The present article provides an alternative framework for evaluating mediated relationships. From this perspective. a mediated process is a chain reaction, beginning with an independent variable that affects a mediator that in turn affects an outcome. The definition of mediation offered here, presented for stage sequences, states three conditions for establishing mediation: (a) the independent variable affects the probability of the sequence no mediator to mediator to outcome; (b) the independent variable affects the probability of a transition into the mediator stage; (c) the mediator affects the probability of a transition into the outcome stage at every level of the independent variable. This definition of mediation is compared and contrasted with the well-known definition of mediation for continuous variables discussed in Baron and Kenny (1986), Judd and Kenny (1981), and Kenny, Kashy, and Bolger (1997). The definition presented in this article emphasizes the intraindividual, time-ordered nature of mediation.

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.

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