Advanced Studies in Behaviormetrics and Data Science: Essays in Honor of Akinori Okada (Behaviormetrics: Quantitative Approaches to Human Behavior, 5)

This book focuses on the latest developments in behaviormetrics and data science, covering a wide range of topics in data analysis and related areas of data science, including analysis of complex data, analysis of qualitative data, methods for high-dimensional data, dimensionality reduction, visualization of such data, multivariate statistical methods, analysis of asymmetric relational data, and various applications to real data. In addition to theoretical and methodological results, it also shows how to apply the proposed methods to a variety of problems, for example in consumer behavior, decision making, marketing data, and social network structures. Moreover, it discuses methodological aspects and applications in a wide range of areas, such as behaviormetrics; behavioral science; psychology; and marketing, management and social sciences. Combining methodological advances with real-world applications collected from a variety of research fields, the book is a valuable resource for researchers and practitioners, as well as for applied statisticians and data analysts. Foreword Preface Contents Contributors Part I Theoretically-Oriened Co-Clustering for Object by Variable Data Matrices 1 Co-Clustering 2 Co-clustering with Class-Specific Variances in the Variable Clusters 3 Clustering of Variables Around Latent Factors 4 Co-Clustering, Where Variable Clusters are Characterized by Class-Specific Factors 5 Discussion and Extensions References How to Use the Hermitian Form Model for Asymmetric MDS 1 Introduction 2 Revisit of HFM 3 Interpretation of the Configuration of Objects by HFM 4 Applications of HFM to Empirical Asymmetric Relational Matrices 5 Applications of HFM to Theoretical or Hypothetical Asymmetric Relational Data Matrices 6 Decomposition of ASM to Elementary ASMs via HFM 7 Hypothetical Force Acting on the Hilbert Space and Its Interpretation 8 Conclusions References Asymmetric Scaling Models for Square Contingency Tables: Points, Circles, Arrows and Odds Ratios 1 Introduction 2 Modelling of Square Contingency Tables 2.1 Poisson Model 2.2 Model Fit 2.3 Marginal Heterogeneity and Association 3 Three Distance Formulations 3.1 Distance-Radius Model 3.2 Slide-Vector Model 3.3 Symmetric Distance-Association Model 4 Odds Ratio Structures 4.1 Symmetric Distance-Association Model 4.2 The Distance-Radius Model 4.3 The Slide-Vector Model 5 Data Analysis 5.1 Symmetric Distance-Association Model 5.2 Distance-Radius Model 5.3 Slide-Vector Model 5.4 Models Without Main Effects 6 Discussion and Conclusion References Flight Passenger Behavior and Airline Fleet Assignment 1 Introduction 2 Notation 2.1 Airline Fleet Assignment 2.2 Flight Passenger Behavior 3 Model 4 Example 4.1 Starting Situation and Data 4.2 Results 5 Concluding Remarks References Comparing Partitions of the Petersen Graph 1 Motivation 2 The Automorphism Group of the Petersen Graph 3 Multiple Isomorphic Solutions of Graph Clustering Algorithms 4 Measures for Comparing Partitions and for Comparing Isomorphic Sets of Partitions 5 Comparing Partitions of the Petersen Graph 6 Summary and Outlook References Minkowski Distances and Standardisation for Clustering and Classification on High-Dimensional Data 1 Introduction 2 Distance Construction 2.1 Clustering Versus Supervised Classification 2.2 Standardisation 2.3 Boxplot Transformation 2.4 Aggregation 3 Experiments 3.1 Setups 3.2 Results 4 Conclusion References On Detection of the Unique Dimensions of Asymmetry in Proximity Data 1 Introduction 2 Overview of Models 2.1 Asymmetric Scaling 2.2 The Circle Model 2.3 Ellipse Model 2.4 Other Variants 3 Algorithm 4 Application 5 Conclusion References Multiple Regression Analysis from Data Science Perspective 1 Introduction 2 Relationship Between Variables and Type of Study 3 Formulation and Functions of