Exploratory Hidden Markov Factor Models for Longitudinal Mobile Health Data: Application to Adverse Posttraumatic Neuropsychiatric Sequelae

Adverse posttraumatic neuropsychiatric sequelae (APNS) are common among veterans and millions of Americans after traumatic events and cause tremendous burdens for trauma survivors and society. Many studies have been conducted to investigate the challenges in diagnosing and treating APNS symptoms. However, progress has been limited by the subjective nature of traditional measures. This study is motivated by the objective mobile device data collected from the Advancing Understanding of RecOvery afteR traumA (AURORA) study. We develop both discrete-time and continuous-time exploratory hidden Markov factor models to model the dynamic psychological conditions of individuals with either regular or irregular measurements. The proposed models extend the conventional hidden Markov models to allow high-dimensional data and feature-based nonhomogeneous transition probability between hidden psychological states. To find the maximum likelihood estimates, we develop a Stabilized Expectation-Maximization algorithm with Initialization Strategies (SEMIS). Simulation studies with synthetic data are carried out to assess the performance of parameter estimation and model selection. Finally, an application to the AURORA data is conducted, which captures the relationships between heart rate variability, activity, and APNS consistent with existing literature.