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REVIEWS Shizuhiko Nishisato. Elements of Dual Scaling: An Introduction to Practical Data Analysis. Hillsdale, NJ: Lawrence Erlbaum, 1994, xiv + 381, $79.95. The preface of this book starts with a discussion of dual scaling and the related technique of correspondence analysis. The author talks of the phenomenon of "branching out" and says that " w e may see the day when the name dual scaling will no longer be used synonymously with correspondence analysis". In my view the distinction between these two approaches is quite clear and one should not think of them as being strictly synonymous. Correspondence analysis is a method of multidimensional scalingma variant of classical (Torgerson-Householder-Gower) scalingmwhich reduces a table of categorical data to a graphical display where rows and columns of the table are represented as points. In such a " m a p " interpoint distances and relative positions of the points bear direct relationship to theoretical distances and concepts defined on the original data. Dual scaling, on the other hand, is a more general method of categorical data analysis which has at its heart Guttman's principle of internal consistency. When this principle is expressed in a certain simple form involving familiar sums-of-squares and variances, and when this principle is applied to certain data types, dual scaling coincides algebraically with correspondence analysis. When the two techniques do coincide it is the graphical displays which distinguish correspondence analysis from dual scaling. Nishisato's 1980 book on dual scaling contained very little reference to graphical displays. The present book differs notably from the 1980 book in two aspects: (a) the presence of many graphical displays as well as commentary about the utility and interpretation of these displays, and (b) discussion and examples of a variant of dual scaling called "forced classification". This review will mainly cover these two aspects, although some general comments about the book will be given first. In the preface Nishisato refers to books such as Girl (1990), Greenacre (1984), Lebart, Morineau and Warwick (1984) and Nishisato (1980) as "too advanced for many people who are primarily interested in applications" and contrasts these books with Nishisato and Nishisato (1984) which is "introductory". The present book is intended to fill the gap of a "medium-level book which bridges the two extremes". There is not a great difference in technical level between this book and Nishisato's earlier 1980 book, and the other four books described as "too advanced" are full of examples of applications. It does seem, however, that the present book is intended to be more pedagogic in style than its predecessor. The book is written in a very informal style, almost conversational. Phrases such as "It's worth a try", "Can you see that?", "Is this clear?", "You would probably agree t h a t . . . " are found regularly, as if the author is speaking to and trying to convince the reader. The headings are often quite informal as well, with the first three chapters called respectively " T o Begin With", "What Can Dual Scaling Do for Y o u " and "Is Your Data Set Appropriate to Dual Scaling?". These are short chapters giving the reader a flavor of the types of data and types of results expected for dual scaling. The accent is very much on graphical displays of the dual scaling results. Chapters 4, 5 and 6 give respectively "Some Fundamentals for Dual Scaling" in 0033-3123/96/$00.75/0 © 1996The PsychometricSociety

