Cusp catastrophe regression and its application in public health and behavioral research

The cusp catastrophe model is an innovative approach for investigating a phenomenon that consists of both continuous and discrete changes in one modeling framework. However, its application to empirical health and behavior data has been hindered by the complexity in data-model fit. In this study, we reported our work in the development of a new modeling method—cusp catastrophe regression (RegCusp in short) by casting the cusp catastrophe into a statistical regression. With the RegCusp approach, unbiased model parameters can be estimated with the maximum likelihood estimation method. To validate the RegCusp method, a series of simulations were conducted to demonstrate the unbiasedness of parameter estimation. Since the estimated residual variance with the Fisher information matrix method was over-dispersed, a bootstrap re-sampling procedure was developed and used as a remedy. We also demonstrate the practical applicability of the RegCusp with empirical data from an NIH-funded project to evaluate an HIV prevention intervention program to educate adolescents in the Bahamas for condom use. Study findings indicated that the model parameters estimated with RegCusp were practically more meaningful than those estimated with comparable methods, especially the estimated cusp point.