Applied Multiway Data Analysis

From a preeminent authority--a modern and applied treatment of multiway data analysis This 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: href="http://three-mode.leidenuniv.nl/">http://three-mode.leidenuniv.nl/, to view data from the book.

Auteur

Pieter M. Kroonenberg, PhD, is Professor of Multivariate Analysis in the Department of Education and Child Studies at Leiden University in the Netherlands. He has over thirty years of academic and consulting experience and has published over fifty articles on the subject of three-mode data analysis.

Résumé
From a preeminent authoritya modern and applied treatment of multiway data analysis This 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.

Contenu
Foreword 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 10…