Ingwer Borg

Subjektiver wert, praferenz und utilitat: einige offene und ges...

Samuel Shye

Facet Theory (FT) is presented in this volume as a methodological approach that combines content design and data analysis. Following a brief overview of FT design, FT data analysis and the correspondence hypotheses between the two, the authors consider the role facets play in observations and equivalence relations and discuss in detail: mapping sentences and their common range; constructing questionnaire items; correspondence hypotheses relating to FT design; bivariate regression hypotheses; and how to analyze data profiles with hypotheses for structuples and similarity structures. In conclusion, the issues of using FT in practice including measurement theory and significance testing are addressed.

Form and Content

Facet Theory

Peter P. Mohler

Trends and Perspectives in Empirical Social Research

Patrick Mair

Patrick J.F. Groenen

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).

Applied Multidimensional Scaling and Unfolding

Patrick Groenen

Multidimensional scaling (MDS) is a technique for the analysis of similarity or dissimilarity data on a set of objects. Such data may be intercorrelations of test items, ratings of similarity on political candidates, or trade indices for a set of countries. MDS attempts to model such data as distances among points in a geometric space. The main reason for doing this is that one wants a graphical display of the structure of the data, one that is much easier to understand than an array of numbers and, moreover, one that displays the essential information in the data, smoothing out noise. There are numerous varieties of MDS. Some facets for distinguishing among them are the particular type of geometry into which one wants to map the data, the mapping function, the algorithms used to find an optimal data representation, the treatment of statistical error in the models, or the possibility to represent not just one but several similarity matrices at the same time. Other facets relate to the different purposes for which MDS has been used, to various ways of looking at or "interpreting" an MDS representation, or to differences in the data required for the particular models. In this book, we give a fairly comprehensive presentation of MDS. For the reader with applied interests only, the first six chapters of Part I should be sufficient. They explain the basic notions of ordinary MDS, with an emphasis on how MDS can be helpful in answering substantive questions.

Theory and Applications

Modern Multidimensional Scaling

Ingwer Borg

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