Modeling self-exciting diurnal processes with applications to smartphone use in populations with affective disorders

Improving strength of routine is a target for many therapies and treatments of mood and affective disorders. Smartphone usage data enables us to model person-specific diurnal patterns of usage that provide useful insight into a person's routine and behavior. Considering phone usage as a point process, existing approaches focus on capturing self-exciting behavior, the phenomenon where the rate of usage is heightened during and immediately after using one's phone. While this self-exciting phenomenon is important, there are limited methods that also allow for flexible modeling of diurnal effects on the rate of smartphone usage. We propose a framework that can combine the self-exciting Hawkes process with a truncated Fourier series to capture important diurnal trends. Due to the challenges with optimization under this first framework, we additionally propose a model to capture self-exciting and diurnal behaviors with improved estimation. Through simulation experiments and an application to a cohort of patients with affective disorders, we show the benefit of models that account for self-exciting and diurnal patterns concurrently.