Biplots. (English) Zbl 0867.62053

Gower, J. C.; Hand, D. J.

Monographs on Statistics and Applied Probability. 54. London: Chapman & Hall. xvi, 277 p. (1996).

This book is concerned with representing information on samples and variables in a single diagram, and with how to interpret such diagrams. Biplots are the multivariate analogue of scatter plots. They approximate the multivariate distribution of a sample in a few dimensions, typically two.
The book consists of 11 chapters and an appendix. The basic methods of multidimensional scaling are principal components analysis (PCA), multiple correspondence analysis (MCA), canonical variate analysis (CVA) and principal coordinates analysis (PCO). The inter-sample distances used in this book are the Pythagorean distance for PCA, distance for MCA, Mahalanobis distance for CVA, any Euclidean embeddable distance for PCO. The titles of the chapters are the following.
Chapter 1: Introduction. Chapter 2: Principal components analysis. Chapter 3: Other linear biplots. Chapter 4: Multiple correspondence analysis. Chapter 5: Canonical biplots. Chapter 6: Nonlinear biplots. Chapter 7: Generalized biplots. Chapter 8: Biadditive models. Chapter 9: Correspondence analysis. Chapter 10: Relationship between CA and MCA. Chapter 11: Other topics.
The appendix contains some important and useful algebraic results for the reader. This monograph is very useful for applied statisticians and statistical consultants, especially those in ecology, psychology and marketing.

Reviewer: Wang Songgui (Beijing)

MSC:

62H25	Factor analysis and principal components; correspondence analysis
62-02	Research exposition (monographs, survey articles) pertaining to statistics
62A09	Graphical methods in statistics
91C15	One- and multidimensional scaling in the social and behavioral sciences
62H99	Multivariate analysis

Keywords:

biadditive models; multidimensional scaling; principal components; multiple correspondence analysis; canonical variate analysis; principal coordinates analysis; Mahalanobis distance; biplots