Exploratory multivariate analysis by example using R.pdf

Exploratory Multivariate Analysis

by Example Using R

Chapman & Hall/CRC

Computer Science and Data Analysis Series

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and Bioinformatics

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Computational Statistics Handbook with

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Exploratory Multivariate Analysis by

Example Using R

François Husson, Sébastien Lê, and

Jérôme Pagès

Introduction to Data Technologies

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Exploratory Multivariate Analysis

by Example Using R

François Husson

Sébastien Lê

Jérôme Pagès

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Library of Congress Cataloging‑in‑Publication Data

Husson, François.

Exploratory multivariate analysis by example using R / François Husson, Sébastien Lê, Jérôme

Pagès.

p. cm. -- (Chapman & Hall/CRC computer science & data analysis)

Summary: “An introduction to exploratory techniques for multivariate data analysis, this book

covers the key methodology, including principal components analysis, correspondence analysis,

mixed models, and multiple factor analysis. The authors take a practical approach, with examples

leading the discussion of the methods and many graphics to emphasize visualization. They present

the concepts in the most intuitive way possible, keeping mathematical content to a minimum

or relegating it to the appendices. The book includes examples that use real data from a range of

scientific disciplines and implemented using an R package developed by the authors.”-- Provided

by publisher.

Includes bibliographical references and index.

ISBN 978-1-4398-3580-7 (hardback)

1. Multivariate analysis. 2. R (Computer program language) I. Lê, Sébastien. II. Pagès, Jérôme. III.

Title. IV. Series.

QA278.H87 2010

519.5’3502855133--dc22

2010040339

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Contents

Preface

x i

1 Principal Component Analysis (PCA)

1.1 Data | Notation | Examples . . . . . . . . . . . . . . . . .

1.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.2.1 Studying Individuals . . . . . . . . . . . . . . . . . . .

1.2.2 Studying Variables . . . . . . . . . . . . . . . . . . . .

1.2.3 Relationships between the Two Studies . . . . . . . .

1.3 Studying Individuals . . . . . . . . . . . . . . . . . . . . . .

1.3.1 The Cloud of Individuals . . . . . . . . . . . . . . . .

1.3.2 Fitting the Cloud of Individuals . . . . . . . . . . . .

1.3.2.1 Best Plane Representation of N I . . . . . . .

1.3.2.2 Sequence of Axes for Representing N I . . . .

1.3.2.3 How Are the Components Obtained? . . . .

1.3.2.4 Example . . . . . . . . . . . . . . . . . . . .

1.3.3 Representation of the Variables as an Aid for

Interpreting the Cloud of Individuals . . . . . . . . . . 11

1.4 Studying Variables . . . . . . . . . . . . . . . . . . . . . . . . 13

1.4.1 The Cloud of Variables . . . . . . . . . . . . . . . . . 13

1.4.2 Fitting the Cloud of Variables . . . . . . . . . . . . . . 14

1.5 Relationships between the Two Representations N I and N K 16

1.6 Interpreting the Data . . . . . . . . . . . . . . . . . . . . . .

1.6.1 Numerical Indicators . . . . . . . . . . . . . . . . . . .

1.6.1.1 Percentage of Inertia Associated with a

Component . . . . . . . . . . . . . . . . . . .

1.6.1.2 Quality of Representation of an Individual or

Variable . . . . . . . . . . . . . . . . . . . . .

1.6.1.3 Detecting Outliers . . . . . . . . . . . . . . .

1.6.1.4 Contribution of an Individual or Variable to

the Construction of a Component . . . . . .

1.6.2 Supplementary Elements . . . . . . . . . . . . . . . . .

1.6.2.1 Representing Supplementary Quantitative

Variables . . . . . . . . . . . . . . . . . . . .

1.6.2.2 Representing Supplementary Categorical

Variables . . . . . . . . . . . . . . . . . . . .

1.6.2.3 Representing Supplementary Individuals . .

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