Multiple Regression Analysis 4 Variable Selection 5 Concluding Remarks References Multiway Extensions of the SVD 1 Introduction 2 Two and Three-Way Data 2.1 A View of Three-Way Data 2.2 Some Types of Three-Way Data 3 Four-Way Data 4 Traditional Ways to Handle Three-Way Data 5 The Singular Value Decomposition (SVD) 6 Three-Way SVDs 6.1 Replicated SVD 6.2 Tucker2 Model 6.3 Parafac/Candecomp; Canonical Polyadic Decomposition 6.4 Weighted Two-Way SVD 6.5 Two-Way SVD on Average of Xk 6.6 Tucker3 Model 6.7 Higher-Order SVD (HOSVD) [=Tucker (1996) Method I] 6.8 Parafac/Candecomp/Canonical Polyadic Model 6.9 Three-Way SVD: Core Arrays 6.10 Relationships Between Models 7 Conclusion 8 Treatments of the Multiway Singular Value Decomposition: Some Literature References Seriation and Matrix Reordering Methods for Asymmetric One-Mode Two-Way Datasets 1 Introduction 2 Data 3 Methods 4 Experiments 5 Discussion 6 Conclusions References Parsimonious Mixtures of Matrix Variate Bilinear Factor Analyzers 1 Introduction 2 Background 2.1 Model-Based Clustering 2.2 Parsimonious Gaussian Mixture Models 2.3 Matrix Variate Normal Distribution 2.4 Mixture of Matrix Variate Bilinear Factor Analyzers 3 Methodology 3.1 Parsimonious MMVBFA Models 3.2 Model Selection, Convergence, Performance Evaluation Criteria, and Initialization 4 Simulations 4.1 Simulation 1 4.2 Simulation 2 4.3 Simulation 3 5 MNIST Data Analysis 6 Discussion 7 Appendix 7.1 Updates for Scale Matrices and Factor Loadings References Interval-Valued Scaling of Successive Categories 1 Introduction 2 Scaling of Successive Categories in Contingency Table 2.1 Motivation and Basic Idea 2.2 Scaling Method for Successive Categories 3 Numerical Examples 3.1 Asbestos Exposure Data 3.2 Drugs' Effectiveness Data 4 Scaling of Successive Categories in a Concatenated Contingency Table 5 Discussions References Orthonormal Principal Component Analysis for Categorical Data as a Transformation of Multiple Correspondence Analysis 1 Introduction 2 MCA and Transformations of the Solution 2.1 The Basic Formulation and the Algorithm of MCA 2.2 The Decomposition of Quantifications 2.3 Indeterminacies in Local Quantifications 3 Orthonormal Principal Component Analysis 3.1 Terminologies for Introducing PCA Formulation 3.2 Arbitrary Quantifications to Categories 3.3 Equivalence of OPCA to MCA 3.4 Rotation Problem 3.5 Use of Orthogonal Polynomials for Ordered Categorical Variables 4 Illustrative Example 4.1 Analyzed Data and MCA Solution 4.2 Solution of OPCA 4.3 Interpretations of OPCA Solution 5 Discussion References Identifying Groups With Different Traits Using Fourteen Domains of Social Consciousness: A Multidimensional Latent Class Graded Item Response Theory Model 1 Introduction 2 Data 3 Latent Class Graded Item Response Theory Model 4 Results 5 Conclusions References Quantification Theory: Categories, Variables and Modal Analysis 1 Principal Component Analysis and Graphs 2 Quantification Theory and Graphs 3 Decompostion of Quantification Space 4 Distribution of Information 5 Categories, Variables and Standardization 6 Concluding Remarks References Clustering via Ant Colonies: Parameter Analysis and Improvement of the Algorithm 1 Introduction 2 Clustering 3 Artificial Ant Colonies 4 Description of the Proposed ACO Algorithm 5 Parameter Analysis 6 Extra Data Sets, Results, and Discussion 7 Conclusions References PowerCA: A Fast Iterative Implementation of Correspondence Analysis 1 Introduction 2 Correspondence Analysis 3 Efficient Computation of the Burt Matrix 4 The Power Method 4.1 Comparison with Standard EVD Implementation 5 PowerCA and the Bootstrap 6 Conclusion References Modeling Asymmetric Exchanges Between Clusters 1 Introduction and Background 2 Illustrative Example: Language Data 3 The Model 3.1 A Constrained Model 4 ALS Algorithm 4.1 Algorithm for the Constrained Model 5 On the Estimates 5.1 Weight Matrix D 5.2 Weight Matrix C and Constant b 6 Application: Language Data 7 Concluding