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

24 Pages Posted: 23 Dec 2006

See all articles by Ivo A. van der Lans

Ivo A. van der Lans

Wageningen University and Research (WUR)

Patrick J. F. Groenen

Erasmus University Rotterdam (EUR)

Date Written: October 30, 2006

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.

Keywords: Axial Partitioning, Constrained Estimation, Facet Theory, Iterative Majorization, Multidimensional Scaling, Regional Restrictions

Suggested Citation

Lans, Ivo A. van der and Groenen, Patrick J. F., Multidimensional Scaling with Regional Restrictions for Facet Theory: An Application to Levi's Political Protest Data (October 30, 2006). ERIM Report Series Reference No. ERS-2006-057-MKT, Available at SSRN: https://ssrn.com/abstract=942152

Ivo A. van der Lans

Wageningen University and Research (WUR) ( email )

Hollandseweg 1
6706KN
Netherlands

Patrick J. F. Groenen (Contact Author)

Erasmus University Rotterdam (EUR) ( email )

P.O. Box 1738
3000 DR Rotterdam, NL 3062 PA
Netherlands

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