Richard GonzalezRichard Gonzalez

Center Director, Research Center for Group Dynamics, Institute for Social Research
Director, BioSocial Methods Collaborative, RCGD
Amos N Tversky Collegiate Professor, Psychology and Statistics, LSA
Professor of Marketing, Stephen M Ross School of Business
Professor of Integrative Systems and Design, College of Engineering


E-mail: Email Richard Gonzalez
Address: Research Center for Group Dynamics
Institute for Social Research
University of Michigan
426 Thompson Street
Ann Arbor, Michigan 48106
Phone: 734-647-6785

Understanding circumplex models: An application to vocational interest

Jan 4, 2013 | Psychology, Statistics/Methods

In trying to understand an application of the circumplex structure to vocational structure, I struggled with geometric representation in theory development and data analysis. This short paper discusses some diagnostics one could apply to data to test the circumplex structure and provides some thoughts on the role of models in theory development.

Gonzalez, R. (1996). Circles and squares, spheres and cubes:  What’s the deal with circumplex models?. Journal of Vocational Behavior, 48, 77-84. doi: 10.1006/jvbe.1996.0008


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 disadvan- tages. 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 advance- ment in applied areas can occur if more attention is given to the particular representa- tional space in which the circumplex is used. I also present three diagnostic properties that all perfect circumplex models must satisfy.