Advances in multidimensional unfolding
Busing, F.M.T.A.
Citation
Busing, F. M. T. A. (2010, April 21). Advances in multidimensional
unfolding. Retrieved from https://hdl.handle.net/1887/15279Version: Not Applicable (or Unknown)
License: Licence agreement concerning inclusion of doctoral thesis in the Institutional Repository of the University of Leiden
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advances in
multidimensional
unfolding
advances in multidimensional unfolding
Proefschrift
ter verkrijging van de graad van Doctor aan de Universiteit Leiden, op gezag van Rector Magnificus prof. mr. P.F. van der Heijden, volgens besluit van het College voor Promoties te verdedigen op woensdag 21 april 2010 klokke 15:00 uur door Franciscus Martinus Theodorus Antonius Busing geboren te Amsterdam in 1963
promotiecommissie
Promotor: prof. dr. W. J. Heiser
Overige leden: prof. dr. I. van Mechelen(Katholieke Universiteit Leuven)
prof. dr. P. J. F. Groenen (Erasmus Universiteit Rotterdam)
prof. dr. J. J. Meulman (Universiteit Leiden)
dr. M. de Rooij (Universiteit Leiden)
Busing, Franciscus Martinus Theodorus Antonius Advances in Multidimensional Unfolding
Subject headings: unfolding / penalty / restrictions / least squares Copyright © 2010 by Frank Busing
Cover design by Josefien Croese
Printed by Gildeprint Drukkerijen, Enschede, the Netherlands
All rights reserved. This work may not be copied, reproduced, or translated in whole or in part without written permission of the publisher(s), except for brief excerpts in connection with reviews or scholarly analysis. Use with any form of information storage and retrieval, electronic adaptation or whatever, computer software, or by similar or dissimilar methods now known or developed in the future is also strictly forbidden without written permission of the publisher.
Some parts of this work are reproduced by permission; those copyright-holders are: The British Psychological Society, Springer Science+Business Media, and Reed Elsevier.
isbn 978-94-610-8025-7
weet je wat nu zo zonde is dat ik dit op schrijf zonder jou
— Bert Schierbeek
Dedicated to the loving memory of Ton Busing 1931 – 1990
publications
Some ideas have appeared previously in the following publications from the same author:
Busing, F.M.T.A., Commandeur, J.J.F., & Heiser, W.J. (1997). PROXSCAL:
A multidimensional scaling program for individual differences scaling with constraints. In W. Bandilla & F. Faulbaum (Eds.), Softstat ’97, advances in statistical software (pp. 237–258). Stuttgart, Germany: Lucius.
Heiser, W.J., & Busing, F.M.T.A. (2004). Multidimensional scaling and unfold- ing of symmetric and asymmetric proximity relations. In D. Kaplan (Ed.), The Sage handbook of quantitative methodology for the social sciences (pp. 25–48).
Thousand Oaks, CA: Sage Publications, Inc.
Busing, F.M.T.A., & Van Deun, K. (2005). Unfolding Degeneracies’ History.
In K. Van Deun, Degeneracies in multidimensional unfolding (pp. 29–75). Un- published doctoral dissertation, Catholic University Leuven.
Van Deun, K., Groenen, P.J.F., Heiser, W.J., Busing, F.M.T.A., & Delbeke, L.
(2005). Interpreting degenerate solutions in unfolding by use of the vector model and the compensatory distance model. Psychometrika, 70(1), 23–47.
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(1), 71–98.
Busing, F.M.T.A. (2006). Avoiding degeneracy in metric unfolding by penaliz- ing the intercept. British Journal of Mathematical and Statistical Psychology, 59, 419–427.
Busing, F.M.T.A., & de Rooij, M. (2009). Unfolding incomplete data: Guide- lines for unfolding row-conditional rank order data with random missings.
Journal of Classification, 26, 329–360.
Busing, F.M.T.A., Heiser, W.J., & Cleaver, G. (2010). Restricted unfolding:
Preference analysis with optimal transformations of preferences and attributes.
Food Quality and Preference, 21(1), 82–92.
contents
1 Introduction
2 Unfolding degeneracies’ history
. Introduction
. Foundations of multidimensional unfolding
. Roskam, 1968
. Kruskal and Carroll, 1969
. Lingoes, 1977
. Heiser, 1981
. Borg and Bergermaier, 1982
. De Leeuw, 1983
. DeSarbo and Rao, 1984
. Heiser, 1989
. Kim, Rangaswamy, and DeSarbo, 1999
. Summary
. Recent developments
3 The intercept penalty
. Introduction
. Example
. Metric unfolding
. Degeneracy
. Penalizing the intercept
. Example (continued)
. Conclusion
.A Penalized interval transformation
.B Example: ibm spss prefscal specification for pmse
.C Example: matlab code for pmse
4The coefficient of variation penalty
. Introduction
. Badness-of-fit functions
. Penalizing the coefficient of variation
. Simulation study
. Applications
. Summary
5 Restricted Unfolding
. Introduction
. The restricted unfolding model
. Case study
. Optimizing product development
. Comparison
. Discussion
6 Unfolding incomplete data
. Introduction
. Unfolding
. Missing data
. Monte Carlo simulation study
. Example
. Conclusion
.A Simulation study
7 Conclusion
. The intercept penalty
. The coefficient of variation penalty
. Restricted unfolding
. Unfolding incomplete data
. Final conclusions
Technical appendix A Notation overview 141
A. Notation conventions
A. Symbols
A. Functions
A. Acronyms
B Least squares unfolding algorithm 147 C Pre-Processing 151
C. Preliminary work
C. Initial configuration
D Transformation update 161 D. Majorization functions
D. Transformation functions
E Configuration update 175 E. Common space update
E. Two-way unfolding models
E. Three-way unfolding models
E. Coordinate restrictions
E. Variable restrictions
E. Other restrictions
F Post-Processing 193
F. Algorithm termination
F. Uniqueness
F. Multiple analyses
F. Additional analyses
G Results 207
G. Table output
G. Figure output
G. Fit measures
G. Variation measures
G. Degeneracy indices
Glossary of Solutions
References
Author index
Subject index
Summary (in Dutch)
Curriculum vitae
Colophon
