From a preeminent authority—a modern and applied treatment of multiway data analysisThis groundbreaking book is the first of its kind to present methods for analyzing multiway data by applying multiway component techniques. Multiway analysis is a specialized branch of the larger field of multivariate statistics that extends the standard methods for two-way data, such as component analysis, factor analysis, cluster analysis, correspondence analysis, and multidimensional scaling to multiway data. Applied Multiway Data Analysis presents a unique, thorough, and authoritative treatment of this relatively new and emerging approach to data analysis that is applicable across a range of fields, from the social and behavioral sciences to agriculture, environmental sciences, and chemistry.General introductions to multiway data types, methods, and estimation procedures are provided in addition to detailed explanations and advice for readers who would like to learn more about applying multiway methods. Using carefully laid out examples and engaging applications, the book begins with an introductory chapter that serves as a general overview of multiway analysis, including the types of problems it can address. Next, the process of setting up, carrying out, and evaluating multiway analyses is discussed along with commonly encountered issues, such as preprocessing, missing data, model and dimensionality selection, postprocessing, and transformation, as well as robustness and stability issues.Extensive examples are presented within a unified framework consisting of a five-step structure: objectives; data description and design; model and dimensionality selection; results and their interpretation; and validation. Procedures featured in the book are conducted using 3WayPack, which is software developed by the author, and analyses can also be carried out within the R and MATLAB® systems. Several data sets and 3WayPack can be downloaded via the book's related Web site.The author presents the material in a clear, accessible style without unnecessary or complex formalism, assuring a smooth transition from well-known standard two-analysis to multiway analysis for readers from a wide range of backgrounds. An understanding of linear algebra, statistics, and principal component analyses and related techniques is assumed, though the author makes an effort to keep the presentation at a conceptual, rather than mathematical, level wherever possible. Applied Multiway Data Analysis is an excellent supplement for component analysis and statistical multivariate analysis courses at the upper-undergraduate and beginning graduate levels. The book can also serve as a primary reference for statisticians, data analysts, methodologists, applied mathematicians, and social science researchers working in academia or industry.Visit the Related Website: http://three-mode.leidenuniv.nl/, to view data from the book.
Author(s): Pieter M. Kroonenberg
Edition: 1
Year: 2008
Language: English
Pages: 579
Tags: Математика;Теория вероятностей и математическая статистика;Математическая статистика;Прикладная математическая статистика;
Front Cover......Page 1
Title......Page 6
Copyright......Page 7
CONTENTS......Page 10
Foreword......Page 18
Preface......Page 20
PART I DATA, MODELS, AND ALGORITHMS......Page 26
1 Overture......Page 28
1.1 Three-way and multiway data......Page 29
1.2 Multiway data analysis......Page 30
1.3 Before the arrival of three-mode analysis......Page 31
1.5 Example: Judging Chopin's preludes......Page 32
1.7 Current status of multiway analysis......Page 37
2.1 What are multiway data?......Page 40
2.2 Why multiway analysis?......Page 42
2.3 What is a model?......Page 43
2.4 Some history......Page 45
2.6 Conclusions......Page 49
3.1 Chapter preview......Page 52
3.2 Terminology......Page 53
3.3 Two-way solutions to three-way data......Page 55
3.4 Classification principles......Page 56
3.6 Fully crossed designs......Page 58
3.7 Nested designs......Page 63
3.8 Scaling designs......Page 65
3.9 Categorical data......Page 66
4.1 Introduction......Page 68
4.3 Two-mode modeling of three-way data......Page 70
4.4 Extending two-mode component models to three-mode models......Page 72
4.5 Tucker models......Page 76
4.6 Parafac models......Page 82
4.7 ParaTuck2 model......Page 88
4.8 Core arrays......Page 89
4.9 Relationships between component models......Page 91
4.10 Multiway component modeling under constraints......Page 93
4.11 Conclusions......Page 99
5.1 Introduction......Page 102
5.2 Chapter preview......Page 103
5.3 Terminology and general issues......Page 104
5.4 An example of an iterative algorithm......Page 106
5.5 General behavior of multiway algorithms......Page 109
5.6 The Parallel factor model – Parafac......Page 110
5.7 The Tucker models......Page 122
5.8 STATIS......Page 130
5.9 Conclusions......Page 131
PART II DATA HANDLING, MODEL SELECTION, AND INTERPRETATION......Page 132
6.1 Introduction......Page 134
6.3 General considerations......Page 137
6.4 Model-based arguments for preprocessing choices......Page 142
6.5 Content-based arguments for preprocessing choices......Page 153