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which the simplest implementation of the internal consistency principle is derived, "Useful Quantitative Tools" which is a review of standard matrix algebra, and "Mathematics of Dual Scaling" which is a more complete mathematical version of chapter 4. At the end of chapter 6 we find a short section on graphical display and a first mention of joint plots, under the heading "Cautionary Notes on Graphical Display". Chapters 7, 8 and 9 are concerned with the dual scaling of three different types of categorical data under the general title of "incidence data", first contingency/frequency tables, second multiple-choice data and third sorting data. The first two situations are prime examples of applications where correspondence analysis and dual scaling coincide, usually called simple and multiple correspondence analysis respectively. The third situation is also multiple correspondence analysis, but with the respondents being thought of as the categorical variables since each subject allocates category numbers to a group of objects. Chapters 10, I1 and 12 treat three more data types under the general title of "dominance data", first paired comparison data, second rank-order data and third successive categories data (or ratings). This is where we move away from correspondence analysis and where the graphical solutions of dual scaling no longer have the interpretation as points in a high-dimensional space projected onto a subspace. Since correspondence analysis may be used to analysis rankings and ratings, often after a so-called "doubling" of the data, it would be interesting to compare the two approaches more closely. The remaining chapters cover "Special Topics". Chapter 13 is on what Nishisato calls "forced classification". The "Principle of Equivalent Partitioning" (PEP), on which forced classification is based, is said to be closely related to Benz6cri's principle of distributional equivalence, although it seems to be exactly the same. By forced classification Nishisato means that some data columns, for example, are increased in weight (by multiplying by a constant k) so that they are forced to dominate the solution. This is equivalent to an idea called "focusing" discussed by Greenacre (1984) as an example of the French practice of modifying the masses in a correspondence analysis. As Nishisato shows, this can be seen in the limit as a linear restriction on the subspace of the solution, an idea appearing in many variations in later literature (ter Braak 1986; Takane & Shibiyama 1991; BOckenholt & Takane 1994). In chapter 14, Nishisato tackles the graphical display aspect of dual scaling. Much of this discussion is concerned with the perennial confusion between the "symmetric map" and the "asymmetric map" and the dangers of over-interpreting joint plots. In my opinion, one of the best ways of thinking of the asymmetric map is as a biplot, so it is a pity that this aspect is given a very brief reference only. I disagree with the conclusion on the same page that the symmetric and asymmetric plots are "misleading" and "practically unsatisfactory" (page 268). The examples presented to support these statements are not convincing, especially the artificial example of a multiple correspondence analysis (page 267), which is presented as a problematic case but which is actually quite straightforward to interpret. An alternative display is proposed later in the chapter, consisting of representing only the unique response patterns (i.e., case points), but this is a very cumbersome type of graphical display except for data sets with very few categorical variables. It is clear from this chapter that there is still a lot of confusion about the graphical displays from correspondence analysis. On the production side, the book appears to have been prepared on a laser printer in camera-ready form. The typeface is not always as clear as it might have been using a photo-typesetting process. Pages 187-202 all appear in a smaller font size, for no apparent reason. In summary, this book is a distinct improvement over Nishisato (1980). The beauty

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of the book is that it contains many examples and data sets and these are discussed at length. For teaching purposes this would be useful. However, I find the explanation of the graphical displays lacking in completeness and clarity and readers would be justified in feeling ill-equipped to cope with the interpretation of the displays. UNIVERSITAT POMPEU FABRA

Michael J. Greenacre References

B6ckenholt, U., & Takane, Y. (1994). Linear constraints in correspondence analysis. In M. J. Greenacre & J. Blasius (Eds.), Correspondence analysis in the social sciences (pp. 112-127). London: Academic Press. Girl, A. (1990). Nonlinear multivariate analysis. Chichester: Wiley. Greenacre, M. J. (1984). Theory and applications of correspondence analysis. London: Academic Press. Lebart, L., Morineau, A., & Warwick, K. (1984). Multivariate descriptive statistical analysis. New York: Wiley. Nishisato, S. (1980). Analysis of categorical data: Dual scaling and its application. Toronto: University of Toronto Press. Nishisato, S., & Nishisato, I. (1984). Introduction to dual scaling. Toronto, Canada: MicroStats. Takane, Y., & Shibayama, T. (1991). Principal component analysis with external information on both subjects and variables. Psychometrika, 56, 667-684. ter Braak, C. J. F. (1986). Canonical correspondence analysis: A new eigen-vector technique for multivariate direct gradient analysis. Ecology, 67, 1167-1179.

