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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.
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.
This collection of essays is in honor of Shizuhiko Nishisato on his
88th birthday and consists of invited contributions only. The book
contains essays on the analysis of categorical data, which includes
quantification theory, cluster analysis, and other areas of
multidimensional data analysis, covering more than half a century
of research by the 41 interdisciplinary and international
researchers who are contributors. Thus, it offers the wisdom and
experience of work past and present and attracts a new generation
of researchers to this field. Central to this wisdom and experience
is that of Prof. Nishisato, who has spent much of the past 60 years
mentoring and providing leadership in the research of
quantification theory, especially that of “dual scaling”. The
book includes contributions by leading researchers who have worked
alongside Prof. Nishisato, published with him, been mentored by
him, or whose work has been influenced by the research he has
undertaken over his illustrious career. This book inspires
researchers young and old as it highlights the significant
contributions, past and present, that Prof. Nishisato has made in
his field.
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