symmetrical matrices of similarity or dissimilarity data, others take rectangular matrices of ratings or rankings of objects, another set handle multiple similarity or dissimilarity matrices which might arise when a variety of judges are asked to compare different things. The scaling methods can take a variety of approaches to the presumed level of scaling (ratio, ordinal) in the data and in the mapping, and can take different approaches to the handling of ties in both the data and the mappings. One of the oldest methods, known as "classical scaling" or "principal coordinate analysis" (PCO) is mathematically and logically very closely related to principal component analysis (PDA) but other methods are computationally vastly more complicated. PCO was used by the late Patrick Slater to extend his repertory grid/PCA methods to the exploration of disagreements between people as reflected in what he called "Logical Equivalence Matrices" (Slater, Chetwynd & Farnsworth, 1989). Other MDS methods have been used for the analysis of repertory grids (Rathod, 1981; van der Kloot, 1981) and underpin the "circumplex" models of affect and personality (e.g. Walters & Jackson, 1966; Rosenberg, Nelson & Vivekananthan, 1968; Widiger, Trull, Hurt, Clarkin & Frances, 1987) and also the "Facet Analysis" methods pioneered by Louis Guttman which have been vehemently championed at a Ravenscar meeting some years ago by David Canter.

That's a flavour of why this book might be important. How was it? I found large hunks pretty heavy going and much of the matrix algebra was quite beyond me. I felt I got a much more definite picture of the relationships between the different methods and their implementations in a variety of programs (I'm most familiar with ALSCAL which is present in various forms in SAS, SPSSX and in STATISTICA). The book sets a fine example in providing simple PC-compatible software to carry out many of these analyses and data from the examples used in the book. However, there was an error in my copy of the front end menu program. It wouldn't call the program which provides Shepard plots but SHEP_PLO runs fine from DOS command line. It looked as if menu program is trying to call SHEP_PL0 (that's what it says on its menu) so that seemed a bit of an own goal!

The other major problem is that the few examples considered are used only very sparsely and some seem to prove just how badly the methods have been used in published literature. I wanted some examples of good MDS practice exploring a single subject area (it wouldn't have to be psychotherapy research!) taken through the various types of data and different methods of analysis and perhaps moving into the inferential and Monte Carlo simulative methods that the authors themselves have pioneered. I guess you can't have everything. With the growing willingness to look at the complexity of therapists' perceptions of the therapy process and of their "texts" there is a crying need for these methods to be employed well. This book is good but the obvious only first step for those of greater mathematic ability than me.


Chris Evans