Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 10, Iss. 4, October, 2006, pp. 445-470
@2006 Society for Chaos Theory in Psychology & Life Sciences


A Cusp Catastrophe Model Analysis of Changes in Adolescent Substance Use: Assessment of Behavioural Intention as a Bifurcation Variable

Jason Mazanov, University of New South Wales
D. G. Byrne, The Australian National University

Abstract: Behavioural intention was advanced as an alternative bifurcation variable to peer pressure in the context of a cusp catastrophe model of changes in adolescent substance use (Clair, 1998; Byrne, Mazanov & Gregson, 2001). Three sets of models were tested using data from a 12 month longitudinal study of adolescent smoking in Australia: the first with peer pressure only as the bifurcation term, the second with behavioural intention only and the third with both. In isolation both bifurcation variables performed similarly (adjusted-R2 and beta). In the third model, peer pressure edged out behavioural intention as an indicator of catastrophic change. Post hoc analysis revealed the polynomial and simple terms of initial conditions were more important than the bifurcation variable to explain change in smoking behaviour. This provoked a call for more work on finding an appropriately complex (non-straight line), theoretically justifiable mathematical model of adolescent substance use. Overall, behavioural intention was considered equivalent to peer pressure as a bifurcation variable although further research is needed to confirm this result.

Keywords: adolescent, smoking, nonlinear, catastrophe