PSYCHOMETRIKA--VOL.61, NO. 2, 391-393 JUNE 1996 REVIEWS

Michael J. Greenacre. Correspondence Analysis in Practice. London: Academic Press, 1993.

General Description The preface states that this book "is an educational text which is aimed at an audience with minimal statistical background" and that "this highly structured nature of the book lends itself readily to being a self-instruction manual". The book contains 20 modules (comments in parentheses are those of the reviewer):

(1) Scatterplots and maps (An elementary, but necessary, starting point). (2) Profiles and the profile space (A good introduction to a geometric framework). (3) Masses and centroids (Important concepts for geometric interpretations). (4) Inertia and the chi-squared distance (Key concepts, well explained). (5) Plotting chi-squared distances (Is the explanation sufficient?). (6) Reduction of dimensionality (Good to introduce measures of quality of approximation to the total space, but lacking sufficient explanation). (7) Optimal scaling (Correspondence analysis, so far explained, happens to provide the same scale values as optimal scaling? The two are mathematically identical). (8) Symmetry of row and column analysis (Is this not a good place to introduce the term duality of correspondence analysis, with practical implications for the relation between canonical correlation, correlation ratio and product-moment correlation?). (9) Two-dimensional displays (A good introduction to symmetric and asymmetric mapping). (10) More examples (Needed to familiarize readers with interpretation of data through graphical display. Are the examples sufficient for readers to appreciate the difference between symmetric and asymmetric graphs?). (11) Row and column contributions (Helpful to look at the decomposition in a concrete way). (12) Supplementary points (A popular application of CA extension). (13) Biplot interpretation (An excellent introduction to the topic). (14) Clustering rows and columns (An answer to a practical question). (15) Analysis of multiway tables (Exploratory applications of CA to multiway tables, but should there not be a more synthetic or convergent discussion than divergent?). (16) Joint correspondence analysis (JCA) (In extending CA to multiway cases, JCA and MCA are available. While MCA has been well investigated, JCA has not. JCA is a method developed by Greenacre, and there should be much more discussion of its rationale and implications for data analysis. For example, what objective functions does JCA optimize?). (17) Multiple correspondence analysis. (18) Homogeneity analysis ("In this module you will learn how optimal scaling can be generalized to accommodate more than two variables." What? Is homogeneity analysis an MCA version of optimal scaling? Of course not, but the author seems to think so). (19) Ratings and doubling (Rating data are treated in a different way in dual scaling 0033-3123/96/$00.75/0 © 1996 The Psychometric Society

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from Greenacre's treatment. In the former, doubling is not needed, and readers may wonder why doubling is used for rating data). (20) Stability of maps (An important topic). Each of these modules starts with objectives and ends with a summary of the key points. (21) Appendix 1. (Bibliography consists of general and specific literature, and good suggestions for additional reading and references). (21) Appendix 2. (A short but useful summary of theory). (22) Appendix 3. (Computer software, which introduces a number of currently available computer programs). All of these are contained within I95 pages.

Matters of Opinion From the beginning, it is made very clear that Greenacre wants readers to view correspondence analysis as a graphical method of data analysis. In this regard, he has done a commendable job, and is successful in providing many newcomers to this field with a reasonable and understandable textbook. However, too great an emphasis on a geometric approach might turn away readers who are used to an algebraic approach. This latter group might find some of the modules tedious and boring, or unnecessarily repetitious and long-winded. The essential question is whether readers can maintain their interest in the method until the end of the book. This book would be excellent as a textbook in a workshop or class, where explanations and interesting examples could augment the content of the book. However, as a self-teaching tool, those motivated to study the method may prefer a more mathematical text than this book. As noted in the previous review on Greenacre and Blasius (Eds.), the current book by Greenacre has the same "CA-exclusive" tone, as amplified in its PREFACE: The publication of my first book Theory and Applications of Correspondence Analysis (Academic Press, London, 1984) coincided with the beginning of a wider dissemination of correspondence analysis outside of France. At that time I expressed the hope that my book would serve as a springboard for a much wider and more routine application of correspondence analysis in the future. The subsequent evolution and growing popularity of the method could not have been more gratifying, as hundreds of researchers were introduced to the method . . . . (p. vii). "Parallel" developments in the Netherlands and Japan were mentioned as a historical note, but no mention is made of optimal scaling in the US and Canada, dual scaling in Canada, or, correspondence analysis in UK. Considering the enormous and outstanding contributions made by Greenacre to this field, he should perhaps have confined himself to his preferred territory of French correspondence analysis, by so declaring in the preface. Without that, his preface is misleading and discourteous to the researchers outside of France, the Netherlands and Japan. The greatest blunder, however, is Greenacre's statement that homogeneity analysis is an MCA (multiple correspondence analysis) version of optimal scaling (OS), implying that OS handles only contingency tables. The name OS was changed to dual scaling (DS) around 1979, and DS handles not only contingency tables and multiple choice data, but also sorting data (Takane, 1980), paired comparison, rank order, rating and multiway data (Nishisato, 1994).

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Conclusion In spite o f s o m e negative c o m m e n t s , this b o o k is a w e l c o m e addition to the literature in this field. G r e e n a c r e ' s modules are b a s e d on his expert knowledge of the rationale of c o r r e s p o n d e n c e analysis and his experiences as a teacher and user o f the method. H e has done a c o m m e n d a b l e job, and this b o o k will serve the needs o f m a n y data analysts. THE ONTARIO INSTITUTE FOR STUDIES IN EDUCATION, AND THE UNIVERSITY OF TORONTO Shizuhiko Nishisato References Greenacre, M. J. (1984). Theory and applications of correspondence analysis. London: Academic Press. Nishisato, S. (1994). Elements of dual scaling. Hillsdale, NJ: Lawrence Erlbaum Associates. Takane, Y. (1980). Analysis of categorizing behavior. Behaviormetrika, 8, 75-86. Torgerson, W. S. (1958). Theory and methods of scaling. New York: Wiley.