Multivariate Data Reduction and Discrimination with SAS Software

by Khattree, Ravindra; Naik, Dayanand N.

• ISBN13: 9780471323006
• ISBN10: 0471323004
• Edition: 1st
• Format: Paperback
• Copyright: 2000-08-14
• Publisher: Wiley-SAS

Summary

Easy to read and comprehensive, this book presents descriptive multivariate (DMV) statistical methods using real-world problems and data sets. It offers a unique approach to integrating statistical methods, various kinds of advanced data analyses, and applications of the popular SAS software aids. Emphasis is placed on the correct interpretation of output to draw meaningful conclusions in a variety of disciplines and industries.

Author Biography

Ravindra Khattree is professor of applied statistics at Oakland University, Rochester, Michigan Dayanand N. Naik is an associate professor of statistics at Old Dominion University, Norfolk, Virginia

Table of Contents

Preface	ix
Commonly Used Notation	xiii
Basic Concepts for Multivariate Statistics	1	(24)
Introduction	1	(1)
Population Versus Sample	2	(1)
Elementary Tools for Understanding Multivariate Data	3	(3)
Data Reduction, Description, and Estimation	6	(1)
Concepts from Matrix Algebra	7	(14)
Multivariate Normal Distribution	21	(2)
Concluding Remarks	23	(2)
Principal Component Analysis	25	(52)
Introduction	25	(1)
Population Principal Components	26	(3)
Sample Principal Components	29	(11)
Selection of the Number of Principal Components	40	(6)
Some Applications of Principal Component Analysis	46	(11)
Principal Component Analysis of Compositional Data	57	(3)
Principal Component Regression	60	(5)
Principal Component Residuals and Detection of Outliers	65	(4)
Principal Component Biplot	69	(7)
PCA Using SAS/INSIGHT Software	76	(1)
Concluding Remarks	76	(1)
Canonical Correlation Analysis	77	(34)
Introduction	77	(1)
Population Canonical Correlations and Canonical Variables	78	(1)
Sample Canonical Correlations and Canonical Variables	79	(12)
Canonical Analysis of Residuals	91	(1)
Partial Canonical Correlations	92	(3)
Canonical Redundancy Analysis	95	(6)
Canonical Correlation Analysis of Qualitative Data	101	(5)
`Partial Tests' in Multivariate Regression	106	(2)
Concluding Remarks	108	(3)
Factor Analysis	111	(100)
Introduction	111	(1)
Factor Model	112	(4)
A Difference between PCA and Factor Analysis	116	(2)
Noniterative Methods of Estimation	118	(21)
Iterative Methods of Estimation	139	(16)
Heywood Cases	155	(1)
Comparison of the Methods	156	(2)
Factor Rotation	158	(19)
Estimation of Factor Scores	177	(7)
Factor Analysis Using Residuals	184	(4)
Some Applications	188	(21)
Concluding Remarks	209	(2)
Discriminant Analysis	211	(136)
Introduction	211	(1)
Multivariate Normality	212	(19)
Statistical Tests for Relevance	231	(11)
Discriminant Analysis: Fisher's Approach	242	(13)
Discriminant Analysis for k Normal Populations	255	(27)
Canonical Discriminant Analysis	282	(14)
Variable Selection in Discriminant Analysis	296	(8)
When Dimensionality Exceeds Sample Size	304	(10)
Logistic Discrimination	314	(19)
Nonparametric Discrimination	333	(11)
Concluding Remarks	344	(3)
Cluster Analysis	347	(96)
Introduction	347	(1)
Graphical Methods for Clustering	348	(8)
Similarity and Dissimilarity Measures	356	(3)
Hierarchical Clustering Methods	359	(21)
Clustering of Variables	380	(13)
Nonhierarchical Clustering: k-Means Approach	393	(28)
How Many Clusters: Cubic Clustering Criterion	421	(6)
Clustering Using Density Estimation	427	(8)
Clustering with Binary Data	435	(6)
Concluding Remarks	441	(2)
Correspondence Analysis	443	(68)
Introduction	443	(1)
Correspondence Analysis	444	(19)
Multiple Correspondence Analysis	463	(13)
CA as a Canonical Correlation Analysis	476	(3)
Correspondence Analysis Using Andrews Plots	479	(11)
Correspondence Analysis Using Hellinger Distance	490	(8)
Canonical Correspondence Analysis	498	(11)
Concluding Remarks	509	(2)
Appendix: Data Sets	511	(24)
References	535	(8)
Index	543