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.
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