Applied Multiway Data Analysis

✍ Scribed by Pieter M. Kroonenberg

• Publisher: Wiley-Interscience
• Year: 2008
• Tongue: English
• Leaves: 612
• Edition: 1
• Category: Library

✦ Synopsis

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: http://three-mode.leidenuniv.nl/, to view data from the book.

✦ Table of Contents

Front Cover
Title
Copyright
CONTENTS
Foreword
Preface
PART I DATA, MODELS, AND ALGORITHMS
1 Overture
1.1 Three-way and multiway data
1.2 Multiway data analysis
1.3 Before the arrival of three-mode analysis
1.4 Three-mode data-analytic techniques
1.5 Example: Judging Chopin's preludes
1.6 Birth of the Tucker model
1.7 Current status of multiway analysis
2 Overview
2.1 What are multiway data?
2.2 Why multiway analysis?
2.3 What is a model?
2.4 Some history
2.5 Multiway models and methods
2.6 Conclusions
3 Three-Way and Multiway Data
3.1 Chapter preview
3.2 Terminology
3.3 Two-way solutions to three-way data
3.4 Classification principles
3.5 Overview of three-way data designs
3.6 Fully crossed designs
3.7 Nested designs
3.8 Scaling designs
3.9 Categorical data
4 Component Models for Fully-Crossed Designs
4.1 Introduction
4.2 Chapter preview
4.3 Two-mode modeling of three-way data
4.4 Extending two-mode component models to three-mode models
4.5 Tucker models
4.6 Parafac models
4.7 ParaTuck2 model
4.8 Core arrays
4.9 Relationships between component models
4.10 Multiway component modeling under constraints
4.11 Conclusions
5 Algorithms for Multiway Models
5.1 Introduction
5.2 Chapter preview
5.3 Terminology and general issues
5.4 An example of an iterative algorithm
5.5 General behavior of multiway algorithms
5.6 The Parallel factor model – Parafac
5.7 The Tucker models
5.8 STATIS
5.9 Conclusions
PART II DATA HANDLING, MODEL SELECTION, AND INTERPRETATION
6 Preprocessing
6.1 Introduction
6.2 Chapter preview
6.3 General considerations
6.4 Model-based arguments for preprocessing choices
6.5 Content-based arguments for preprocessing choices
6.6 Preprocessing and specific multiway data designs
6.7 Centering and analysis-of-variance models: Two-way data
6.8 Centering and analysis-of-variance models: Three-way data
6.9 Recommendations
7 Missing Data in Multiway Analysis
7.1 Introduction
7.2 Chapter preview
7.3 Handling missing data in two-mode PCA
7.4 Handling missing data in multiway analysis
7.5 Multiple imputation in multiway analysis: Data matters
7.6 Missing data in multiway analysis: Practice
7.7 Example: Spanjer's Chromatography data
7.8 Example: NICHD Child care data
7.9 Further applications
7.10 Computer programs for multiple imputation
8 Model and Dimensionality Selection
8.1 Introduction
8.2 Chapter preview
8.3 Sample size and stochastics
8.4 Degrees of freedom
8.5 Selecting the dimensionality of a Tucker model
8.6 Selecting the dimensionality of a Parafac model
8.7 Model selection from a hierarchy
8.8 Model stability and predictive power
8.9 Example: Chopin prelude data
8.10 Conclusions
9 Interpreting Component Models
9.1 Chapter preview
9.2 General principles
9.3 Representations of component models
9.4 Scaling of components
9.5 Interpreting core arrays
9.6 Interpreting extended core arrays
9.7 Special topics
9.8 Validation
9.9 Conclusions
10 Improving Interpretation through Rotations
10.1 Introduction
10.2 Chapter preview
10.3 Rotating components
10.4 Rotating full core arrays
10.5 Theoretical simplicity of core arrays
10.6 Conclusions
11 Graphical Displays for Components
11.1 Introduction
11.2 Chapter preview
11.3 General considerations
11.4 Plotting single modes
11.5 Plotting different modes together
11.6 Conclusions
12 Residuals, Outliers, and Robustness
12.1 Introduction
12.2 Chapter preview
12.3 Goals
12.4 Procedures for analyzing residuals
12.5 Decision schemes for analyzing multiway residuals
12.6 Structured squared residuals
12.7 Unstructured residuals
12.8 Robustness: Basics
12.9 Robust methods of multiway analysis
12.10 Examples
12.11 Conclusions
PART III MULTIWAY DATA AND THEIR ANALYSIS
13 Modeling Multiway Profile Data
13.1 Introduction
13.2 Chapter preview
13.3 Example: Judging parents' behavior
13.4 Multiway profile data: General issues
13.5 Multiway profile data: Parafac in practice
13.6 Multiway profile data: Tucker analyses in practice
13.7 Conclusions
14 Modeling Multiway Rating Scale Data
14.1 Introduction
14.2 Chapter preview
14.3 Three-way rating scale data: Theory
14.4 Example: Coping at school
14.5 Analyzing three-way rating scales: Practice
14.6 Example: Differences within a multiple personality
14.7 Conclusions
15 Exploratory Multivariate Longitudinal Analysis
15.1 Introduction
15.2 Chapter preview
15.3 Overview of longitudinal modeling
15.4 Longitudinal three-mode modeling
15.5 Example: Organizational changes in Dutch hospitals
15.6 Example: Morphological development of French girls
15.7 Further reading
15.8 Conclusions
16 Three-Mode Clustering
16.1 Introduction
16.2 Chapter preview
16.3 Three-mode clustering analysis: Theory
16.4 Example: Identifying groups of diseased blue crabs
16.5 Three-mode cluster analysis: Practice
16.6 Example: Behavior of children in the Strange Situation
16.7 Extensions and special topics
16.8 Conclusions
17 Multiway Contingency Tables
17.1 Introduction
17.2 Chapter preview
17.3 Three-way correspondence analysis: Theory
17.4 Example: Sources of happiness
17.5 Three-way correspondence analysis: Practice
17.6 Example: Playing with peers
17.7 Conclusions
18 Three-Way Binary Data
18.1 Introduction
18.2 Chapter preview
18.3 A graphical introduction
18.4 Formal description of the Tucker–HICLAS models
18.5 Additional issues
18.6 Example: Hostile behavior in frustrating situations
18.7 Conclusion
19 From Three-Way Data to Four-Way Data and Beyond
19.1 Introduction
19.2 Chapter preview
19.3 Examples of multiway data
19.4 Multiway techniques: Theory
19.5 Example: Differences within a multiple personality
19.6 Example: Austrian aerosol particles
19.7 Further reading and computer programs
19.8 Conclusions
Appendix A: Standard Notation for Multiway Analysis
Appendix B: Biplots and Their Interpretation
B.1 Introduction
B.2 Singular value decomposition
B.3 Biplots
B.4 Relationship with PCA
B.5 Basic vector geometry relevant to biplots
References
Glossary
Acronyms
Author Index
Subject Index