6.6 Preprocessing and specific multiway data designs......Page 155
6.7 Centering and analysis-of-variance models: Two-way data......Page 159
6.8 Centering and analysis-of-variance models: Three-way data......Page 162
6.9 Recommendations......Page 166
7.1 Introduction......Page 168
7.2 Chapter preview......Page 172
7.3 Handling missing data in two-mode PCA......Page 173
7.4 Handling missing data in multiway analysis......Page 179
7.5 Multiple imputation in multiway analysis: Data matters......Page 181
7.6 Missing data in multiway analysis: Practice......Page 182
7.7 Example: Spanjer's Chromatography data......Page 184
7.8 Example: NICHD Child care data......Page 193
7.9 Further applications......Page 197
7.10 Computer programs for multiple imputation......Page 199
8.1 Introduction......Page 200
8.3 Sample size and stochastics......Page 201
8.4 Degrees of freedom......Page 202
8.5 Selecting the dimensionality of a Tucker model......Page 204
8.6 Selecting the dimensionality of a Parafac model......Page 209
8.7 Model selection from a hierarchy......Page 211
8.8 Model stability and predictive power......Page 212
8.9 Example: Chopin prelude data......Page 215
8.10 Conclusions......Page 233
9.1 Chapter preview......Page 234
9.2 General principles......Page 235
9.3 Representations of component models......Page 240
9.4 Scaling of components......Page 243
9.5 Interpreting core arrays......Page 250
9.6 Interpreting extended core arrays......Page 256
9.7 Special topics......Page 257
9.8 Validation......Page 258
9.9 Conclusions......Page 260
10.1 Introduction......Page 262
10.2 Chapter preview......Page 265
10.3 Rotating components......Page 266
10.4 Rotating full core arrays......Page 269
10.5 Theoretical simplicity of core arrays......Page 279
10.6 Conclusions......Page 281
11.1 Introduction......Page 282
11.2 Chapter preview......Page 283
11.3 General considerations......Page 284
11.4 Plotting single modes......Page 285
11.5 Plotting different modes together......Page 295
11.6 Conclusions......Page 304
12.1 Introduction......Page 306
12.2 Chapter preview......Page 307
12.3 Goals......Page 308
12.4 Procedures for analyzing residuals......Page 309
12.6 Structured squared residuals......Page 312
12.7 Unstructured residuals......Page 317
12.8 Robustness: Basics......Page 319
12.9 Robust methods of multiway analysis......Page 322
12.10 Examples......Page 326
12.11 Conclusions......Page 332
PART III MULTIWAY DATA AND THEIR ANALYSIS......Page 334
13.1 Introduction......Page 336
13.3 Example: Judging parents' behavior......Page 338
13.4 Multiway profile data: General issues......Page 345
13.5 Multiway profile data: Parafac in practice......Page 347
13.6 Multiway profile data: Tucker analyses in practice......Page 356
13.7 Conclusions......Page 367
14.1 Introduction......Page 370
14.3 Three-way rating scale data: Theory......Page 371
14.4 Example: Coping at school......Page 379
14.5 Analyzing three-way rating scales: Practice......Page 385
14.6 Example: Differences within a multiple personality......Page 386
14.7 Conclusions......Page 395
15.1 Introduction......Page 398
15.3 Overview of longitudinal modeling......Page 400
15.4 Longitudinal three-mode modeling......Page 403
15.5 Example: Organizational changes in Dutch hospitals......Page 410
15.6 Example: Morphological development of French girls......Page 419
15.7 Further reading......Page 425
15.8 Conclusions......Page 426
16.1 Introduction......Page 428
16.3 Three-mode clustering analysis: Theory......Page 430
16.4 Example: Identifying groups of diseased blue crabs......Page 434
16.5 Three-mode cluster analysis: Practice......Page 436
16.6 Example: Behavior of children in the Strange Situation......Page 449
16.7 Extensions and special topics......Page 455
16.8 Conclusions......Page 457
17.1 Introduction......Page 458
17.2 Chapter preview......Page 459
17.3 Three-way correspondence analysis: Theory......Page 460
17.4 Example: Sources of happiness......Page 469
17.5 Three-way correspondence analysis: Practice......Page 473
17.6 Example: Playing with peers......Page 479
17.7 Conclusions......Page 483
18.1 Introduction......Page 484
18.3 A graphical introduction......Page 485
18.4 Formal description of the Tucker–HICLAS models......Page 487
18.6 Example: Hostile behavior in frustrating situations......Page 490
18.7 Conclusion......Page 492
19.1 Introduction......Page 494
19.3 Examples of multiway data......Page 496
19.4 Multiway techniques: Theory......Page 499
19.5 Example: Differences within a multiple personality......Page 501
19.6 Example: Austrian aerosol particles......Page 505
19.7 Further reading and computer programs......Page 512
19.8 Conclusions......Page 513
Appendix A: Standard Notation for Multiway Analysis......Page 514
Appendix B: Biplots and Their Interpretation......Page 516
B.2 Singular value decomposition......Page 517
B.3 Biplots......Page 519
B.5 Basic vector geometry relevant to biplots......Page 524
References......Page 526
Glossary......Page 552
Acronyms......Page 568
Author Index......Page 570
Subject Index......Page 578