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Michael J. Greenacre and J6rg Blasius (Eds.). Correspondence Analysis in the Social Sciences. London: Academic Press, 1994, 370 + xxi pages. General Description of the Book When Joachim Mucha of Berlin told me that an international conference on "Recent Developments and Applications in Correspondence Analysis" had been held in 1991 in Germany, I was most anxious to know about the participants and their studies. Finding out that this book was based on the presentations at the conference, I gladly accepted the invitation to review it. As expected, the contributors to the book are major players in the field of correspondence analysis, and the book offers a good bird's-eyeview of what correspondence analysis is and is for. The book consists of four parts: General introduction (chapters 1-6), generalizations to multivariate data (chapters 7-I0), analysis of longitudinal data (chapters 11-13), and further applications of correspondence analysis in social science research (chapters 14-16). Part One starts with three chapters devoted to familiarizing readers with the theme of the book: "Correspondence analysis and its interpretation" (Greenacre), "Correspondence analysis in social science research" (Blasius), and "Computation of correspondence analysis" (Greenacre and Blasius). Chapter 4 is on "Correspondence analysis and contingency table models" by van der Heijden, Mooijaart and Takane, who discuss the relations of correspondence analysis to loglinear models, association models and ideal point discriminant analysis. In Chapter 5, B6ckenholt and Takane present "Linear constraints in correspondence analysis", where they discuss two approaches to the imposition of constraints, the null-space method and the reparameterization method. Chapter 6 is entitled "Correspondence analysis: A history and French sociological perspective" by van Meter, Schilitz, Cibois and Mounier, providing us with a fresh and interesting account of French data analysis. Part Two starts with Greenacre's introduction to correspondence analysis of multiple-choice data, entitled "Multiple and joint correspondence analysis". Chapter 8 contains a delightful presentation on "Contemporary use of correspondence analysis and cluster analysis" by Lebart. This chapter is followed by a thorough and selfcontained paper, "Homogeneity analysis: Exploring the distribution of variables and their nonlinear relationships", by Heiser and Meulman. Chapter 10 is "Visualizing solutions in more than two dimensions" by Rovan, who discusses useful ways for two-, three- and multi-dimensional graphs. Part Three contains three chapters on analysis of longitudinal data, that is, event history data, panel data and trend data: "Analysing event history data by cluster analysis and multiple correspondence analysis: an example using data about work and occupations of scientists and engineers" by Martens, "The 'significance' of minor changes in panel data: A correspondence analysis of the division of household tasks" by Thiessen, Rohlinger and Blasius, and "Visualization of structural change by means of correspondence analysis" by M011er-Schneider. Part Four contains three applications of correspondence analysis to different problems: "Correspondence analysis of textual data from personal advertisements" by Giegler and Klein, "Explorations in social spaces: Gender, age, class fractions and photographic choices of objects" by Wuggenig and Mnich, and "Product perception 0033 -3123/96/$00.75/0 © 1996 The Psychometric Society

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and preference in consumer decision-making" by Snelders and Stokmans. The book ends with references and a subject index.

Matters of Opinion Conference proceedings are generally difficult to use as a textbook for teaching because they lack a progression in the complexity of the topics. This book is an attempt to combine the advantages of the wide coverage of conference proceedings and the careful arrangement of topics of a textbook. Have the editors succeeded in this attempt? Partly yes, and partly no. Let me explain.

Edited by Greenacre and Blasius. It is not easy to tell what role the editors played in this book, but it seems that they should have read all the papers, edited some of them, and unified the notation. This comment assumes that their intention was to make this book useful as a textbook, rather than mere conference proceedings. Chapter 1 (Greenacre). The author sets the stage by stating that the primary goal of correspondence analysis (CA) is to transform data into a graphical display. Although Greenacre tries to provide a nonthreatening, simple explanation of basic concepts, it seems that there is too much content included in this short chapter. Chapter 2 (Blasius). The author states that CA (correspondence analysis) is very stable, when further variables are included in analysis, while techniques like PCA (principal component analysis) are very sensitive. This depends on what kinds of variables are added to the data set. Indeed, it is well-known that both CA and PCA can be extremely sensitive to an addition of even a single variable or response. In fact, a very small subset of responses can produce the first dimension that has the largest inertia (see Nishisato, 1994, p. 296). Chapter 3 (Greenacre & Blasius). "There are many similarities between CA and PCA, which was a reason for the French to label correspondence analysis as analyse factorielle des correspondances" (p. 53). Why "factorielle" and not "composantes principales"? The last half would sound better if we replaced it with "which was a reason for Torgerson (1958) to label it as principal component analysis of categorical data". Another sentence "The e i g e n v a l u e s , . . . , factor loadings and the communalities are the coefficients used for interpretation of a PCA solution" is problematic, because the "communality" is a term defined for the common-factor analysis model, which refers to the variance of the variable in the common-factor space. There is no sense in using it for PCA. Chapter 4 (van der Heijden, Mooijaart & Takane). An excellent review, but readers are referred for detail to original papers. Some readers would definitely want a little more detail presented in this chapter. The authors and readers would presumably also be interested in the 1991 Millones study, which is not cited here, but which presents many numerical comparisons between different association models and correlation models (dual scaling and partially optimal scaling). Chapter 5 (Brckenholt & Takane). Another informative article. There are a number of places where "reparametrization" is discussed, but should it not be spelled "reparameterization" ? Chapter 6 (van Meter, Schlitz, Cibois & Mounier). It is good to read a history of French exploratory data analysis written by French researchers. Although they seem to

183 imply that the Anglo-Saxon approach to data analysis is inference-oriented, this is not necessarily so. Exploratory common factor analysis, optimal scaling and the Tukeytype exploratory data analysis have also been popular in the Anglo-Saxon world.

