Multidimensional Nonlinear Descriptive Analysis
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Summary
Quantification of categorical, or non-numerical, data is a problem that scientists face across a wide range of disciplines. Exploring data analysis in various areas of research, such as the social sciences and biology, Multidimensional Nonlinear Descriptive Analysis presents methods for analyzing categorical data that are not necessarily sampled randomly from a normal population and often involve nonlinear relations.
This reference not only provides an overview of multidimensional nonlinear descriptive analysis (MUNDA) of discrete data, it also offers new results in a variety of fields. The first part of the book covers conceptual and technical preliminaries needed to understand the data analysis in subsequent chapters. The next two parts contain applications of MUNDA to diverse data types, with each chapter devoted to one type of categorical data, a brief historical comment, and basic skills peculiar to the data types. The final part examines several problems and then concludes with suggestions for future progress.
Covering both the early and later years of MUNDA research in the social sciences, psychology, ecology, biology, and statistics, this book provides a framework for potential developments in even more areas of study.
Table of Contents
MOTIVATION
Why Multidimensional Analysis?
Why Nonlinear Analysis?
Why Descriptive Analysis?
QUANTIFICATION WITH DIFFERENT PERSPECTIVES
Is Likert-Type Scoring Appropriate?
Method of Reciprocal Averages (MRA)
One-Way Analysis of Variance Approach
Bivariate Correlation Approach
Geometric Approach
Other Approaches
Multidimensional Decomposition
HISTORICAL OVERVIEW
Mathematical Foundations in Early Days
Pioneers of MUNDA in the 20th Century
Rediscovery and Further Developments
Additional Notes
CONCEPTUAL PRELIMINARIES
Stevens’ Four Levels of Measurement
Classification of Categorical Data
Euclidean Space
Multidimensional Space
TECHNICAL PRELIMINARIES
Linear Combination and Principal Space
Eigenvalue and Singular Value Decompositions
Finding the Largest Eigenvalue
Dual Relations and Rectangular Coordinates
Discrepancy between Row Space and Column Space
Information of Different Data Types
CONTINGENCY TABLES
Example
Early Work
Some Basics
Is My Pet a Flagrant Biter?
Supplementary Notes
MULTIPLE-CHOICE DATA
Example
Early Work
Some Basics
Future Use of English by Students in Hong Kong
Blood Pressures, Migraines and Age Revisited
Further Discussion
SORTING DATA
Example
Early Work
Sorting Familiar Animals into Clusters
Some Notes
FORCED CLASSIFICATION OF INCIDENCE DATA
Early Work
Some Basics
Age Effects on Blood Pressures and Migraines
Ideal Sorter of Animals
Generalized Forced Classification
PAIRED COMPARISON DATA
Example
Early Work
Some Basics
Travel Destinations
Criminal Acts
RANK ORDER DATA
Example
Early Work
Some Basics
Total Information and Number of Components
Distribution of Information
Sales Points of Hot Springs
SUCCESSIVE CATEGORIES DATA
Example
Some Basics
Seriousness of Criminal Acts
Multidimensionality
FURTHER TOPICS OF INTEREST
Forced Classification of Dominance Data
Order Constraints on Ordered Categories
Stability, Robustness and Missing Responses
Multiway Data
Contingency Tables and Multiple-Choice Data
Permutations of Categories and Scaling
FURTHER PERSPECTIVES
Geometry of Multiple-Choice Items
A Concept of Correlation
A Statistic Related to Singular Values
Correlation for Categorical Variables
Properties of Squared Item-Total Correlation
Decomposition of Nonlinear Correlation
Interpreting Data in Reduced Dimension
Towards an Absolute Measure of Information
Final Word
References
AUTHOR INDEX
SUBJECT INDEX
Editorial Reviews
"…The strengths of the book lie in the accessibility of the material, the author’s undisputed expertise in MUNDA, and the fact that the material is mostly self-contained. … In summary, this book presents an accessible, authoritative treatment of the subject."
—J. Wade Davis, University of Missouri, The American Statistician, August 2008
