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