Chapter 7 (Greenacre). As CA is analogous to PCA, so JCA (joint correspondence analysis) is to FA (common factor analysis). This analogy by Greenacre is a good one, but does it extend to other aspects of PCA and FA? For instance, are the solutions of JCA nonunique like those of FA, and, if so, do they have to be rotated for the purpose of interpretation? Are there always solutions? If so, how many? The piecewise method of reciprocal averages (Nishisato & Sheu, 1980) may provide some mathematically interesting results for JCA. Chapter 8 (Lebart). Both specialists and practioners would find this chapter full of insightful remarks and excellent numerical examples. A masterful presentation. Chapter 9 (Heiser & Meulman). Another chapter full of information and an excellent summary. The permutation test could have been explained by an example, rather than by cited references, since it is a key for an important question on how many eigenvalues are to be maximized. Chapter 10 (Rovan). An excellent chapter on two-dimensional, three-dimensional and multidimensional graphs. These discussions would have been more useful, however, if an overview on tricky problems in graphical display (e.g., discrepant rowand column-spaces, effects of frequencies) is first provided as an introduction. The cutting point of I/n for the eigenvalue was also proposed by Nishisato from different points of view: when the eigenvalue is 1/n, the internal consistency reliability becomes zero (Nishisato, 1980), and the average of all the eigenvalues of given multiple-choice data is 1/n (Nishisato, 1994). Chapter 11 (Martens). Super indicator matrices are subjected to CA and cluster analysis, and the results are presented with good illustrations. Although CA is strongly favored over cluster analysis, the stated rationale for this support for CA is not convincing enough. Chapter 12 (Thiessen, Rohlinger & Blasius). Panel data are analyzed with supplementary variables. Although the analyses are thorough, it is difficult to digest "numerical parameters of CA" and "parameters INR1 and INR2." What do "parameters" mean? Chapter 13 (Miiller-Schneider). A good introduction to historic profiles, but what is meant by the assertion that "historic profiles provide a model of structural change"? In two places, the author faces difficulty in interpreting the second principal axis. Why should we only be concerned about interpretation of projections? Should we not look at clusters of variables in a multidimensional space rather than their projections on unimportant principal axes? Chapter 14 (Giegler & Klein). CA is applied to content analysis of textual data, and the authors present a good convincing discussion, capitalizing on characteristics of CA. The results of CA, however, are so dependent on those of content analysis, in particular, on the number of categories used in content analysis. See a remarkable example on this point in Nishisato (1994, pp. 322-323). It would have been useful if

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some cautions on the use of content analysis results or demonstrations of the consequences of different content analyses on CA results had been given.

