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.
Highlights
Popularized in the 1970’s by Thom [1], Thom and Fowler [2], Cobb and Ragade [3], Cobb and Watson [4], and Cobb and Zack [5], catastrophe theory was proposed to understand a complicated set of behaviors including both gradual and continuous changes and sudden and discrete or catastrophical changes
One direction is operationalized by Guastello [6] [7] with the implementation into a polynomial regression approach and another direction by a stochastic cusp catastrophe model from Cobb and his colleagues [5] with implementation in an R package in [8]
Typical examples include modeling of accident process [7], adolescent alcohol use [9], changes in adolescent substance use [10], binge drinking among college students [11], sexual initiation among young adolescents [12], nursing turnover [13], and effect of HIV prevention among adolescents [12] [14]
Summary
Popularized in the 1970’s by Thom [1], Thom and Fowler [2], Cobb and Ragade [3], Cobb and Watson [4], and Cobb and Zack [5], catastrophe theory was proposed to understand a complicated set of behaviors including both gradual and continuous changes and sudden and discrete or catastrophical changes. This paper is to discuss the first direction on polynomial cusp catastrophe regression model due to its relative simplicity and ease for implementation as simple regression approach This model has been used extensively in research. Typical examples include modeling of accident process [7], adolescent alcohol use [9], changes in adolescent substance use [10], binge drinking among college students [11], sexual initiation among young adolescents [12], nursing turnover [13], and effect of HIV prevention among adolescents [12] [14] Even though this polynomial regression method has been widely applied in behavioral studies to investigate the existence of cusp catastrophe, to the best of our knowledge, no reported research has addressed the determination of sample size and statistical power for this analytical approach. Conclusions and discussions are given at the end of the paper (Section 5)
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