Modeling Time-Dependent Association in Longitudinal Data: A Lag as Moderator Approach

We describe a straightforward, yet novel, approach to examine time-dependent association between variables. The approach relies on a measurement-lag research design in conjunction with statistical interaction models. We base arguments in favor of this approach on the potential for better understanding the associations between variables by describing how the association changes with time. We introduce a number of different functional forms for describing these lag-moderated associations, each with a different substantive meaning. Finally, we use empirical data to demonstrate methods for exploring functional forms and model fitting based on this approach.