Chapter 15 (Wuggenig & Mnich). Another interesting method of data collection, photo questioning, is introduced and used to collect data for CA. After an interesting application, however, I am completely lost when the chapter is concluded by the statement that "The structuring of the projective o b j e c t - c h o i c e s . . , indicates that the philosophical assumption of the "cognitive autonomy of s u b j e c t s " . . , seems to rest on an imaginary anthropology." Chapter 16 (Snelders & Stokmans). The authors introduce readers to the methods of laddering and natural grouping. Conjoint analysis and CA are discussed for analysis of the "attribute-by-rank" aggregate matrix of rankings. But, are we not interested in analyzing subjects and attributes? Is it not, therefore, more appropriate to use the Guttman-type dual scaling for such a super-matrix? Dual scaling handles the aggregate rank-order matrix of "respondent-by-attribute" matrix. There is a discussion on CA and MDS, stating that CA is preferred to MDS. But CA is equivalent to PCA, the metric MDS is nothing but PCA, and metric MDS and nonmetric MDS provide very similar results. In view of these considerations, how far can we go in discussing preferences of CA over MDS? Historical Notes In spite of my strong endorsement of the sixteen chapters, I must confess some bewilderment about the way in which the editors, in the PREFACE, forcibly attempted to jolt readers into believing that French correspondence analysis was the only mainstream approach. Granting that French contributions to the quantification of categorical data are outstanding, most of us know that the ideas behind French correspondence analysis have been called by many other names such as homogeneity analysis, Hayashi's theory of quantification, optimal scaling and dual scaling. Thus, it would have been courteous if the editors had been sufficiently open-minded to give appropriate credits to publications under other aliases, or, if they had restricted the coverage of the book to the realm of French correspondence analysis ~t la Greenacre. The editors have done neither. As a result, readers are left free to form a false impression about the field. Consider the following two quotations: (i) "The first published applications of correspondence analysis in the social sciences can be traced back to the 1970s in F r a n c e . . . " . But there are many other earlier applications of this quantification method to social science problems! Consider, for instance, the well-known exemplary applications by Johnson (1950) and Bock (1956). Paul Horst would remind us that he, Marion Richardson and others at Proctor Gamble used the method of reciprocal averages for social science problems in the 1930s. Chikio Hayashi would also tell us that he and his group applied his theory of quantification to analysis of many social survey data in the 1950s. (ii) "outside France it was only in the middle of the 1980s when correspondence analysis became known by social scientists in the English-speaking w o r l d , . . . , This growth of i n t e r e s t . . , was assisted by the publication of the first books in English by Greenacre in 1984 and by Lebart, Morineau and Warwick in the same year" (italics are the reviewer's). Two points to note: (a) many people, even those outside statistics (including this reviewer), in Japan were exposed to Hayashi's theory of quantification in the 1950s. Nishisato saw the connection between Hayashi's method and optimal scaling, taught by R. Darrell Bock in the early 1960s. Yes, optimal scaling was one of the topics in Bock's scaling course at the University of North Carolina. (b) Before 1984, Girl's 1981 prepublication draft on homogeneity analysis was widely circulated. Nish-

185 isato's book on dual scaling, based on six book-size technical reports from 1972 to 1976, was published in 1980. It covered the same methods as correspondence analysis, multiple correspondence analysis, analysis with linear constraints, multiway data and preference data (e.g., rank order, paired comparison data). The relevance of these books to correspondence analysis is made clear by the following quotation: " F o r a large part the results of Greenacre (1984) and Tenenhaus & Young (1985) are found already in Nishisato (1980) and Girl (1981)" (van der Heijden, 1987, p. 4). This may be a good place to shed some light on how the name "dual scaling" was introduced as an alternative name. It was not Nishisato's capricious invention, but was born within the history of the Psychometric Society: "At the 1976 annual meeting of the Psychometric Society, a symposium on optimal scaling was held with speakers Forrest W. Young (U.S.A.), Jan de Leeuw (The Netherlands), Gilbert Saporta (France) and Shizuhiko Nishisato (Canada), with discussant Joseph B. Kruskal (U.S.A.). During the discussion period, Joseph L. Zinnes (U.S.A.) posed a question about the adequacy of the name "optimal scaling". Upon examination of all the existing aliases at that time, Nishisato proposed the name "dual scaling" and adopted it in his 1980 book". (Nishisato & Nishisato, 1994, p. 115). Although this is not the place to argue about the name for the method, the name "analyse des correspondances" may be difficult to translate into other languages with its original meaning intact, while the word "dual" can be readily translated into other languages as a mathematical term for "symmetric". Conclusion In spite of the editors' emphasis in the preface on " a minimum of technical details," this book is probably too difficult for most of first-time learners, especially those in the social sciences. First-learners would likely prefer more elementary books such as Greenacre (1993) (see following review), Nishisato and Nishisato (1994) and Nishisato (1994). For specialists, Greenacre and Blasius have presented a good compact book on French correspondence analysis, and the other contributors have provided competent and admirable discussions on their own special topics. Accordingly, I would recommend this book to those who have some prior knowledge about CA, homogeneity analysis, Hayashi's theory of quantification and dual scaling. That being said, many other topics, dealt with in dual scaling, could also have been incorporated into this book. THE ONTARIO INSTITUTE FOR STUDIES IN EDUCATION, AND THE UNIVERSITY OF TORONTO Shizuhiko Nishisato References Book, R. D. (1956). The selection of judges for preference testing. Psychometrika, 21,349-366. Girl, A. (1981). Nonlinear multivariate analysis. New York: Wiley. (A prepublication edition of Girl, A., 1990). Greenacre, M. J. (1973). Correspondence analysis in practice. London: Academic Press. Greenacre, M. J. (1984). Theory and applications of correspondence analysis. London, England: Academic Press. Johnson, P. O. (1950). The quantification of qualitative data in discriminant analysis. Journal of the American Statistical Association, 45, 65076. Lebart, L., Morineau, A., & Warick, K. M. (1984). Multivariate descriptive statistical analysis. New York: Wiley.

