Shizuhiko Nishisato's Books

Optimal Quantification and Symmetry

By: Shizuhiko Nishisato

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Optimal Quantification and Symmetry

By: Shizuhiko Nishisato

This book offers a unique new look at the familiar quantification theory from the point of view of mathematical symmetry and spatial symmetry. Symmetry exists in many aspects of our life—for instance, in the arts and biology as an ingredient of beauty and equilibrium, and more importantly, for data analysis as an indispensable representation of functional optimality. This unique focus on symmetry clarifies the objectives of quantification theory and the demarcation of quantification space, something that has never caught the attention of researchers. Mathematical symmetry is well known, as can be inferred from Hirschfeld’s simultaneous linear regressions, but spatial symmetry has not been discussed before, except for what one may infer from Nishisato’s dual scaling. The focus on symmetry here clarifies the demarcation of quantification analysis and makes it easier to understand such a perennial problem as that of joint graphical display in quantification theory. The new framework will help advance the frontier of further developments of quantification theory. Many numerical examples are included to clarify the details of quantification theory, with a focus on symmetry as its operational principle. In this way, the book is useful not only for graduate students but also for researchers in diverse areas of data analysis.

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Page Count

199

Publisher

Springer Nature

Published Date

ISBN 10

9811691703

ISBN 13

9789811691706

Multidimensional Nonlinear Descriptive Analysis

By: Shizuhiko Nishisato

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Multidimensional Nonlinear Descriptive Analysis

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 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.

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Page Count

336

Publisher

CRC Press

Published Date

ISBN 10

1584886129

ISBN 13

9781584886129

Optimal Analysis of Qualitative Data with Illustrations

By: Shizuhiko Nishisato

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Optimal Analysis of Qualitative Data with Illustrations

By: Shizuhiko Nishisato

This is an introductory book on how to optimally analyze non-quantitative data, based on the author’s experiences over 60 years of research. The major message to the readers is that qualitative (non-quantitative) data are much more informative than quantitative data. This is good news for readers in applied areas of statistics such as those in the social sciences and marketing research, where qualitative data are everywhere. But how can one analyze qualitative data quantitatively and extract more information than from the sophisticated analysis of quantitative data? The key rests in illustrations of difficult topics in a way that anyone can understand. It is the author’s wish soon the use of AI will open a gate for simple means for optimal analysis of qualitative data, as illustrated throughout the book.

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Page Count

275

Publisher

Cambridge Scholars Publishing

Published Date

ISBN 10

1036412989

ISBN 13

9781036412982

Modern Quantification Theory

Joint Graphical Display, Biplots, and Alternatives

By: Shizuhiko Nishisato,Eric J. Beh,Rosaria Lombardo,Jose G. Clavel

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Modern Quantification Theory

Joint Graphical Display, Biplots, and Alternatives

By: Shizuhiko Nishisato,Eric J. Beh,Rosaria Lombardo,Jose G. Clavel

This book offers a new look at well-established quantification theory for categorical data, referred to by such names as correspondence analysis, dual scaling, optimal scaling, and homogeneity analysis. These multiple identities are a consequence of its large number of properties that allow one to analyze and visualize the strength of variable association in an optimal solution. The book contains modern quantification theory for analyzing the association between two and more categorical variables in a variety of applicative frameworks. Visualization has attracted much attention over the past decades and given rise to controversial opinions. One may consider variations of plotting systems used in the construction of the classic correspondence plot, the biplot, the Carroll-Green-Schaffer scaling, or a new approach in doubled multidimensional space as presented in the book. There are even arguments for no visualization at all. The purpose of this book therefore is to shed new light on time-honored graphical procedures with critical reviews, new ideas, and future directions as alternatives. This stimulating volume is written with fresh new ideas from the traditional framework and the contemporary points of view. It thus offers readers a deep understanding of the ever-evolving nature of quantification theory and its practice. Part I starts with illustrating contingency table analysis with traditional joint graphical displays (symmetric, non-symmetric) and the CGS scaling and then explores logically correct graphs in doubled Euclidean space for both row and column variables. Part II covers a variety of mathematical approaches to the biplot strategy in graphing a data structure, providing a useful source for this modern approach to graphical display. Part II is also concerned with a number of alternative approaches to the joint graphical display such as bimodal cluster analysis and other statistical problems relevant to quantification theory.

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Page Count

231

Publisher

Springer Nature

Published Date

ISBN 10

9811624704

ISBN 13

9789811624704

Elements of Dual Scaling

An Introduction To Practical Data Analysis

By: Shizuhiko Nishisato

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Elements of Dual Scaling

An Introduction To Practical Data Analysis

By: Shizuhiko Nishisato

Quantification methodology of categorical data is a popular topic in many branches of science. Most books, however, are either too advanced for those who need it, or too elementary to gain insight into its potential. This book fills the gap between these extremes, and provides specialists with an easy and comprehensive reference, and others with a complete treatment of dual scaling methodology -- starting with motivating examples, followed by an introductory discussion of necessary quantitative skills, and ending with different perpsectives on dual scaling with examples, advanced topics, and future possibilities. This book attempts to successively upgrade readers' readiness for handling analysis of qualitative, categorical, and non-metric data, without overloading them. The writing style is very friendly, and difficult topics are always accompanied by simple illlustrative examples. There are a number of topics on dual scaling which were previously addressed only in journal articles or in publications that are not readily available. Integration of these topics into the standard framework makes the current book unique, and its extensive coverage of relevant topics is unprecedented. This book will serve as both reference and textbook for all those who want to analyze categorical data effectively.

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Page Count

379

Publisher

Psychology Press

Published Date

ISBN 10

1317781937

ISBN 13

9781317781936

Measurement, Mathematics and New Quantification Theory

By: Shizuhiko Nishisato

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Measurement, Mathematics and New Quantification Theory

By: Shizuhiko Nishisato

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.

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Page Count

214

Publisher

Springer Nature

Published Date

ISBN 10

981992295X

ISBN 13

9789819922956

Analysis of Categorical Data

Dual Scaling and Its Applications

By: Shizuhiko Nishisato

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Analysis of Categorical Data

Dual Scaling and Its Applications

By: Shizuhiko Nishisato

This volume presents a unified and up-to-date account of the theory and methods of applying one of the most useful and widely applicable techniques of data analysis, 'dual scaling.

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