The Differential Time-Varying Effect Model (DTVEM): A tool for diagnosing and modeling time lags in intensive longitudinal data

With the recent growth in intensive longitudinal designs and the corresponding demand for methods to analyze such data, there has never been a more pressing need for user-friendly analytic tools that can identify and estimate optimal time lags in intensive longitudinal data. The available standard exploratory methods to identify optimal time lags within univariate and multivariate multiple-subject time series are greatly underpowered at the group (i.e., population) level. We describe a hybrid exploratory-confirmatory tool, referred to herein as the Differential Time-Varying Effect Model (DTVEM), which features a convenient user-accessible function to identify optimal time lags and estimate these lags within a state-space framework. Data from an empirical ecological momentary assessment study are then used to demonstrate the utility of the proposed tool in identifying the optimal time lag for studying the linkages between nervousness and heart rate in a group of undergraduate students. Using a simulation study, we illustrate the effectiveness of DTVEM in identifying optimal lag structures in multiple-subject time-series data with missingness, as well as its strengths and limitations as a hybrid exploratory-confirmatory approach, relative to other existing approaches.