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.