Multidimensional Scaling with Regional Restrictions for Facet Theory: An Application to Levi's Political Protest Data
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|
|JEL||Statistical Decision Theory; Operations Research (jel C44), Econometric and Statistical Methods: Special Topics: Other (jel C49), Business Administration and Business Economics; Marketing; Accounting (jel M), Marketing (jel M31)|
|Publisher||Erasmus Research Institute of Management|
|Series||ERIM Report Series Research in Management|
|Journal||ERIM report series research in management Erasmus Research Institute of Management|
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 (No. ERS-2006-057-MKT). ERIM report series research in management Erasmus Research Institute of Management. Erasmus Research Institute of Management. Retrieved from http://hdl.handle.net/1765/8045