Title: An Exponential Effect Persistence Model for Intensive Longitudinal Data
Abstract:
The idea behind this study came out of a discussion I had with Dennis Cook once: Big data is a
buzz word now in statistics and data sciences, but outside of data size, are there different ways
we should look at big data? In this context, the effects of discrete interventions and naturally-
occurring events on a person's thoughts, emotions, behaviors, and physical functioning often
vary over time. As such, understanding temporal persistence or decay of effects is of central
importance in behavioral sciences and it entails recognizing changes after a person has been
subject to a treatment, establishing a cause-and-effect and evaluating the persistence of the
effect with the passage of time. In this study, we develop an effect persistence model for
intensive longitudinal data (a type of “big data”) under a general assumption of an exponential
loss of association between exposure and outcome over time. The proposed model may be
useful for understanding the complexity of phenomena where subjects can be repeatedly
exposed to an intervention while at the same time, the effect of any one exposure is expected to
diminish over time. The method is 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.
The performance of the proposed method is investigated.