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2018 | OriginalPaper | Chapter

8. Unfolding

Authors : Ingwer Borg, Patrick J. F. Groenen, Patrick Mair

Published in: Applied Multidimensional Scaling and Unfolding

Publisher: Springer International Publishing

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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.

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previous chapter Typical Mistakes in MDS
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Footnotes
1
Note that you can use this script and hold the s2 matrix of the initial configuration fixed if you want to do external unfolding with a theory-derived configuration of value points. To do this, you add the argument fix = "columns" to the unfolding() call.
 
3
The vector model cannot represent cases where a person’s preference strengths keep going up until a certain point is reached and then drop monotonically as one continues moving further on the person’s vector. If, however, all ideal points move far outside the configuration of the choice objects, the vector model approximates the ideal-point model as a special case (Coombs, 1975).
 
4
The reconstructed values are obtained by projecting each item onto the direction of the person arrow multiplied by the length of the person arrow.
 
Literature
Borg, I., & Groenen, P. J. F. (2005). Modern multidimensional scaling (2nd ed.). New York: Springer.MATH
Borg, I., & Staufenbiel, T. (2007). Theorien und methoden der skalierung (4th ed.). Berne: Huber.
Busing, F. M. T. A., Groenen, P. J. F., & Heiser, W. J. (2005). Avoiding degeneracy in multidimensional unfolding by penalizing on the coefficient of variation. Psychometrika, 70, 71–98.MathSciNetCrossRef
Carroll, J. D. (1980). Models and methods for multidimensional analysis of preferential choice or other dominance data. In E. D. Lantermann & H. Feger (Eds.), Similarity and choice. Bern: Huber.
Coombs, C. H. (1975). A note on the relation between the vector model and the unfolding model for preferences. Psychometrika, 40, 115–116.CrossRef
Norpoth, H. (1979). The parties come to order! Dimensions of preferential choice in the West German electorate, 1961–1976. The American Political Science Review, 73, 724–736.CrossRef
Schwartz, S. H. (1992). Universals in the content and structure of values: Theoretical advances and empirical tests in 20 countries. Advances in Experimental Social Psychology, 25, 1–65.
Metadata
Title
Unfolding
Authors
Ingwer Borg
Patrick J. F. Groenen
Patrick Mair
Copyright Year
2018
Book
Applied Multidimensional Scaling and Unfolding

Print ISBN: 978-3-319-73470-5

Electronic ISBN: 978-3-319-73471-2

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-73471-2_8

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