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Millones, O. (1991). Dual scaling in the framework of the association and correlation models under maximum likelihood. Unpublished doctoral dissertation, University of Toronto, Canada. Nishisato, S. (1980). Analysis of categorical data: Dual scaling and its applications. Toronto: University of Toronto Press. Nishisato, S. (1994). Elements of dual scaling. Hillsdale, NJ: Lawrence Erlbaum. Nishisato, S., & Nishisato, I. (1994). Dual scaling in a nutshell. Toronto, Canada: MicroStats. Nishisato, S., Sheu, W. J. (1980). Piecewise method of reciprocal averages for dual scaling of multiple-choice data. Psychometrika, 45, 467--478. Tenenhaus, M., & Young, F. W. (1985). An analysis and synthesis of multiple correspondence analysis, optimal scaling, dual scaling, homogeneity analysis and other methods for quantifying multivariate categorical data. Psychometrika, 50, 91-119. Torgerson, W. S. (1958). Theory and methods of scaling. New York: Wiley. van der Heijden, P. G. M. (1987). Correspondence analysis of longitudinal categorical data. Leiden, The Netherlands: DSWO Press.

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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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some cautions on the use of content analysis results or demonstrations of the consequences of different content analyses on CA results had been given.

Chapter 15 (Wuggenig & Mnich). Another interesting method of data collection, photo questioning, is introduced and used to collect data for CA. After an interesting application, however, I am completely lost when the chapter is concluded by the statement that "The structuring of the projective o b j e c t - c h o i c e s . . , indicates that the philosophical assumption of the "cognitive autonomy of s u b j e c t s " . . , seems to rest on an imaginary anthropology." Chapter 16 (Snelders & Stokmans). The authors introduce readers to the methods of laddering and natural grouping. Conjoint analysis and CA are discussed for analysis of the "attribute-by-rank" aggregate matrix of rankings. But, are we not interested in analyzing subjects and attributes? Is it not, therefore, more appropriate to use the Guttman-type dual scaling for such a super-matrix? Dual scaling handles the aggregate rank-order matrix of "respondent-by-attribute" matrix. There is a discussion on CA and MDS, stating that CA is preferred to MDS. But CA is equivalent to PCA, the metric MDS is nothing but PCA, and metric MDS and nonmetric MDS provide very similar results. In view of these considerations, how far can we go in discussing preferences of CA over MDS? Historical Notes In spite of my strong endorsement of the sixteen chapters, I must confess some bewilderment about the way in which the editors, in the PREFACE, forcibly attempted to jolt readers into believing that French correspondence analysis was the only mainstream approach. Granting that French contributions to the quantification of categorical data are outstanding, most of us know that the ideas behind French correspondence analysis have been called by many other names such as homogeneity analysis, Hayashi's theory of quantification, optimal scaling and dual scaling. Thus, it would have been courteous if the editors had been sufficiently open-minded to give appropriate credits to publications under other aliases, or, if they had restricted the coverage of the book to the realm of French correspondence analysis h la Greenacre. The editors have done neither. As a result, readers are left free to form a false impression about the field. Consider the following two quotations: (i) "The first published applications of correspondence analysis in the social sciences can be traced back to the 1970s in F r a n c e . . . " . But there are many other earlier applications of this quantification method to social science problems! Consider, for instance, the well-known exemplary applications by Johnson (1950) and Bock (1956). Paul Horst would remind us that he, Marion Richardson and others at Proctor Gamble used the method of reciprocal averages for social science problems in the 1930s. Chikio Hayashi would also tell us that he and his group applied his theory of quantification to analysis of many social survey data in the 1950s. (ii) "outside France it was only in the middle of the 1980s when correspondence analysis became known by social scientists in the English-speaking w o r l d , . . . , This growth of i n t e r e s t . . , was assisted by the publication of the first books in English by Greenacre in 1984 and by Lebart, Morineau and Warwick in the same year" (italics are the reviewer's). Two points to note: (a) many people, even those outside statistics (including this reviewer), in Japan were exposed to Hayashi's theory of quantification in the 1950s. Nishisato saw the connection between Hayashi's method and optimal scaling, taught by R. Darrell Bock in the early 1960s. Yes, optimal scaling was one of the topics in Bock's scaling course at the University of North Carolina. (b) Before 1984, Girl's 1981 prepublication draft on homogeneity analysis was widely circulated. Nish-

