Dynamical Outcome Modeling of Fragmented Intensive Longitudinal Data

Abstract

The advent of new sensing technologies has enabled the collection of high frequency individual data. Not only can this allow for the identification of personalized behavior models, it also opens up the possibility of developing just-in-time interventions that leverage the information collected to determine when and which micro intervention should be provided. However, there are significant challenges in the analysis of this type of data. First, due to the high rate of data collection, one can no longer assume that the stimulus (independent excitation or micro intervention) only has an instantaneous effect on the outcome, one has to also allow for delayed effects. Moreover, one is also frequently faced with fragmented data; i.e., poor placement of sensors, non-wear of the data collecting device and/or external disturbances can lead to intervals of time where the data collected is not reliable; i.e., missing or corrupted. To deal with these challenges, we leverage concepts from the areas of dynamical systems and signal processing to develop tools that i) can identify models that take into account the delayed stimuli effects and ii) are able to handle fragmented data. In this paper, we provide both the mathematical foundation of the tools proposed and the description of a package that implements them. We also discuss ways to interpret the results obtained.