Methods of Multivariate Analysis, Second Edition (Wiley Series in Probability and Statistics)

✍ Scribed by Alvin C. Rencher

• Publisher: Wiley-Interscience
• Year: 2002
• Tongue: English
• Leaves: 731
• Series: Wiley Series in Probability and Statistics
• Edition: 2nd
• Category: Library

✦ Synopsis

Amstat News asked three review editors to rate their top five favorite books in the September 2003 issue. Methods of Multivariate Analysis was among those chosen.When measuring several variables on a complex experimental unit, it is often necessary to analyze the variables simultaneously, rather than isolate them and consider them individually. Multivariate analysis enables researchers to explore the joint performance of such variables and to determine the effect of each variable in the presence of the others. The Second Edition of Alvin Rencher's Methods of Multivariate Analysis provides students of all statistical backgrounds with both the fundamental and more sophisticated skills necessary to master the discipline.To illustrate multivariate applications, the author provides examples and exercises based on fifty-nine real data sets from a wide variety of scientific fields. Rencher takes a "methods" approach to his subject, with an emphasis on how students and practitioners can employ multivariate analysis in real-life situations. The Second Edition contains revised and updated chapters from the critically acclaimed First Edition as well as brand-new chapters on:Cluster analysisMultidimensional scalingCorrespondence analysisBiplotsEach chapter contains exercises, with corresponding answers and hints in the appendix, providing students the opportunity to test and extend their understanding of the subject. Methods of Multivariate Analysis provides an authoritative reference for statistics students as well as for practicing scientists and clinicians.

