An exponential effect persistence model for intensive longitudinal data

We develop an effect persistence model for intensive longitudinal data under a general assumption of an exponential loss of association between exposure and outcome over time. The working model proposed may be useful for understanding the complexity of phenomena where subjects can be repeatedly exposed to an intervention or a naturally occurring event while at the same time, the effect of any one exposure is expected to diminish over time. Under the main assumption, we specify a semi-linear model with extensions to generalized linear models. These methods are motivated by, and applied to, data from a study of adolescent exposure to pro-smoking advertisement where the impact of pro-smoking media exposure on young adults’ susceptibility to smoking is assessed along with the decay of the effect over time. We investigate the performance of the proposed method when the model assumptions are correctly specified or not. Supplementary materials for this article are available online.