ASYMMETRIC MULTIDIMENSIONAL-SCALING OF 2-MODE 3-WAY PROXIMITIES

Authors
Citation
A. Okada, ASYMMETRIC MULTIDIMENSIONAL-SCALING OF 2-MODE 3-WAY PROXIMITIES, Journal of classification, 14(2), 1997, pp. 195-224
Citations number
42
Categorie Soggetti
Social Sciences, Mathematical Methods","Mathematical, Methods, Social Sciences","Mathematics, Miscellaneous
Journal title
ISSN journal
01764268
Volume
14
Issue
2
Year of publication
1997
Pages
195 - 224
Database
ISI
SICI code
0176-4268(1997)14:2<195:AMO23P>2.0.ZU;2-9
Abstract
An asymmetric multidimensional scaling model and an associated non-met ric algorithm to analyze two-mode three-way proximities (object x obje ct x source) are introduced. The model consists of a common object con figuration and two kinds of weights, i.e., for both symmetry and asymm etry. In the common object configuration, each object is represented b y a point and a circle (sphere, hypersphere) in a Euclidean space. The common object configuration represents pairwise proximity relationshi ps between pairs of objects for the 'group' of all sources. Each sourc e has its own symmetry weight and a set of asymmetry weights. Symmetry weights represent individual differences among sources of data in sym metric proximity relationships, and asymmetry weights represent indivi dual differences among sources in asymmetric proximity relationships. The associated nonmetric algorithm, based on Kruskal's (1964b) nonmetr ic multidimensional scaling algorithm, is an extension of the algorith m for the asymmetric multidimensional scaling of one mode two-way prox imities developed earlier (Okada and Imaizumi 1987). As an illustrativ e example, we analyze intergenerational occupational mobility from 195 5 to 1985 in Japan among eight occupational categories.