189 isato's book on dual scaling, based on six book-size technical reports from 1972 to 1976, was published in 1980. It covered the same methods as correspondence analysis, multiple correspondence analysis, analysis with linear constraints, multiway data and preference data (e.g., rank order, paired comparison data). The relevance of these books to correspondence analysis is made clear by the following quotation: "For a large part the results of Greenacre (1984) and Tenenhaus & Young (1985) are found already in Nishisato (1980) and Girl (1981)" (van der Heijden, 1987, p. 4). This may be a good place to shed some light on how the name "dual scaling" was introduced as an alternative name. It was not Nishisato's capricious invention, but was born within the history of the Psychometric Society: "At the 1976 annual meeting of the Psychometric Society, a symposium on optimal scaling was held with speakers Forrest W. Young (U.S.A.), Jan de Leeuw (The Netherlands), Gilbert Saporta (France) and Shizuhiko Nishisato (Canada), with discussant Joseph B. Kruskal (U.S.A.). During the discussion period, Joseph L. Zinnes (U.S.A.) posed a question about the adequacy of the name "optimal scaling". Upon examination of all the existing aliases at that time, Nishisato proposed the name "dual scaling" and adopted it in his 1980 book". (Nishisato & Nishisato, 1994, p. 115). Although this is not the place to argue about the name for the method, the name "analyse des correspondances" may be difficult to translate into other languages with its original meaning intact, while the word "dual" can be readily translated into other languages as a mathematical term for "symmetric". Conclusion In spite of the editors' emphasis in the preface on " a minimum of technical details," this book is probably too difficult for most of first-time learners, especially those in the social sciences. First-learners would likely prefer more elementary books such as Greenacre (1993) (see following review), Nishisato and Nishisato (1994) and Nishisato (1994). For specialists, Greenacre and Blasius have presented a good compact book on French correspondence analysis, and the other contributors have provided competent and admirable discussions on their own special topics. Accordingly, I would recommend this book to those who have some prior knowledge about CA, homogeneity analysis, Hayashi's theory of quantification and dual scaling. That being said, many other topics, dealt with in dual scaling, could also have been incorporated into this book.

THE ONTARIO INSTITUTE FOR STUDIES IN EDUCATION, AND THE UNIVERSITY OF TORONTO Shizuhiko Nishisato References Bock, R. D. (1956). The selection of judges for preference testing. Psychometrika, 21,349-366. Girl, A. (1981). Nonlinear multivariate analysis. New York: Wiley. (A prepublication edition of Girl, A., 1990). Greenacre, M. J. (1973). Correspondence analysis in practice. London: Academic Press. Greenacre, M. J. (1984). Theory and applications of correspondence analysis. London, England: Academic Press. Johnson, P. O. (1950). The quantification of qualitative data in discriminant analysis. Journal of the American Statistical Association, 45, 65076. Lebart, L., Morineau, A., & Warick, K. M. (1984). Multivariate descriptive statistical analysis. New York: Wiley.

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Millones, O. (1991). Dual scaling in the framework of the association and correlation models under maximum likelihood. Unpublished doctoral dissertation, University of Toronto, Canada. Nishisato, S. (1980). Analysis of categorical data: Dual scaling and its applications. Toronto: University of Toronto Press. Nishisato, S. (1994). Elements of dual scaling. Hillsdale, NJ: Lawrence Erlbaum. Nishisato, S., & Nishisato, I. (1994). Dual scaling in a nutshell. Toronto, Canada: MicroStats. Nishisato, S., Sheu, W. J. (1980). Piecewise method of reciprocal averages for dual scaling of multiple-choice data. Psychometrika, 45, 467-478. Tenenhaus, M., & Young, F. W. (1985). An analysis and synthesis of multiple correspondence analysis, optimal scaling, dual scaling, homogeneity analysis and other methods for quantifying multivariate categorical data. Psychometrika, 50, 91-119. Torgerson, W. S. (1958). Theory and methods of scaling. New York: Wiley. van der Heijden, P. G. M. (1987). Correspondence analysis of longitudinal categorical data. Leiden, The Netherlands: DSWO Press.