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 sam

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.

This book expounds the principle and related applications of nonlinear principal component analysis (PCA), which is useful method to analyze mixed measurement levels data. In the part dealing with the principle, after a brief introduction of ordinary PCA, a PCA for categorical data (nominal and ordinal) is introduced as nonlinear PCA, in which an optimal scaling technique is used to quantify the categorical variables. The alternating least squares (ALS) is the main algorithm in the method. Multiple correspondence analysis (MCA), a special case of nonlinear PCA, is also introduced. All formulations in these methods are integrated in the same manner as matrix operations. Because any measurement levels data can be treated consistently as numerical data and ALS is a very powerful tool for estimations, the methods can be utilized in a variety of fields such as biometrics, econometrics, psychometrics, and sociology. In the applications part of the book, four applications are introduced: variable selection for mixed measurement levels data, sparse MCA, joint dimension reduction and clustering methods for categorical data, and acceleration of ALS computation. The variable selection methods in PCA that originally were developed for numerical data can be applied to any types of measurement levels by using nonlinear PCA. Sparseness and joint dimension reduction and clustering for nonlinear data, the results of recent studies, are extensions obtained by the same matrix operations in nonlinear PCA. Finally, an acceleration algorithm is proposed to reduce the problem of computational cost in the ALS iteration in nonlinear multivariate methods. This book thus presents the usefulness of nonlinear PCA which can be applied to different measurement levels data in diverse fields. As well, it covers the latest topics including the extension of the traditional statistical method, newly proposed nonlinear methods, and computational efficiency in the methods.

This edited book is the first one written in English that deals comprehensively with behavior metrics. The term “behaviormetrics” comprehends the research including all sorts of quantitative approaches to disclose human behavior. Researchers in behavior metrics have developed, extended, and improved methods such as multivariate statistical analysis, survey methods, cluster analysis, machine learning, multidimensional scaling, corresponding analysis or quantification theory, network analysis, clustering, factor analysis, test theory, and related factors. In the spirit of behavior metrics, researchers applied these methods to data obtained by surveys, experiments, or websites from a diverse range of fields. The purpose of this book is twofold. One is to represent studies that display how the basic elements of behavior metrics have developed into present-day behavior metrics. The other is to represent studies performed mainly by those who would like to pioneer new fields of behavior metrics and studies that display elements of future behavior metrics. These studies consist of various characteristics such as those dealing with theoretical or conceptual subjects, the algorithm, the model, the method, and the application to a wide variety of fields. This book helps readers to understand the present and future of behavior metrics.

The purpose of this book is to thoroughly prepare diverse areas of researchers in quantification theory. As is well known, quantification theory has attracted the attention of a countless number of researchers, some mathematically oriented and others not, but all of them are experts in their own disciplines. Quantifying non-quantitative (qualitative) data requires a variety of mathematical and statistical strategies, some of which are quite complicated. Unlike many books on quantification theory, the current book places more emphasis on preliminary requisites of mathematical tools than on details of quantification theory. As such, the book is primarily intended for readers whose specialty is outside mathematical sciences. The book was designed to offer non-mathematicians a variety of mathematical tools used in quantification theory in simple terms. Once all the preliminaries are fully discussed, quantification theory is then introduced in the last section as a simple application of those mathematical procedures fully discussed so far. The book opens up further frontiers of quantification theory as simple applications of basic mathematics.

This volume provides approaches and solutions to challenges occurring at the interface of research fields such as data analysis, computer science, operations research, and statistics. It includes theoretically oriented contributions as well as papers from various application areas, where knowledge from different research directions is needed to find the best possible interpretation of data for the underlying problem situations. Beside traditional classification research, the book focuses on current interests in fields such as the analysis of social relationships as well as statistical musicology.

Master the fundamentals of correspondence analysis with this illuminating resource An Introduction to Correspondence Analysis assists researchers in improving their familiarity with the concepts, terminology, and application of several variants of correspondence analysis. The accomplished academics and authors deliver a comprehensive and insightful treatment of the fundamentals of correspondence analysis, including the statistical and visual aspects of the subject. Written in three parts, the book begins by offering readers a description of two variants of correspondence analysis that can be applied to two-way contingency tables for nominal categories of variables. Part Two shifts the discussion to categories of ordinal variables and demonstrates how the ordered structure of these variables can be incorporated into a correspondence analysis. Part Three describes the analysis of multiple nominal categorical variables, including both multiple correspondence analysis and multi-way correspondence analysis. Readers will benefit from explanations of a wide variety of specific topics, for example: Simple correspondence analysis, including how to reduce multidimensional space, measuring symmetric associations with the Pearson Ratio, constructing low-dimensional displays, and detecting statistically significant points Non-symmetrical correspondence analysis, including quantifying asymmetric associations Simple ordinal correspondence analysis, including how to decompose the Pearson Residual for ordinal variables Multiple correspondence analysis, including crisp coding and the indicator matrix, the Burt Matrix, and stacking Multi-way correspondence analysis, including symmetric multi-way analysis Perfect for researchers who seek to improve their understanding of key concepts in the graphical analysis of categorical data, An Introduction to Correspondence Analysis will also assist readers already familiar with correspondence analysis who wish to review the theoretical and foundational underpinnings of crucial concepts.