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Applied factor analysis in the natural sciences. Appendix by Leslie F. Marcus. (English) Zbl 0868.62051

Cambridge: Cambridge University Press. xii, 371 p. (1996).
The book was first published in 1976 under the title “Geological factor analysis” (Elsevier, Amsterdam). The present book is a revised version containing developments of several topics of fundamental importance in applied multivariate analysis such as, for example, the stability of eigenvectors, the identification of atypical and influential observations, the analysis of compositional data, the rise of tensor biometry as a valuable tool in evolutionary biology, and canonical correspondence analysis. According to authors, the term factor analysis has been used in the vernacular mode, i.e., to signify the statistical application of the algebra of eigenvalues and eigenvectors to the analysis of single multivariate samples. To a certain degree, the usage agrees with ‘L’Analyse factorielle des correspondances’ of the francophone literature.
The book has been divided into eight chapters and an appendix containing computer programs. Chapter 1 introduces the concept of multivariate data analysis by factoring methods. Chapter 2 gives the basic concepts of multivariate algebra (linear algebra, matrix algebra) and the most commonly occurring matrix arithmetic operations of factor analysis.
Chapters 3 and 4 give theoretical concepts of factor analysis and the statistical interpretation of models, in which the presentation is made in terms of fixed mode and random mode: an account of the methods of principal components and “true” factor analysis is given. In Chapter 5, \(Q\)-mode factor analysis, principal coordinates and correspondence analysis are presented. Chapter 6 is concerned with every day practical problems dealing with diverse topics such as selection of the most suitable method, choosing the number of meaningful factors and data transformations. Chapter 7 gives examples of each of the major techniques. The last chapter presents reviews of randomly chosen applications of factor analysis from the literature.
The book requires a good knowledge of linear algebra and matrix algebra, as detailed in Chapter 2, and a background in statistics. Although the book has been written for Geologists in mind, it can be used in fields of research also. It can also be used for a one semester course at postgraduate level.
Reviewer: V.P.Gupta (Jaipur)

MSC:

62H25 Factor analysis and principal components; correspondence analysis
62-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics
62P99 Applications of statistics
86A32 Geostatistics
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