Sample Size Determination to Detect Cusp Catastrophe in Stochastic Cusp Catastrophe Model: A Monte-Carlo Simulation-Based Approach

Abstract

Stochastic cusp catastrophe model has been utilized extensively to model the nonlinear social and behavioral outcomes to detect the exisitance of cusp catastrophe. However the foundamental question on sample size needed to detect the cusp catastrophe from the study design point of view has never been investigated. This is probably due to the complexity of the cusp model. This paper is aimed at filling the gap. In this paper, we propose a novel Monte-Carlo simulation-based approach to calculate the statistical power for stochastic cusp catastrophe model so the sample size can be determined. With this approach, a power curve can be produced to depict the relationship between its statistical power and samples size under different specifications. With this power curve, researchers can estimate sample size required for specified power in design and analysis data from stochastic cusp catastrophe model. The implementation of this novel approach is illustrated with data from Zeeman’s cusp machine.