Understanding Biplots

, by Gower, John C.; Lubbe, Sugnet Gardner; Le Roux, Niel J.

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ISBN: 9780470012550 | 0470012552
Cover: Hardcover
Copyright: 1/18/2011

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The aim of the book is to popularize what is now seen to be a useful and reliable methods for the visualization of multivariate data where the researcher wants to consider, for example, principal component analysis (PCA), canonical variates analysis (CVA) or various types of correspondence analysis. The theory is introduced and explained and the techniques then applied to problems from a variety of areas from ecology, biostatistics, demography and other social sciences, and finance. This latter area provides the best source of applications for the technique. Software is described and made available on a website.

Introduction
Types of biplots
Overview of the book
Software
Notation
Biplot basics
A simple example revisited
The biplot as a multidimensional scatterplo
Calibrated biplot axes
Refining the biplot display
Scaling the data
A closer look at biplot axes
Adding new variables: the regression method
Biplots and large data sets
Enclosing a configuration of sample points
Principal component analysis biplots
An example: Risk management
Understanding PCA and constructing its biplot
Measures of fit for PCA biplots
Predictivities of newly interpolated samples
Adding new axes to a PCA biplot and defining their predictivities
Scaling the data in a PCA biplot
Functions for constructing a PCA biplot
Canonical variate analysis biplots
An example: Revisiting the Ocotea data of Table 3.9
Understanding CVA and constructing its biplot
Geometric interpretation of the transformation to the canonical space
CVA biplot axes
Adding new points and variables to a CVA biplot
Measures of fit for CVA biplots
Functions for constructing a CVA biplot
Continuing the Ocotea example
CVA biplots for two classes
A five classes CVA biplot example
Overlap in two dimensional biplots
Multidimensional Scaling and Nonlinear Biplots
Introduction
The regression method
Nonlinear Biplots
Providing nonlinear biplot axes for variables 5-12
A PCA biplot as a Nonlinear biplot
Constructing Nonlinear biplots 5
Examples
Analysis of Distance
Functions AODplot and PermutationAnova
Introduction
A Biadditive Model
Statistical Analysis of the Biadditive Model
Biplots associated with Biadditive Models
Interpolating new rows or columns
Functions for constructing biadditive biplots
Examples of biadditive biplots: the wheat data
Diagnostic Biplots
Two-way Tables: Biplots associated with Correspondence Analysis
Introduction
The Correspondence Analysis Biplot
Interpolation of new points (supplementary points) in CA biplots
Other CA related methods
Functions for constructing CA biplots
Examples
Conclusion
Multiple Correspondence analysis
Introduction
Multiple correspondence analysis of the Indicator Matrix
The Burt Matrix
Similarity Matrices, and the Extended Matching Coefficient (EMC)
Category Level Points (CLPs)
Homals
Correlational Approach
Categorical (Nonlinear) Principal Components Analysis
Functions for constructing MCA related biplots
Revisiting the Remuneration data: Examples of MCA and Categorical PCA biplots
Generalized Biplots
Introduction
Calculating inter-sample distances
Constructing a generalized biplot
Reference system
The Basic Points
Interpolation
Prediction
An example
Constructing Generalized biplots
Monoplots
Multidimensional Scaling
Monoplots related to the Covariance matrix
Skew-symmetry
Area Biplots
Functions for constructing monoplots
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Understanding Biplots

Summary

Author Biography

Table of Contents

Supplemental Materials