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2018 | Buch

Applied Multidimensional Scaling and Unfolding

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Über dieses Buch

This book introduces multidimensional scaling (MDS) and unfolding as data analysis techniques for applied researchers. MDS is used for the analysis of proximity data on a set of objects, representing the data as distances between points in a geometric space (usually of two dimensions). Unfolding is a related method that maps preference data (typically evaluative ratings of different persons on a set of objects) as distances between two sets of points (representing the persons and the objects, resp.).

This second edition has been completely revised to reflect new developments and the coverage of unfolding has also been substantially expanded. Intended for applied researchers whose main interests are in using these methods as tools for building substantive theories, it discusses numerous applications (classical and recent), highlights practical issues (such as evaluating model fit), presents ways to enforce theoretical expectations for the scaling solutions, and addresses the typical mistakes that MDS/unfolding users tend to make. Further, it shows how MDS and unfolding can be used in practical research work, primarily by using the smacof package in the R environment but also Proxscal in SPSS. It is a valuable resource for psychologists, social scientists, and market researchers, with a basic understanding of multivariate statistics (such as multiple regression and factor analysis).

Inhaltsverzeichnis

Frontmatter
Chapter 1. First Steps
Abstract
The basic ideas of MDS are introduced doing MDS by hand. Then, MDS is done using statistical software. The goodness of the MDS configuration is evaluated by correlating its distances with the data. Unfolding is introduced with a small example.
Ingwer Borg, Patrick J. F. Groenen, Patrick Mair
Chapter 2. The Purpose of MDS and Unfolding
Abstract
The different purposes of MDS are explained: MDS for visualizing proximity data; MDS for uncovering latent dimensions; MDS as a psychological theory about judgments of similarity; MDS for testing structural hypotheses; unfolding as a psychological theory about judgments of preference.
Ingwer Borg, Patrick J. F. Groenen, Patrick Mair
Chapter 3. The Fit of MDS and Unfolding Solutions
Abstract
Ways to assess the goodness of an MDS solution are discussed. The Stress measure is defined as an index that aggregates representation errors. Criteria for evaluating Stress are presented. Stress per Point (SPP) is defined as a way to assess the fit of single points.
Ingwer Borg, Patrick J. F. Groenen, Patrick Mair
Chapter 4. Proximities
Abstract
The data for MDS, proximities, are discussed. Proximities can be collected directly as judgments of similarity; proximities can be derived from data vectors; proximities may result from converting other indexes; and co-occurrence data are yet another popular form of proximities.
Ingwer Borg, Patrick J. F. Groenen, Patrick Mair
Chapter 5. Variants of MDS Models
Abstract
Various forms of MDS are discussed: ordinal MDS, metric MDS, MDS with different distance functions, MDS for asymmetric proximities, individual difference MDS models, MDS for more than one proximity value per distance, and weighting proximities in MDS.
Ingwer Borg, Patrick J. F. Groenen, Patrick Mair
Chapter 6. Confirmatory MDS
Abstract
Different forms of confirmatory MDS are introduced, from weak forms with external starting configurations to enforcing theoretical constraints onto the MDS point coordinates or onto certain regions of the MDS space.
Ingwer Borg, Patrick J. F. Groenen, Patrick Mair
Chapter 7. Typical Mistakes in MDS
Abstract
Various mistakes that users tend to make when using MDS are discussed, from using MDS for the wrong type of data, using MDS programs with suboptimal specifications, to misinterpreting MDS solutions.
Ingwer Borg, Patrick J. F. Groenen, Patrick Mair
Chapter 8. Unfolding
Abstract
Unfolding is discussed again in a realistic and more complex application that requires a 3d solution with a special rotation. For mixed samples, multidimensional unfolding can sometimes be replaced by multiple low-dimensional unfolding. One must also clarify whether the data are unconditionally comparable. The stability of unfolding solutions is discussed, and some special unfolding models such as the vector model and circular unfolding are introduced.
Ingwer Borg, Patrick J. F. Groenen, Patrick Mair
Chapter 9. MDS Algorithms
Abstract
Two types of solutions for MDS are discussed. If the proximities are Euclidean distances, classical MDS yields an easy algebraic solution. In most MDS applications, iterative methods are needed, because they admit many types of data and distances. They use a two-phase optimization algorithm, moving the points in MDS space in small steps while holding the data and their transforms fixed, and vice versa, until convergence is reached.
Ingwer Borg, Patrick J. F. Groenen, Patrick Mair
Chapter 10. MDS Software
Abstract
Two modern programs for MDS are described: proxscal, an spss module, and smacof, an R package. Commands and/or GUI menus are presented and illustrated with practical applications.
Ingwer Borg, Patrick J. F. Groenen, Patrick Mair
Backmatter
Metadaten
Titel
Applied Multidimensional Scaling and Unfolding
verfasst von
Prof. Dr. Ingwer Borg
Prof. Patrick J.F. Groenen
Patrick Mair
Copyright-Jahr
2018
Electronic ISBN
978-3-319-73471-2
Print ISBN
978-3-319-73470-5
DOI
https://doi.org/10.1007/978-3-319-73471-2