✦ Table of Contents

Contents v......Page 6
Preface xv......Page 16
Acknowledgments xix......Page 20
1.1 Why Multivariate Analysis? 1......Page 24
1.4 Basic Types of Data and Analysis 3......Page 26
2.2 Notation and Basic Definitions 5......Page 28
2.3 Operations 9......Page 32
2.4 Partitioned Matrices 20......Page 43
2.5 Rank 22......Page 45
2.6 Inverse 23......Page 46
2.7 Positive Definite Matrices 25......Page 48
2.8 Determinants 26......Page 49
2.9 Trace 30......Page 53
2.10 Orthogonal Vectors and Matrices 31......Page 54
2.11 Eigenvalues and Eigenvectors 32......Page 55
3.1 Mean and Variance of a Univariate Random Variable 43......Page 66
3.2 Covariance and Correlation of Bivariate Random Variables 45......Page 68
3.3 Scatter Plots of Bivariate Samples 50......Page 73
3.4 Graphical Displays for Multivariate Samples 52......Page 75
3.5 Mean Vectors 53......Page 76
3.6 Covariance Matrices 57......Page 80
3.7 Correlation Matrices 60......Page 83
3.8 Mean Vectors and Covariance Matrices for Subsets of Variables 62......Page 85
3.9 Linear Combinations of Variables 66......Page 89
3.10 Measures of Overall Variability 73......Page 96
3.11 Estimation of Missing Values 74......Page 97
3.12 Distance between Vectors 76......Page 99
4.1 Multivariate Normal Density Function 82......Page 105
4.2 Properties of Multivariate Normal Random Variables 85......Page 108
4.3 Estimation in the Multivariate Normal 90......Page 113
4.4 Assessing Multivariate Normality 92......Page 115
4.5 Outliers 99......Page 122
5.1 Multivariate versus Univariate Tests 112......Page 135
5.2 Tests on mu with Sigma Known 113......Page 136
5.3 Tests on mu When Sigma Is Unknown 117......Page 140
5.4 Comparing Two Mean Vectors 121......Page 144
5.5 Tests on Individual Variables Conditional on Rejection of H_0 by the T^2-Test 126......Page 149
5.6 Computation of T^2 130......Page 153
5.7 Paired Observations Test 132......Page 155
5.8 Test for Additional Information 136......Page 159
5.9 Profile Analysis 139......Page 162
6.1 One-Way Models 156......Page 179
6.2 Comparison of the Four Manova Test Statistics 176......Page 199
6.3 Contrasts 178......Page 201
6.4 Tests on Individual Variables Following Rejection of H_0 by the Overall MANOVA Test 183......Page 206
6.5 Two-Way Classification 186......Page 209
6.6 Other Models 195......Page 218
6.7 Checking on the Assumptions 198......Page 221
6.8 Profile Analysis 199......Page 222
6.9 Repeated Measures Designs 204......Page 227
6.10 Growth Curves 221......Page 244
6.11 Tests on a Subvector 231......Page 254
7.2 Testing a Specified Pattern for Sigma 248......Page 271
7.3 Tests Comparing Covariance Matrices 254......Page 277
7.4 Tests of Independence 259......Page 282
8.1 Introduction 270......Page 293
8.2 The Discriminant Function for Two Groups 271......Page 294
8.3 Relationship between Two-Group Discriminant Analysis and Multiple Regression 275......Page 298
8.4 Discriminant Analysis for Several Groups 277......Page 300
8.5 Standardized Discriminant Functions 282......Page 305
8.6 Tests of Significance 284......Page 307
8.7 Interpretation of Discriminant Functions 288......Page 311
8.8 Scatter Plots 291......Page 314
8.9 Stepwise Selection of Variables 293......Page 316
9.1 Introduction 299......Page 322
9.2 Classification into Two Groups 300......Page 323
9.3 Classification into Several Groups 304......Page 327
9.4 Estimating Misclassification Rates 307......Page 330
9.5 Improved Estimates of Error Rates 309......Page 332
9.6 Subset Selection 311......Page 334
9.7 Nonparametric Procedures 314......Page 337
10.1 Introduction 322......Page 345
10.2 Multiple Regression: Fixed x's 323......Page 346
10.4 Multivariate Multiple Regression: Estimation 337......Page 360
10.5 Multivariate Multiple Regression: Hypothesis Tests 343......Page 366
10.6 Measures of Association between the y's and the x's 349......Page 372
10.7 Subset Selection 351......Page 374
10.8 Multivariate Regression: Random x's 358......Page 381
11.2 Canonical Correlations and Canonical Variates 361......Page 384
11.3 Properties of Canonical Correlations 366......Page 389
11.4 Tests of Significance 367......Page 390
11.5 Interpretation 371......Page 394
11.6 Relationships of Canonical Correlation Analysis to Other Multivariate Techniques 374......Page 397
12.1 Introduction 380......Page 403
12.2 Geometric and Algebraic Bases of Principal Components 381......Page 404
12.3 Principal Components and Perpendicular Regression 387......Page 410
12.4 Plotting of Principal Components 389......Page 412
12.5 Principal Components from the Correlation Matrix 393......Page 416
12.6 Deciding How Many Components to Retain 397......Page 420
12.8 Interpretation of Principal Components 401......Page 424
12.9 Selection of Variables 404......Page 427
13.1 Introduction 408......Page 431
13.2 Orthogonal Factor Model 409......Page 432
13.3 Estimation of Loadings and Communalities 415......Page 438
13.4 Choosing the Number of Factors, m 426......Page 449
13.5 Rotation 430......Page 453
13.6 Factor Scores 438......Page 461
13.7 Validity of the Factor Analysis Model 443......Page 466
13.8 The Relationship of Factor Analysis to Principal Component Analysis 447......Page 470
14.1 Introduction 451......Page 474
14.2 Measures of Similarity or Dissimilarity 452......Page 475
14.3 Hierarchical Clustering 455......Page 478
14.4 Nonhierarchical Methods 481......Page 504
14.5 Choosing the Number of Clusters 494......Page 517
14.6 Cluster Validity 496......Page 519
14.7 Clustering Variables 497......Page 520
15.1 Multidimensional Scaling 504......Page 527
15.2 Correspondence Analysis 514......Page 537
15.3 Biplots 531......Page 554
Table A.1 Upper Percentiles for √b1......Page 572
Table A.2 Coefficients for Transforming √b1 to a Standard Normal......Page 573
Table A.3 Percentiles for b2......Page 574
Table A.4 Percentiles for D’Agostino’s Test for Normality......Page 575
Table A.5 Upper Percentiles for b1,p and Upper and Lower Percentiles for b2,p......Page 576
Table A.6 Upper Percentiles for Test of Single Multivariate Normal Outlier......Page 580
Table A.7 Upper Percentage Points of Hotelling’s T2 Distribution......Page 581
Table A.8 Bonferonni t-Values, tα/2k,ν, α = .05......Page 585
Table A.9 Lower Critical Values of Wilks Λ, α = .05......Page 589
Table A.10 Upper Critical Values for Roy’s Test, α = .05......Page 597
Table A.11 Upper Critical Values of Pillai’s Statistic V(s), α = .05......Page 601
Table A.12 Upper Critical Values for the Lawley–Hotelling Test Statistic, α = .05......Page 605
Table A.13 Orthogonal Polynomial Contrasts......Page 610
Table A.14 Test for Equal Covariance Matrices, α = .05......Page 611
Table A.15 Test for Independence of p Variables......Page 613
CHAPTER 2......Page 614
CHAPTER 3......Page 619
CHAPTER 4......Page 622
CHAPTER 5......Page 628
CHAPTER 6......Page 630
CHAPTER 7......Page 640
CHAPTER 8......Page 643
CHAPTER 9......Page 647
CHAPTER 10......Page 652
CHAPTER 11......Page 657
CHAPTER 12......Page 660
CHAPTER 13......Page 669
CHAPTER 14......Page 677
CHAPTER 15......Page 684
C Data Sets and SAS Files 679......Page 702
References 681......Page 704
Index 695......Page 718