A Dynamical Systems Analysis of Adolescent Substance Abuse

Abstract

Models from dynamical systems theory were fit to the intraindividual variability In adolescent self-reported cigarette and alcohol use. A dampened linear oscillator model (potentially like a pendulum with friction) and a nonlinear oscillator model with two attractors were compared. The nonlinear oscillator model and two coupled oscillators for cigarette and alcohol use were rejected. Independent dampened linear oscillators for smoking and drinking provided high internal R(2) but were unable to account for a substantial correlation between the acceleration in cigarette usage and alcohol usage; thus evidence was found for an intrinsic self-regulation mechanism in both smoking and drinking behavior, but the hypothesis was rejected that the intrinsic mechanism leading to increases in use in one substance directly predicted increased use in the other substance. Given the hypothesis of independent linear oscillators, the sign of the dampening parameter was found to be positive, indicating a system with dynamic instability; a self-regulation mechanism in which small changes in substance use lead to amplified changes after a short period of time.

A Method for Modeling the Intrinsic Dynamics of Intraindividual Variability: Recovering the Parameters of Simulated Oscillators in Multi-Wave Panel Data

“…The point is that the behavior of the damped linear oscillator is sufficiently similar to aspects of compelling intraindividual variability in human beings that its usefulness for representing the latter, especially from the standpoint of prediction, needs to be explored and evaluated. For instance, the damped linear oscillator model has provided evidence of self-regulating oscillations in adolescent substance use (Boker & Graham, 1998) and has been used to elucidate the development of postural control (Boker, 2001).…”

Dynamical Analyses for Developmental Science: A Primer for Intrigued Scientists

“…Lastly, in an amplified pattern the amplitude of the oscillations increases over time. Boker and Graham [1998] found evidence of this pattern in adolescent substance use, where changes in cigarette and alcohol use became larger over time.…”

“…DiDonato /England /Martin /Amazeen Perhaps the greatest advantage of the damped oscillator model is that it requires relatively little data. Boker and Graham [1998] and Nicholson and colleagues [Nicholson, Deboeck, Farris, Boker, & Borkowski, 2011] estimated damped oscillator models using only 4 data points. Conventional longitudinal methods can be used to collect such data.…”

“…These derivatives are then used within a structural equation modeling or multilevel modeling framework to estimate the amplitude and frequency of the linear oscillator model. If necessary, the linear model can be expanded to include a variety of nonlinear terms to examine the effect of escapements on the oscillatory trajectory [Boker & Graham, 1998;Butner et al, 2005;Finan et al, 2010]. Alternatively, the first and second derivatives can be estimated as latent variables in a structural equation model while simultaneously estimating the amplitude and frequency of the linear oscillator model [Boker & Laurenceau, 2006].…”

Latent Differential Equation Modeling with Multivariate Multi-Occasion Indicators

“…Many psychological processes may fit within the framework of self-regulation. Some possible examples of self-regulating psychological processes include lifespan development of cognitive abilities (Donaldson & Horn, 1992;McArdle, Hamagami, Meredith, & Bradway, in press), adolescent substance abuse (Boker & Graham, 1998), self-reported mental health in recent widowhood (Bisconti, 2001), or anxiety levels of children (Cummings & Davies, 2002).…”