title: Cusp Catastrophe Polynomial Model: Power and Sample Size Estimation.
abstract: Guastello's polynomial regression method for solving cusp catastrophe model has been widely applied to analyze nonlinear behavior outcomes. However, no statistical power analysis for this modeling approach has been reported probably due to the complex nature of the cusp catastrophe model. Since statistical power analysis is essential for research design, we propose a novel method in this paper to fill in the gap. The method is simulation-based and can be used to calculate statistical power and sample size when Guastello's polynomial regression method is used to cusp catastrophe modeling analysis. With this novel approach, a power curve is produced first to depict the relationship between statistical power and samples size under different model specifications. This power curve is then used to determine sample size required for specified statistical power. We verify the method first through four scenarios generated through Monte Carlo simulations, and followed by an application of the method with real published data in modeling early sexual initiation among young adolescents. Findings of our study suggest that this simulation-based power analysis method can be used to estimate sample size and statistical power for Guastello's polynomial regression method in cusp catastrophe modeling.
authors.affiliation: Center of Research, School of Nursing, University of Rochester Medical Center, Rochester, USA; Department of Biostatistics and Computational Biology, University of Rochester Medical Center, Rochester, USA; Institute of Data Sciences, University of Rochester, Rochester, USA.
authors.forename: Ding-Geng Din
authors.initials: DD
authors.lastname: Chen
authors.affiliation: Department of Epidemiology, University of Florida, Gainesville, FL, USA; Wuhan University School of Public Health, Wuhan, China.
authors.forename: Xinguang Jim
authors.initials: XJ
authors.lastname: Chen
authors.affiliation: Center of Research, School of Nursing, University of Rochester Medical Center, Rochester, USA; AD-CARE, Department of Psychiatry, University of Rochester Medical Center, Rochester, NY, USA.
authors.forename: Feng
authors.initials: F
authors.lastname: Lin
authors.affiliation: Department of Biostatistics and Computational Biology, University of Rochester Medical Center, Rochester, USA.
authors.forename: Wan
authors.initials: W
authors.lastname: Tang
authors.affiliation: Department of Mathematical Sciences, University of South Dakota, Vermillion, SD, USA.
authors.forename: Y L
authors.initials: YL
authors.lastname: Lio
authors.affiliation: Department of Statistics, Central South University, Changsha, Hunan, P. R. China.
authors.forename: Tammy Yuanyuan
authors.initials: TY
authors.lastname: Guo
keywords: Cusp catastrophe model; Polynomial regression method; Sample size determination; Statistical power analysis