Title:  The circumplex : a slightly stronger than ordinal approach 
Author(s):  Bezembinder, T.G.G. 
Publication year:  2003 
Source:  Journal of Mathematical Psychology, vol. 47, iss. 3, (2003), pp. 323345 
ISSN:  00222496 
Publication type:  Article / Letter to editor 
Please use this identifier to cite or link to this item : http://hdl.handle.net/2066/63606 

Subject:  Mathematical psychology 
Organization:  FSW_PSY_MA Mathematische psychologie 
Journal title:  Journal of Mathematical Psychology 
Volume:  vol. 47 
Issue:  iss. 3 
Page start:  p. 323 
Page end:  p. 345 
Abstract: 
For some proximity matrices, multidimensional scaling yields a roughly circular configuration of the stimuli. Being not symmetric, a rowconditional matrix is not fit for such an analysis. However, suppose its proximities are all different within rows. Calling {{x,y}, {x,z}} a conjoint pair of unordered pairs of stimuli, let {x,y} > {x, z} mean that row x shows a stronger proximity for {x,y} than for {x,z}. We have a cyclic permutation pi of the set of stimuli characterize a subset of the conjoint pairs. If the arcs {x,y} > {x,z} between the pairs thus characterized are in a specific sense monotone with pi, the matrix determines pi uniquely, and is, in that sense, a circumplex with pi as underlying cycle. In the strongest of the 3 circumplexes thus obtained, > has circular paths. We give examples of analyses of, in particular, conditional proximities by these concepts, and implications for the analysis of presumably circumplical proximities. Circumplexes whose underlying permutation is multicyclic are touched. (C) 2003 Elsevier Science (USA). All rights reserved