Remarks References Exploring Hierarchical Concepts: Theoretical and Application Comparisons 1 Introduction 2 Hierarchical Classification of Variables 3 The Ultrametric Correlation Model 4 A Comparison Between the Ultrametric Correlation Model and the Agglomerative Clustering Algorithms 5 Conclusions References Improving Algorithm for Overlapping Cluster Analysis 1 Introduction 2 Overlapping Cluster Analysis 2.1 ADCLUS Model 2.2 MAPCLUS Algorithm 3 Improvement of Algorithm 4 Improvement Byinitial Cluster 5 Conclusion References Part II Application-Oriented Increasing Conversion Rates Through Eye Tracking, TAM, A/B Tests: A Case Study 1 Introduction 2 Increasing Conversions via Improved Landing Pages 3 Tuning Through Eye Tracking, TAM, and A/B Tests 4 Empirical Application: From Idea Generation to Testing 5 Empirical Application: From Testing to Going Live 6 Conclusions and Outlook References Descriptive Analyses of Interrater Agreement for Ordinal Rating Scales 1 Introduction 2 A Measure of Interrater Absolute Agreement for Ordinal Rating Scales 3 Descriptive Analysis of Dependence of Agreement by Raters 4 Descriptive Analysis of Dependence of Agreement by Targets 5 Application 6 Conclusions References The Globality of Brands—A Question of Methods? 1 Introduction 2 Research Background on Brand Image Measures 3 Two-Factor Approach to Capture Global Brand Images 3.1 Overview 3.2 Identification of Brand Image Measurement Methods 3.3 Identification of Target Countries 4 Empirical Application 4.1 Stimulus and Country Selection 4.2 Respondents 4.3 Data Collection 4.4 Descriptive Results 4.5 Brand Image Representation Using MCA 5 Conclusion and Outlook References Mapping Networks and Trees with Multidimensional Scaling of Proximities 1 Introduction 2 Graph Drawing Procedures Based on Least Squares 3 Drawing a Simple Graph: Marital Relations Between Florentine Families 4 Drawing a Weighted Graph: An Additive Tree of Animal Names 5 Conclusions and Discussion References Pitfalls in the Construction of Response Scales in Cross-Cultural Surveys: An Example from East Asian Social Survey 1 Introduction 2 Development of Scales in JGSS and EASS Questionnaires 2.1 Development of JGSS Questionnaires 2.2 Development of EASS Questioners 3 Inclusion of both EASS and JGSS Scales into JGSS Questionnaires 4 Inclusion of Existing International Scales in EASS 2010 Health Module 4.1 Translation Issues on Subjective Health in the EASS 2010 Health Module 4.2 Issues in the Distributions of Subjective Health in the EASS 2010 Health Module 4.3 Issues in the Use of Existing Scales 5 Conclusion References Japanese Women's Attitudes Toward Childrearing: Text Analysis and Multidimensional Scaling 1 Introduction 2 Attribution of Success and Failure Hypothesis 3 Method 3.1 Data 3.2 Classification of Documents According to Mapping of Keywords onto Topics 3.3 Measurement of Similarity Between Topics 3.4 Multidimensional Scaling 4 Results 4.1 Frequency and Co-occurrence of Topics 4.2 Similarity and Dissimilarity Between Topics 4.3 Torgerson's Method 4.4 Symmetric SMACOF 4.5 Slide Vector Model 4.6 Drift Vector Model 5 Concluding Remarks References Consensus or Dissensus in Occupational Prestige Evaluation: A New Approach to Measuring Consensus and Inter-group Variations 1 Introduction 2 Occupational Prestige as a Collective Conscience 3 Theory of Cultural Consensus and Analytical Approach 4 Measuring Consensus 5 Measuring Inter-group Variations 6 On Sample Size 7 Differences in the Level of Agreement 8 Summary and Discussion References People and Trust 1 Introduction: Longitudinal and Cross-National Surveys of National Character by ISM 2 Social Values and Interpersonal Trust 2.1 Fundamental Dimensions of Japanese Social Values 2.2 Interpersonal Trust of the Japanese 3 Cross-National Surveys on Trust 3.1 Sense of Interpersonal Trust 3.2 Trust of Social Institutions and Systems 4 For Future Research—Universal Values of Human Bonds References