Cusp catastrophe model: a nonlinear model for health outcomes in nursing research

Although health outcomes may have fundamentally nonlinear relationships with relevant behavioral, psychological, cognitively, or biological predictors, most analytical models assume a linear relationship. Furthermore, some health outcomes may have multimodal distributions, but most statistical models in common use assume a unimodal, normal distribution. Suitable nonlinear models should be developed to explain health outcomes.

The aim of this study is to provide an overview of a cusp catastrophe model for examining health outcomes and to present an example using grip strength as an indicator of a physical functioning outcome to illustrate how the technique may be used. Results using linear regression, nonlinear logistic model, and the cusp catastrophe model were compared.

Data from 935 participants from the Survey of Midlife Development in the United States (MIDUS) were analyzed. The outcome was grip strength; executive function and the inflammatory cytokine interleukin-6 were predictor variables.

Grip strength was bimodally distributed. On the basis of fit and model selection criteria, the cusp model was superior to the linear model and the nonlinear logistic regression model. The cusp catastrophe model identified interleukin-6 as a significant asymmetry factor and executive function as a significant bifurcation factor.

The cusp catastrophe model is a useful alternative for explaining the nonlinear relationships commonly seen between health outcome and its predictors. Considerations for the use of cusp catastrophe model in nursing research are discussed and recommended.