Nishisato S. Multidimensional Nonlinear Descriptive Analysis

N.-Y.: Chapman & Hall/CRC, 2007. - 301p.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.BackgroundMotivationTraditional Unidimensional Analysis
Multidimensional Analysis
Why Nonlinear Analysis?
Traditional Linear Analysis
Nonlinear Analysis
Why Descriptive Analysis?Is Likert-Type Scoring Appropriate?
Method of Reciprocal Averages (MRA)
One-Way Analysis of Variance Approach
Bivariate Correlation Approach
Geometric Approach
Other Approaches
The Least-Squares Approach
Approach by Cramer’s and Tchuproff ’s Coefficients
Multidimensional DecompositionHistorical OverviewMathematical Foundations in Early Days
Pioneers of MUNDA in the th Century
Rediscovery and Further Developments
Distinct Groups
Books and Papers
A Plethora of Aliases
Notes on Dual Scaling
DedicationsStevens’ Four Levels of Measurement
Incidence Data
Dominance Data
The Cosine Law
Young-Householder Theorem
Chi-Square Distance
Distance in Reduced Space
Correlation in Reduced SpaceLinear Combination and Principal Space
Eigenvalue and Singular Value Decompositions
Some Basics
MRA Revisited
Dual Relations and Rectangular Coordinates
Discrepancy Between Row Space and Column Space
Geometrically Correct Joint Plots (Traditional)
CGS Scaling
Geometrically Correct Joint Plots (New)
Information of Different Data TypesAnalysis of Incidence DataExample
Early Work
Total Information
Information Accounted For By One Component
Is My Pet a Flagrant Biter?
Supplementary NotesExample
Early Work
Some Basics
Future Use of English by Students in Hong Kong
Blood Pressures, Migraines and Age Revisited
Evaluation of alpha
Standardized QuantificationEarly Work
Sorting Familiar Animals into Clusters
Some NotesEarly Work
Principles PEP and PIC
Conditional Analysis
Alternative Formulations
Adjusted Correlation Ratio
Value of Forcing Agent
Age Effects on Blood Pressures and Migraines
Ideal Sorter of Animals
Generalized Forced ClassificationAnalysis of Dominance DataExample
Guttman’s Formulation
Nishisato’s Formulation
Some Basics
Travel Destinations
Criminal ActsExample
Early Work
Some Basics
Tucker-Carroll’s Formulation
Distribution of Information
Coomb’s Unfolding and MUNDA
Goodness of Fit
Sales Points of Hot SpringsSome Basics
Seriousness of Criminal Acts
Multidimensional Decomposition
Rank Conversion without Category Boundaries
Successive Categories Data as Multiple-Choice DataBeyond the BasicsForced Classification of Paired Comparisons: Travel Destinations
Forced Classification of Rank-Order Data: Hot Springs
Order Constraints on Ordered Categories
Stability, Robustness and Missing Responses
Multiway Data
Contingency Tables and Multiple-Choice Data
General Case of Two Variables
Statistic…
Extensions from Two to Many Variables
Permutations of Categories and ScalingGeometry of Multiple-Choice Items
A Concept of Correlation
A Statistic Related to Singular Values
A New Measure ν
Cramer’s Coefficient V
Tchuproff ’s Coefficient T
Properties of Squared Item-Total Correlation
Decomposition of Nonlinear Correlation
Interpreting Data in Reduced Dimension
Why an Absolute Measure?
Union of Sets, Joint Entropy and Covariation
Final Word