Circles and Squares, Spheres and Cubes: What's the Deal with Circumplex Models?

A distinction is made between data description and representational space in the context of circumplex models. The representational space provides the language in which data are described, and different languages have their advantages and disadvantages. For instance, points in a two-dimensional Cartesian grid can form a circle. Such a circular pattern corresponds to a description of the data pattern. However, the same data can also be represented in a polar coordinate system, which is a different representational space than the Cartesian grid. I claim that additional theory advancement in applied areas can occur if more attention is given to the particular representational space in which the circumplex is used. I also present three diagnostic properties that all perfect circumplex models must satisfy. q 1996 Academic Press, Inc.