Description
Book SynopsisThis book covers the most common methods for analyzing single, double, three-way and multi-way data. Geared towards applications and the decisions that have to be made to get meaningful analyses, it presents a variety of models illustrated using commercially available software.
Trade Review"All topics are well illustrated with good examples from a fairly wide range of applications... the book’s usefulness is enhanced by a glossary of multiway terminology, a good index and references to extension work... this is a well-crafted and highly readable book." (
Journal of the Royal Statistical Society- Series A, 2009)
“All in all, Kroonenberg’s book constitutes an extremely valuable tool for applied researchers in almost all domains of investigation, whenever they are faced with the task of analyzing complex statistical data in view of obtaining useful information in their areas of interest.” (Biometrics, June 2009)
“This book is focused primarily toward graduate students in the areas of chemistry, social and behavioral sciences, and environmental sciences, although the techniques and methods used can be more broadly used in other areas, such as finance and engineering, as well.” (Technometrics, May 2009)
"Kroonenberg’s book constitutes an extremely valuable tool for applied researchers in almost all domains of investigation (from economics to psychology, from biomedicine to technology and physical sciences), whenever they are faced with the task of analyzing complex statistical data in view of obtaining useful information in their areas of interest." (Biometrics 2009)
"...the combination of worked-out examples alongside descriptions and critical considerations on the theory behind those analyses make AMDA an interesting book for researchers and practitioners in both academia and industry. (Journal of the American Statistical Association 2009)
"The book is written in a clear style and mostly in conceptual rather than mathematical level. It emphasized the author's over thirty years' personal experience and practical side of performing multiway data analyses. It is easy to recommend this book, as it really open news views of the world." (International Statistical Review, December 2008)
"Good things take time - and this hold for this book as well…Pieter Kroonenberg is one of the few with a profound knowledge of multiway analysis. It is meritorious that he took the effort to share his knowledge. It is to be hoped that a next edition will appear soon...the book deserves a broad reading public." (Vereniging voor Ordinatie en Classificatie, Nieuwsbrief, no 41, November 2008)
"We believe that this book will offer applied researchers a lot of good advice for using three-way techniques. In addition, Applied Multiway Data-Analysis will turn out to be a valuable resource of reference for three-way specialists." (Mathematical Reviews, 2008)
Table of ContentsForeword xv Preface xvii
PART I DATA, MODELS, AND ALGORITHMS
1 Overture 3
1.1 Three-way and multiway data 4
1.2 Multiway data analysis 5
1.3 Before the arrival of three-mode analysis 6
1.4 Three-mode data-analytic techniques 7
1.5 Example: Judging Chopin's preludes 7
1.6 Birth of the Tucker model 12
1.7 Current status of multiway analysis 12
2 Overview 15
2.1 What are multiway data? 15
2.2 Why multiway analysis? 17
2.3 What is a model? 18
2.4 Some history 20
2.5 Multiway models and methods 24
2.6 Conclusions 24
3 Three-Way and Multiway Data 27
3.1 Chapter preview 27
3.2 Terminology 28
3.3 Two-way solutions to three-way data 30
3.4 Classification principles 31
3.5 Overview of three-way data designs 33
3.6 Fully crossed designs 33
3.7 Nested designs 38
3.8 Scaling designs 40
3.9 Categorical data 41
4 Component Models for Fully-Crossed Designs 43
4.1 Introduction 43
4.2 Chapter preview 45
4.3 Two-mode modeling of three-way data 45
4.4 Extending two-mode component models to three-mode models 47
4.5 Tucker models 51
4.6 Parafac models 57
4.7 ParaTuck2 model 63
4.8 Core arrays 64
4.9 Relationships between component models 66
4.10 Multiway component modeling under constraints 68
4.11 Conclusions 74
5 Algorithms for Multiway Models 77
5.1 Introduction 77
5.2 Chapter preview 78
5.3 Terminology and general issues 79
5.4 An example of an iterative algorithm 81
5.5 General behavior of multiway algorithms 84
5.6 The Parallel factor model - Parafac 85
5.7 The Tucker models 97
5.8 STATIS 105
5.9 Conclusions 106
PART II DATA HANDLING, MODEL SELECTION, AND INTERPRETATION
6 Preprocessing 109
6.1 Introduction 109
6.2 Chapter preview 112
6.3 General considerations 112
6.4 Model-based arguments for preprocessing choices 117
6.5 Content-based arguments for preprocessing choices 128
6.6 Preprocessing and specific multiway data designs 130
