Böcker av 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.

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.

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 Nishisatös 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.

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.

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.' It addresses issues of interest to a wide variety of researchers concerned with data that are categorical in nature or by design: in the life sciences, the social sciences, and statistics.The eight chapters introduce the nature of categorical data and concept of dual scaling and present the applications of dual scaling to different forms of categorical data: the contingency table, the response-frequency table, the response-pattern table for multiple-choice data, ranking and paired comparison data, multidimensional tables, partially ordered and successively ordered categories, and incomplete data. The book also includes appendices outlining a minimum package of matrix calculus and a small FORTRAN program.Clear, concise, and comprehensive, Analysis of Categorical Data will be a useful textbook or handbook for students and researcher in a variety of fields.

First Published in 1993. Routledge is an imprint of Taylor & Francis, an informa company.

This text provides a reference and treatment of dual scaling methodology. The author begins with examples, followed by an introductory discussion of necessary quantitative skills, and ends with different perspectives on dual scaling with examples, advanced topics, and future possibilities.

Qualification of categorical, or non-numerical, data is a problem that scientists face across a range of disciplines. This book presents methods for analyzing categorical data that are not necessarily sampled randomly from a normal population and involve nonlinear relations. It offers material on statistical concepts and data analysis techniques.