Multidimensional Scaling. by F. Cox; M. A. A. CoxReview by: J. C. GowerJournal of the Royal Statistical Society. Series A (Statistics in Society), Vol. 159, No. 1 (1996),pp. 184-185Published by: Wiley for the Royal Statistical SocietyStable URL: http://www.jstor.org/stable/2983485 .

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184 REVIEWS [Part 1,

multiplicative) model itself. By the way, most models can be, and are, looked at from more than one perspective. Chapter 4 is 'Other models for two-way tables: symmetry-type models', Chapter 5 is 'Multiple dimensions of association' and Chapter 6 is 'Bivariate association in multiple groups'. The models are built naturally on the earlier foundations, but I will admit to losing track as the book reached its later stages. Several real data sets are used for illustration. And the book remains focused on models and their uses and interpretation rather than other aspects. The final chapter, 'Logit-type regression models for ordinal dependent variables', is a little different. It looks at the ordinal regression situation (ground which has been more well trodden), as distinct from ordinal association modelling, but with emphasis on exploring the relationship between the two.

There having been a delay between my reading of this book and my writing of this review, I cannot claim now to be completely at ease with modelling for ordinal variables. But what I do have on my shelf is what I know to be a fine resource of clear description and explanation of the use of statistical models for ordinal data that I can turn to when the need arises.

M. C. Jones The Open University

Milton Keynes

8. Multidimensional Scaling. By F. Cox and M. A. A. Cox. ISBN 0 412 49120 6. Chapman and Hall, London, 1994. xii + 214 pp. ?32.50.

Multidimensional scaling is concerned with approximating distance-like data by distances in maps, mostly Eucidean and mostly two dimensional. Its psychometric origins are evident; of 238 references in the bibliography about 125 are from the psychometric literature, many from Psychometrika, and only about 20 cite mainline statistical journals. However, the methodology is finding ever-increasing applications in other fields of application. The authors include detailed discussions of data drawn from the fields of animal behaviour, food science and biological cybernetics and illustrate the text with many smaller examples as well as mentioning applications in biometrics, counselling psychology, ecology, ergonomics, forestry, lexicography, marketing and tourism; they might have added molecular biology because of its importance and because of its special status arising from the known three- dimensionality of molecules.

The book reviews the methodology, with chapters on various forms of metric multi- dimensional scaling and non-metric multidimensional scaling, Procrustes analysis (mainly in its orthogonal form), metric and non-metric multidimensional unfolding, correspondence analysis (including multiple correspondence analysis, which is defined as the correspondence analysis of an indicator matrix for categorical variables) and individual differences scaling (INDSCAL). Mostly, the models underpinning these methods are fairly straightforward and they are fitted by minimizing (weighted) least squares criteria. A large part of the research effort has gone into devising efficient algorithms and associated software. More so than in most other areas of data analysis, the models have become identified with the algorithms and are known by software acronyms (e.g. INDSCAL); the development of such software is a major undertaking. Most users will be happy to use available software and the sources of most major software for the forms of multidimensional scaling discussed are given. The authors include a discussion of algorithms, which I welcome, because some understanding of algorithms supports an informed interpretation of results. A diskette is included, containing programs and standard data sets analysed in the book. The programs run under DOS and I could not get them to work on my Macintosh; however, a quick examination on a PC showed that some, and possibly all, of them run correctly. The idea of supplying software to allow readers to get 'hands-on' experience of multidimensional scaling methods is good but the

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1996] REVIEWS 185

control of these programs seems not to be very easy and I suspect that successful users will have to be PC buffs or have access to one.

The book has something of the air of a literature review but is none the worse for that. It is addressed to users, or prospective users, of multidimensional scaling methods rather than to experts in the field. The coverage is quite good but there are what seem to me to be serious gaps. An opportunity has been missed for distinguishing the two-way tables of corres- pondence analysis from the multivariate data matrix of most other methods. Remarkably, for a book on the multidimensional scaling of distances, the chapter on correspondence analysis makes no mention of x2-distance. Apart from a brief mention of the regression method, I missed a discussion of biplot methods which simultaneously display information on samples and variables. This particular gap is, of course, reflected by a gap in the literature and has a historic basis, because in psychology the data are often observed distances between objects, from which one wishes to derive a scale. In other fields of application, distances are more usually derived from fundamental data pertaining to objects and variables and both need to be represented in multidimensional scaling maps. The usual non-metric scaling methods that are described seek transformations of distances to reduce dimensionality; an important recent development that should have been mentioned (Meulman, 1992) transforms the variables from which distances are derived. Despite these gaps, a useful discussion is given of many interesting topics and I recommend this book to those who wish for an introduction to multidimensional scaling or who have some knowledge of the field and wish to become better informed.

Reference Meulman, J. J. (1992) The integration of multidimensional scaling and multivariate analysis with

optimal transformations. Psychometrika, 57, 539-565.

J. C. Gower The Open University

Milton Keynes

9. Teaching Statistics at Its Best: a Series of Articles for Teachers. Edited by D. Green. ISBN 0 946554 08 0. Teaching Statistics Trust, Sheffield, 1994. 166 pp. ?12.

I caused some amusement by taking this book on holiday. The fact that I did so and read it for relaxation says much for its enjoyment factor. It consists of a collection of what might be considered to be the 48 best articles published in volumes 6-14 (1984-92) of the journal Teaching Statistics grouped into seven sections called 'Statistics in the classroom', 'Students' understanding', 'Teaching particular topics', 'Practical and project work', 'Using computers', 'Statistics in other subjects and at work' and 'Miscellany'. It includes almost all articles which have won the C. Oswald George prize awarded by the Institute of Statisticians (now administered by the Royal Statistical Society) for the best article in each volume. (I am curious why prizes were awarded for articles which are not considered to be among the best.)

The Best of Teaching Statistics published in 1986 contained the 41 best articles from volumes 1-5. How long must we wait for the next book in this series, how many articles will it contain and what will it be called?

The book is ideal for dipping into, either for interest or as a source book, but I wonder whether the one-page index provided would be adequate for someone who was using the book for ideas as regards specific topics. It is perhaps unfortunate that the first item I looked up was stem and leaf which revealed that the ordering has gone slightly astray for the letter S.

There are no references to the Teaching Statistics issues in which the articles were originally published, which might be good for authors trying to maximize the number of their publications, but it would have been useful to have known at least the dates. Many of the

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