Skip to Content

Multidimensional Nonlinear Descriptive Analysis

By Shizuhiko Nishisato

Chapman and Hall/CRC – 2006 – 328 pages

Purchasing Options:

  • Add to CartHardback: $119.95
    978-1-58488-612-9
    June 25th 2006

Description

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.

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

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

Name: Multidimensional Nonlinear Descriptive Analysis (Hardback)Chapman and Hall/CRC 
Description: By Shizuhiko Nishisato. 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...
Categories: Psychological Methods & Statistics, Statistical Theory & Methods, Quantitative Methods, Statistics for the Biological Sciences