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Multidimensional Scaling with Regional Restrictions for Facet Theory: An Application to Levi's Political Protest Data

Author

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  • Groenen, P.J.F.
  • van der Lans, A.

Abstract

Multidimensional scaling (MDS) is often used for the analysis of correlation matrices of items generated by a facet theory design. The emphasis of the analysis is on regional hypotheses on the location of the items in the MDS solution. An important regional hypothesis is the axial constraint where the items from different levels of a facet are assumed to be located in different parallel slices. The simplest approach is to do an MDS and draw the parallel lines separating the slices as good as possible by hand. Alternatively, Borg and Shye (1995) propose to automate the second step. Borg and Groenen (1997, 2005) proposed a simultaneous approach for ordered facets when the number of MDS dimensions equals the number of facets. In this paper, we propose a new algorithm that estimates an MDS solution subject to axial constraints without the restriction that the number of facets equals the number of dimensions. The algorithm is based on constrained iterative majorization of De Leeuw and Heiser (1980) with special constraints. This algorithm is applied to Levi’s (1983) data on political protests.

Suggested Citation

  • Groenen, P.J.F. & van der Lans, A., 2006. "Multidimensional Scaling with Regional Restrictions for Facet Theory: An Application to Levi's Political Protest Data," ERIM Report Series Research in Management ERS-2006-057-MKT, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    • Handle: RePEc:ems:eureri:8045
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    References listed on IDEAS

    as
    1. Shlomit Levy, 1983. "A cross-cultural analysis of the structure and levels of attitudes towards acts of political protest," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 12(3), pages 281-309, April.
    2. Ingwer Borg & James Lingoes, 1980. "A model and algorithm for multidimensional scaling with external constraints on the distances," Psychometrika, Springer;The Psychometric Society, vol. 45(1), pages 25-38, March.
    3. Patrick Groenen & Bart-Jan Os & Jacqueline Meulman, 2000. "Optimal scaling by alternating length-constrained nonnegative least squares, with application to distance-based analysis," Psychometrika, Springer;The Psychometric Society, vol. 65(4), pages 511-524, December.
    4. Norbert Gaffke & Rudolf Mathar, 1989. "A cyclic projection algorithm via duality," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 36(1), pages 29-54, December.
    5. Mathar, Rudolf, 1990. "Multidimensional scaling with constraints on the configuration," Journal of Multivariate Analysis, Elsevier, vol. 33(2), pages 151-156, May.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Axial Partitioning; Constrained Estimation; Facet Theory; Iterative Majorization; Multidimensional Scaling; Regional Restrictions;
    All these keywords.

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C49 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Other
    • M - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics
    • M31 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Marketing and Advertising - - - Marketing

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