Appearance and reality: Is the Big Five the structure of trait descriptors?

It is argued that contrary to the claims of Big Five investigators, the structure of trait descriptors is still very much an open issue. This is because their methodology, factor/component analysis paired with the dimensional interpretation/simple structure (DISS) procedure, does not investigate the closed topological manifold that constitutes the ‘structure’ of a set of variables. Instead, radex-related configurations are likely candidates for the structure of trait descriptors. Some preliminary support for this claim is given by an analysis of the NEO Personality Inventory (NEO-PI) (Costa & McCrae, Manual for the NEO PI-R. Odessa, FL: Psychological Assessment Resources, 1992), a Big Five questionnaire measure, and the Goldberg-40 (Goldberg, Review of Personality and Social Psychology, Vol. 2, pp. 141–165, 1981. Beverly Hills, CA: Sage), an adjective measure. In particular, the NEO-PI and Goldberg-40 are shown to have radex structures. A facet theory (Guttman, Psychometrika, 36, 329–346, 1971) rationale is provided for these findings.