Understanding Biplots

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

• ISBN13: 9780470012550
• ISBN10: 0470012552
• Edition: 1st
• Format: Hardcover
• Copyright: 2011-01-18
• Publisher: Wiley

Summary

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.

Author Biography

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.

Table of Contents

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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