Moderator regression and the cusp catastrophe: Application of two‐stage personnel selection, training, therapy, and policy evaluation

This article demonstrates the applicability of the cusp catastrophe model to a two‐stage validity study for personnel selection which can simultaneously assess the success of a training program. Personnel selection is of interest substantively since its literature spans psychology, education, economics, management science, political philosophy, statistics, and psychometric theory. The basic problem is, in turn, pertinent to the study of any individuals integrating into an organization, or a therapy or social program. In an empirical example regression coefficients for conventional and cusp‐difference models were compared using partially real and partially simulated data. Subjects were 272 salespersons from a Midwestern firm, of which 17 were Spanish‐speaking Americans. Group membership was the dummy coded bifurcation (moderator) factor. A composite of personality and ability test scores was the asymmetry factor. The cusp model was a more efficient predictor of performance ( R 2 = .39) than the moderator model ( R 2 = .04) or a control equation using a bimodal transformation ( R 2 = .04). It was also possible to obtain implicit discriminant functions ( IDFS ) to predict the top performing 16% of the sample ( R 2 = .71), and the low performing 16% ( R 2 = .95). The results were interpreted as supporting the usefulness of the statistical catastrophe models for two‐stage personnel selection and training, and similar problems. Differential impact, moderator, and interaction effects in organizational literature were discussed vis‐á‐vis the bifurcation concept.