Joint Space Model for Multidimensional Scaling of Two-Mode Three-Way Asymmetric Proximities

A joint space model and an associated nonmetric algorithm to analyze two-mode three-way asymmetric proximities (object × object × source) are presented. Each object is represented as a point and a circle (sphere, hyper sphere) in the common joint configuration which is common to all sources. Each source is represented as a point in the common joint configuration. For each source, the radius of an object is stretched or shrunk according to the distance between the dominance point representing the source and the point representing the object. An application to intergenerational occupational mobility data is shown.