6.7 Centering and analysis-of-variance models: Two-way data 134
6.8 Centering and analysis-of-variance models: Three-way data 137
6.9 Recommendations 141
7 Missing Data in Multiway Analysis 143
7.1 Introduction 143
7.2 Chapter preview 147
7.3 Handling missing data in two-mode PCA 148
7.4 Handling missing data in multiway analysis 154
7.5 Multiple imputation in multiway analysis: Data matters 156
7.6 Missing data in multiway analysis: Practice 157
7.7 Example: Spanjer's Chromatography data 159
7.8 Example: NICHD Child care data 168
7.9 Further applications 172
7.10 Computer programs for multiple imputation 174
8 Model and Dimensionality Selection 175
8.1 Introduction 175
8.2 Chapter preview 176
8.3 Sample size and stochastics 176
8.4 Degrees of freedom 177
8.5 Selecting the dimensionality of a Tucker model 179
8.6 Selecting the dimensionality of a Parafac model 184
8.7 Model selection from a hierarchy 186
8.8 Model stability and predictive power 187
8.9 Example: Chopin prelude data 190
8.10 Conclusions 208
9 Interpreting Component Models 209
9.1 Chapter preview 209
9.2 General principles 210
9.3 Representations of component models 215
9.4 Scaling of components 218
9.5 Interpreting core arrays 225
9.6 Interpreting extended core arrays 231
9.7 Special topics 232
9.8 Validation 233
9.9 Conclusions 235
10 Improving Interpretation through Rotations 237
10.1 Introduction 237
10.2 Chapter preview 240
10.3 Rotating components 241
10.4 Rotating full core arrays 244
10.5 Theoretical simplicity of core arrays 254
10.6 Conclusions 256
11 Graphical Displays for Components 257
11.1 Introduction 257
11.2 Chapter preview 258
11.3 General considerations 259
11.4 Plotting single modes 260
11.5 Plotting different modes together 270
11.6 Conclusions 279
12 Residuals, Outliers, and Robustness 281
12.1 Introduction 281
12.2 Chapter preview 282
12.3 Goals 283
12.4 Procedures for analyzing residuals 284
12.5 Decision schemes for analyzing multiway residuals 287
12.6 Structured squared residuals 287
12.7 Unstructured residuals 292
12.8 Robustness: Basics 294
12.9 Robust methods of multiway analysis 297
12.10 Examples 301
12.1 1 Conclusions 307
PART III MULTIWAY DATA AND THEIR ANALYSIS
13 Modeling Multiway Profile Data 311
13.1 Introduction 311
13.2 Chapter preview 313
13.3 Example: Judging parents' behavior 313
13.4 Multiway profile data: General issues 320
13.5 Multiway profile data: Parafac in practice 322
13.6 Multiway profile data: Tucker analyses in practice 331
13.7 Conclusions 342
14 Modeling Multiway Rating Scale Data 345
14.1 Introduction 345
14.2 Chapter preview 346
14.3 Three-way rating scale data: Theory 346
14.4 Example: Coping at school 354
14.5 Analyzing three-way rating scales: Practice 360
14.6 Example: Differences within a multiple personality 361
14.7 Conclusions 370
15 Exploratory Multivariate Longitudinal Analysis 373
15.1 Introduction 373
15.2 Chapter preview 375
15.3 Overview of longitudinal modeling 375
15.4 Longitudinal three-mode modeling 378
15.5 Example: Organizational changes in Dutch hospitals 385
15.6 Example: Morphological development of French girls 394
15.7 Further reading 400
15.8 Conclusions 401
16 Three-Mode Clustering 403
16.1 Introduction 403
16.2 Chapter preview 405
16.3 Three-mode clustering analysis: Theory 405
16.4 Example: Identifying groups of diseased blue crabs 409
16.5 Three-mode cluster analysis: Practice 411
16.6 Example: Behavior of children in the Strange Situation 424
16.7 Extensions and special topics 430
16.8 Conclusions 432
17 Multiway Contingency Tables 433
17.1 Introduction 433
17.2 Chapter preview 434
17.3 Three-way correspondence analysis: Theory 435
17.4 Example: Sources of happiness 444
17.5 Three-way correspondence analysis: Practice 448
17.6 Example: Playing with peers 454
17.7 Conclusions 458
18 Three-Way Binary Data 459
18.1 Introduction 459
18.2 Chapter preview 460
18.3 A graphical introduction 460
18.4 Formal description of the Tucker-HICLAS models 462
18.5 Additional issues 465
18.6 Example: Hostile behavior in frustrating situations 465
18.7 Conclusion 467
19 From Three-Way Data to Four-Way Data and Beyond 469
19.1 Introduction 469
19.2 Chapter preview 471
19.3 Examples of multiway data 471
19.4 Multiway techniques: Theory 474
19.5 Example: Differences within a multiple personality 476
19.6 Example: Austrian aerosol particles 480
19.7 Further reading and computer programs 487
19.8 Conclusions 488
Appendix A: Standard Notation for Multiway Analysis 489
Appendix B: Biplots and Their Interpretation 491
B. 1 Introduction 492
B.2 Singular value decomposition 492
B.3 Biplots 494
B.4 Relationship with PCA 499
B.5 Basic vector geometry relevant to biplots 499
References 501
Glossary 527
Acronyms 543
Author Index 545
Subject Index 553
