Asymmetric relationship data may arise in various
judgment situations, for instance, when children are asked to rate their
friendship with other children in a class. If friendship of each child with each
other child is rated, it is usually found that the relations are asymmetric:
Child A likes Child B more than vice versa. Special methods for analyzing these
asymmetric similarities by means of component techniques can be used.
Interesting component based methods are Gipscal (developed by N. Chino) and
DEDICOM (developed by R.A. Harshman), for instance, see Kiers & Takane (1994).
Further involvement in computational and conceptual contributions of the
analysis of asymmetric relationship data was published in Ten Berge and Kiers
(1989), Kiers, Ten Berge, Takane and De Leeuw (1990), Kiers (1997), Kiers and
Takane (1993), Takane and Kiers (1997).
If asymmetric relationship data are available for a
number of consecutive years, one has a three-way data set with friendship
ratings of children by children by years, which requires specially designed
multiway techniques. Also, special procedures for graphical display are called
for. In one such approach, in the two-way case, the children are displayed as
points in a two-dimensional plot, and their attraction to (groups of) other
children is indicated by arrows in the relevant directions (with long arrows
indicating higher attraction). How such arrow plots can usefully be applied in
multiway analysis is a matter of further study.