John Gower, Sugnet Gardner Lubbe, Niel Le Roux

Understanding Biplots (eBook, PDF)

• Format: PDF

Produktbeschreibung

Biplots are a graphical method for simultaneously displaying two kinds of information; typically, the variables and sample units described by a multivariate data matrix or the items labelling the rows and columns of a two-way table. This book aims to popularize what is now seen to be a useful and reliable method for the visualization of multidimensional data associated with, for example, principal component analysis, canonical variate analysis, multidimensional scaling, multiplicative interaction and various types of correspondence analysis. Understanding Biplots: * Introduces theory and techniques which can be applied to problems from a variety of areas, including ecology, biostatistics, finance, demography and other social sciences. * Provides novel techniques for the visualization of multidimensional data and includes data mining techniques. * Uses applications from many fields including finance, biostatistics, ecology, demography. * Looks at dealing with large data sets as well as smaller ones. * Includes colour images, illustrating the graphical capabilities of the methods. * Is supported by a Website featuring R code and datasets. Researchers, practitioners and postgraduate students of statistics and the applied sciences will find this book a useful introduction to the possibilities of presenting data in informative ways.

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Produktdetails

• Verlag: John Wiley & Sons
• Seitenzahl: 480
• Erscheinungstermin: 15. Oktober 2010
• Englisch
• ISBN-13: 9780470973202
• Artikelnr.: 37301395

Autorenporträt

John C. Gower, Department of Mathematics, The Open University, Milton Keynes, UK. Over 100 papers. Books include Gower & Hand (1996) Biplots, in which the authors developed a unified theory of biplots. Sugnet Gardner, British American Tobacco, Stellenbosch, South Africa. Niel J. le Roux, Department of Statistics and Actuarial Science, University of Stellenbosch , South Africa.

Inhaltsangabe

Preface. 1 Introduction. 1.1 Types of biplots. 1.2 Overview of the book.
1.3 Software. 1.4 Notation. 2 Biplot basics. 2.1 A simple example
revisited. 2.2 The biplot as a multidimensional scatterplot. 2.3 Calibrated
biplot axes. 2.4 Refining the biplot display. 2.5 Scaling the data. 2.6 A
closer look at biplot axes. 2.7 Adding new variables: the regression
method. 2.8 Biplots and large data sets. 2.9 Enclosing a configuration of
sample points. 2.10 Buying by mail order catalogue data set revisited. 2.11
Summary. 3 Principal component analysis biplots. 3.1 An example: risk
management. 3.2 Understanding PCA and constructing its biplot. 3.3 Measures
of fit for PCA biplots. 3.4 Predictivities of newly interpolated samples.
3.5 Adding new axes to a PCA biplot and defining their predictivities. 3.6
Scaling the data in a PCA biplot. 3.7 Functions for constructing a PCA
biplot. 3.8 Some novel applications and enhancements of PCA biplots. 3.9
Conclusion. 4 Canonical variate analysis biplots. 4.1 An example:
revisiting the Ocotea data. 4.2 Understanding CVA and constructing its
biplot. 4.3 Geometric interpretation of the transformation to the canonical
space. 4.4 CVA biplot axes. 4.5 Adding new points and variables to a CVA
biplot. 4.6 Measures of fit for CVA biplots. 4.7 Functions for constructing
a CVA biplot. 4.8 Continuing the Ocotea example. 4.9 CVA biplots for two
classes. 4.10 A five-class CVA biplot example. 4.11 Overlap in
two-dimensional biplots. 5 Multidimensional scaling and nonlinear biplots.
5.1 Introduction. 5.2 The regression method. 5.3 Nonlinear biplots. 5.4
Providing nonlinear biplot axes for variables. 5.5 A PCA biplot as a
nonlinear biplot. 5.6 Constructing nonlinear biplots. 5.7 Examples. 5.8
Analysis of distance. 5.9 Functions AODplot and PermutationAnova. 6 Two-way
tables: biadditive biplots. 6.1 Introduction. 6.2 A biadditive model. 6.3
Statistical analysis of the biadditive model. 6.4 Biplots associated with
biadditive models. 6.5 Interpolating new rows or columns. 6.6 Functions for
constructing biadditive biplots. 6.7 Examples of biadditive biplots: the
wheat data. 6.8 Diagnostic biplots. 7 Two-way tables: biplots associated
with correspondence analysis. 7.1 Introduction. 7.2 The correspondence
analysis biplot. 7.3 Interpolation of new (supplementary) points in CA
biplots. 7.4 Other CA related methods. 7.5 Functions for constructing CA
biplots. 7.6 Examples. 7.7 Conclusion. 8 Multiple correspondence analysis.
8.1 Introduction. 8.2 Multiple correspondence analysis of the indicator
matrix. 8.3 The Burt matrix. 8.4 Similarity matrices and the extended
matching coefficient. 8.5 Category-level points. 8.6 Homogeneity analysis.
8.7 Correlational approach. 8.8 Categorical (nonlinear) principal component
analysis. 8.9 Functions for constructing MCA related biplots. 8.10
Revisiting the remuneration data: examples of MCA and categorical PCA
biplots. 9 Generalized biplots. 9.1 Introduction. 9.2 Calculating
inter-sample distances. 9.3 Constructing a generalized biplot. 9.4
Reference system. 9.5 The basic points. 9.6 Interpolation. 9.7 Prediction.
9.8 An example. 9.9 Function for constructing generalized biplots. 10
Monoplots. 10.1 Multidimensional scaling. 10.2 Monoplots related to the
covariance matrix. 10.3 Skew-symmetry. 10.4 Area biplots. 10.5 Functions
for constructing monoplots. References. Index.