A Hierarchical Gaussian Process Approach to Understanding Mental Health Trajectories via Item Response Theory Models

Longitudinal mental health assessments in mobile health (mHealth) settings are useful for monitoring subjects' mental health statuses but are often difficult to analyze because they generally appear on an ordinal scale and at unequal time intervals. In this article, we explore the use of Gaussian processes (GPs) and hierarchical modeling techniques to understand mental health trajectories based on repeated multi-item mHealth surveys on a Likert scale. We introduce the GP model for health trajectories, which is based on item response theory. In the study of trajectories, a subject's longitudinal collection of mHealth responses can be thought of as a single high-dimensional observation. We show how the GP is flexible enough to capture trends in individual trajectories even with the challenges associated with high-dimensional data. We also demonstrate how basis splines can be used to effectively capture nonlinear trends in the mean function of the GP. The high-dimension and ordinal nature of the data often make sampling from the posterior distribution in a Bayesian setting too slow to be practical. We show that using a Hilbert approximation for the GP trajectories can facilitate efficient sampling. We apply these methods to a longitudinal study that monitored college students' self-esteem.