Applied Multiway Data Analysis

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.

"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)

• Foreword xv Preface xviiPART I DATA, MODELS, AND ALGORITHMS1 Overture 31.1 Three-way and multiway data 41.2 Multiway data analysis 51.3 Before the arrival of three-mode analysis 61.4 Three-mode data-analytic techniques 71.5 Example: Judging Chopin's preludes 71.6 Birth of the Tucker model 121.7 Current status of multiway analysis 122 Overview 152.1 What are multiway data? 152.2 Why multiway analysis? 172.3 What is a model? 182.4 Some history 202.5 Multiway models and methods 242.6 Conclusions 243 Three-Way and Multiway Data 273.1 Chapter preview 273.2 Terminology 283.3 Two-way solutions to three-way data 303.4 Classification principles 313.5 Overview of three-way data designs 333.6 Fully crossed designs 333.7 Nested designs 383.8 Scaling designs 403.9 Categorical data 414 Component Models for Fully-Crossed Designs 434.1 Introduction 434.2 Chapter preview 454.3 Two-mode modeling of three-way data 454.4 Extending two-mode component models to three-mode models 474.5 Tucker models 514.6 Parafac models 574.7 ParaTuck2 model 634.8 Core arrays 644.9 Relationships between component models 664.10 Multiway component modeling under constraints 684.11 Conclusions 745 Algorithms for Multiway Models 775.1 Introduction 775.2 Chapter preview 785.3 Terminology and general issues 795.4 An example of an iterative algorithm 815.5 General behavior of multiway algorithms 845.6 The Parallel factor model - Parafac 855.7 The Tucker models 975.8 STATIS 1055.9 Conclusions 106PART II DATA HANDLING, MODEL SELECTION, AND INTERPRETATION6 Preprocessing 1096.1 Introduction 1096.2 Chapter preview 1126.3 General considerations 1126.4 Model-based arguments for preprocessing choices 1176.5 Content-based arguments for preprocessing choices 1286.6 Preprocessing and specific multiway data designs 1306.7 Centering and analysis-of-variance models: Two-way data 1346.8 Centering and analysis-of-variance models: Three-way data 1376.9 Recommendations 1417 Missing Data in Multiway Analysis 1437.1 Introduction 1437.2 Chapter preview 1477.3 Handling missing data in two-mode PCA 1487.4 Handling missing data in multiway analysis 1547.5 Multiple imputation in multiway analysis: Data matters 1567.6 Missing data in multiway analysis: Practice 1577.7 Example: Spanjer's Chromatography data 1597.8 Example: NICHD Child care data 1687.9 Further applications 1727.10 Computer programs for multiple imputation 1748 Model and Dimensionality Selection 1758.1 Introduction 1758.2 Chapter preview 1768.3 Sample size and stochastics 1768.4 Degrees of freedom 1778.5 Selecting the dimensionality of a Tucker model 1798.6 Selecting the dimensionality of a Parafac model 1848.7 Model selection from a hierarchy 1868.8 Model stability and predictive power 1878.9 Example: Chopin prelude data 1908.10 Conclusions 2089 Interpreting Component Models 2099.1 Chapter preview 2099.2 General principles 2109.3 Representations of component models 2159.4 Scaling of components 2189.5 Interpreting core arrays 2259.6 Interpreting extended core arrays 2319.7 Special topics 2329.8 Validation 2339.9 Conclusions 23510 Improving Interpretation through Rotations 23710.1 Introduction 23710.2 Chapter preview 24010.3 Rotating components 24110.4 Rotating full core arrays 24410.5 Theoretical simplicity of core arrays 25410.6 Conclusions 25611 Graphical Displays for Components 25711.1 Introduction 25711.2 Chapter preview 25811.3 General considerations 25911.4 Plotting single modes 26011.5 Plotting different modes together 27011.6 Conclusions 27912 Residuals, Outliers, and Robustness 28112.1 Introduction 28112.2 Chapter preview 28212.3 Goals 28312.4 Procedures for analyzing residuals 28412.5 Decision schemes for analyzing multiway residuals 28712.6 Structured squared residuals 28712.7 Unstructured residuals 29212.8 Robustness: Basics 29412.9 Robust methods of multiway analysis 29712.10 Examples 30112.1 1 Conclusions 307PART III MULTIWAY DATA AND THEIR ANALYSIS13 Modeling Multiway Profile Data 31113.1 Introduction 31113.2 Chapter preview 31313.3 Example: Judging parents' behavior 31313.4 Multiway profile data: General issues 32013.5 Multiway profile data: Parafac in practice 32213.6 Multiway profile data: Tucker analyses in practice 33113.7 Conclusions 34214 Modeling Multiway Rating Scale Data 34514.1 Introduction 34514.2 Chapter preview 34614.3 Three-way rating scale data: Theory 34614.4 Example: Coping at school 35414.5 Analyzing three-way rating scales: Practice 36014.6 Example: Differences within a multiple personality 36114.7 Conclusions 37015 Exploratory Multivariate Longitudinal Analysis 37315.1 Introduction 37315.2 Chapter preview 37515.3 Overview of longitudinal modeling 37515.4 Longitudinal three-mode modeling 37815.5 Example: Organizational changes in Dutch hospitals 38515.6 Example: Morphological development of French girls 39415.7 Further reading 40015.8 Conclusions 40116 Three-Mode Clustering 40316.1 Introduction 40316.2 Chapter preview 40516.3 Three-mode clustering analysis: Theory 40516.4 Example: Identifying groups of diseased blue crabs 40916.5 Three-mode cluster analysis: Practice 41116.6 Example: Behavior of children in the Strange Situation 42416.7 Extensions and special topics 43016.8 Conclusions 43217 Multiway Contingency Tables 43317.1 Introduction 43317.2 Chapter preview 43417.3 Three-way correspondence analysis: Theory 43517.4 Example: Sources of happiness 44417.5 Three-way correspondence analysis: Practice 44817.6 Example: Playing with peers 45417.7 Conclusions 45818 Three-Way Binary Data 45918.1 Introduction 45918.2 Chapter preview 46018.3 A graphical introduction 46018.4 Formal description of the Tucker-HICLAS models 46218.5 Additional issues 46518.6 Example: Hostile behavior in frustrating situations 46518.7 Conclusion 46719 From Three-Way Data to Four-Way Data and Beyond 46919.1 Introduction 46919.2 Chapter preview 47119.3 Examples of multiway data 47119.4 Multiway techniques: Theory 47419.5 Example: Differences within a multiple personality 47619.6 Example: Austrian aerosol particles 48019.7 Further reading and computer programs 48719.8 Conclusions 488Appendix A: Standard Notation for Multiway Analysis 489Appendix B: Biplots and Their Interpretation 491B. 1 Introduction 492B.2 Singular value decomposition 492B.3 Biplots 494B.4 Relationship with PCA 499B.5 Basic vector geometry relevant to biplots 499References 501Glossary 527Acronyms 543Author Index 545Subject Index 553