Multivariate Data Reduction and Discrimination with SAS Software / Edition 1

by Ravindra Khattree, Dayanand N. Naik

Overview

Multivariate data commonly encountered in a variety of disciplines is easy to understand with the approaches and methods described in Multivariate Data Reduction and Discrimination with SAS Software. Authors Ravindra Khattree and Dayanand Naik present the conceptual developments, theory, methods, and subsequent data analyses systematically and in an integrated manner. The data analysis is performed using many multivariate analysis components available in SAS software. Illustrations are provided using an ample number of real data sets drawn from a variety of fields, and special care is taken to explain the SAS codes and the interpretation of corresponding outputs. As a companion volume to the authors' previous book, Applied Multivariate Analysis with SAS Software, which discusses multivariate normality-based analyses, this book covers topics where, for the most part, assuming multivariate normality (or any other distributional assumption) is not crucial. Since the techniques discussed in this book also form the foundation of data mining methodology, the book will be of interest to data mining practitioners.

Product Details

ISBN-13:	9781580256964
Publisher:	SAS Institute Inc.
Publication date:	01/17/2012
Edition description:	New Edition
Pages:	574
Product dimensions:	8.25(w) x 11.00(h) x 1.16(d)

About the Author

Ravindra Khattree is an Indian-American statistician and professor of statistics at Oakland University. His contribution to the Fountain-Khattree-Peddada Theorem in Pitman measure of closeness is one of the important results of his work. Khattree is the coauthor of two books and has coedited two volumes. Dayanand N. Naik is the author of Multivariate Data Reduction and Discrimination with SAS Software, published by Wiley.

Table of Contents

	Preface	ix
	Commonly Used Notation	xiii
1	Basic Concepts for Multivariate Statistics	1
1.1	Introduction	1
1.2	Population Versus Sample	2
1.3	Elementary Tools for Understanding Multivariate Data	3
1.4	Data Reduction, Description, and Estimation	6
1.5	Concepts from Matrix Algebra	7
1.6	Multivariate Normal Distribution	21
1.7	Concluding Remarks	23
2	Principal Component Analysis	25
2.1	Introduction	25
2.2	Population Principal Components	26
2.3	Sample Principal Components	29
2.4	Selection of the Number of Principal Components	40
2.5	Some Applications of Principal Component Analysis	46
2.6	Principal Component Analysis of Compositional Data	57
2.7	Principal Component Regression	60
2.8	Principal Component Residuals and Detection of Outliers	65
2.9	Principal Component Biplot	69
2.10	PCA Using SAS/INSIGHT Software	76
2.11	Concluding Remarks	76
3	Canonical Correlation Analysis	77
3.1	Introduction	77
3.2	Population Canonical Correlations and Canonical Variables	78
3.3	Sample Canonical Correlations and Canonical Variables	79
3.4	Canonical Analysis of Residuals	91
3.5	Partial Canonical Correlations	92
3.6	Canonical Redundancy Analysis	95
3.7	Canonical Correlation Analysis of Qualitative Data	101
3.8	'Partial Tests' in Multivariate Regression	106
3.9	Concluding Remarks	108
4	Factor Analysis	111
4.1	Introduction	111
4.2	Factor Model	112
4.3	A Difference between PCA and Factor Analysis	116
4.4	Noniterative Methods of Estimation	118
4.5	Iterative Methods of Estimation	139
4.6	Heywood Cases	155
4.7	Comparison of the Methods	156
4.8	Factor Rotation	158
4.9	Estimation of Factor Scores	177
4.10	Factor Analysis Using Residuals	184
4.11	Some Applications	188
4.12	Concluding Remarks	209
5	Discriminant Analysis	211
5.1	Introduction	211
5.2	Multivariate Normality	212
5.3	Statistical Tests for Relevance	231
5.4	Discriminant Analysis: Fisher's Approach	242
5.5	Discriminant Analysis for k Normal Populations	255
5.6	Canonical Discriminant Analysis	282
5.7	Variable Selection in Discriminant Analysis	296
5.8	When Dimensionality Exceeds Sample Size	304
5.9	Logistic Discrimination	314
5.10	Nonparametric Discrimination	333
5.11	Concluding Remarks	344
6	Cluster Analysis	347
6.1	Introduction	347
6.2	Graphical Methods for Clustering	348
6.3	Similarity and Dissimilarity Measures	356
6.4	Hierarchical Clustering Methods	359
6.5	Clustering of Variables	380
6.6	Nonhierarchical Clustering: k-Means Approach	393
6.7	How Many Clusters: Cubic Clustering Criterion	421
6.8	Clustering Using Density Estimation	427
6.9	Clustering with Binary Data	435
6.10	Concluding Remarks	441
7	Correspondence Analysis	443
7.1	Introduction	443
7.2	Correspondence Analysis	444
7.3	Multiple Correspondence Analysis	463
7.4	CA as a Canonical Correlation Analysis	476
7.5	Correspondence Analysis Using Andrews Plots	479
7.6	Correspondence Analysis Using Hellinger Distance	490
7.7	Canonical Correspondence Analysis	498
7.8	Concluding Remarks	509
Appendix	Data Sets	511
	References	535
	Index	543

Editorial Reviews

...a core or supplementary text for graduate or senior undergraduate students, and a reference for researchers and practitioners.

SciTech Book News

Statisticians Khattree (Oakland U., Rochester, Michigan) and Naik (Old Dominion U., Norfolk, Virginia) present a core or supplementary text for graduate or senior undergraduate students, and a reference for researchers and practitioners. As a companion to their (1999), they discuss further aspects, especially those in which the emphasis is more on data reduction, description, estimation, discrimination, and summarization. In these cases, it is generally not necessary to assume either multivariate normality or any other probability distribution. They assume readers to have taken a course in applied statistics and be familiar with matrix algebra. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Booknews

"...a core or supplementary text for graduate or senior undergraduate students, and a reference for researchers and practitioners." (SciTech Book News, Vol. 24, No. 4, December 2000)

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