Gemcat: A general multivariate methodology for estimating catastrophe models

Abstract

This paper presents a methodology for empirically estimating any specified univariate or multivariate catastrophe theory model. As such, the paper is appropriate for those interested in modeling virtually all levels of living systems and subsystems which can be described by catastrophe theory models, as well as those interested in testing cross-level hypotheses about such systems and subsystems. The lack of such flexible estimation procedures has limited the potential application of catastrophe modeling in the social and behavioral sciences. More specifically, a methodology called GEMCAT is presented, using the cusp model for expositional convenience, which allows the traditional canonical catastrophe model variables to be described as latent constructs of univariate or multivariate observable variable sets. A Monte Carlo analysis is presented demonstrating the performance of the methodology under various conditions. Furthermore, it is shown how this method is superior to the common practice of generating univariate composites (e.g., by summing, averaging, etc.) which has been traditionally used because of either computational convenience or the lack of such a methodology.