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

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

Research output: Book/ReportReportAcademic

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 Heise...
Original languageEnglish
Place of PublicationRotterdam
PublisherRSM Erasmus Univ., Erasmus Research Inst. Management (ERIM)
Number of pages20
Publication statusPublished - 2006

Publication series

NameERIM report series research in management
PublisherRSM Erasmus Univ., Erasmus Research Inst. Management (ERIM)
No.ERS-2006-057-MKT
ISSN (Print)1566-5283

Keywords

  • scaling
  • dimensional analysis
  • mathematical models
  • algorithms
  • equations
  • correlation analysis
  • classification

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