A Continuous-Time Dynamic Factor Model for Intensive Longitudinal Data Arising from Mobile Health Studies

TL;DR

This paper introduces a continuous-time dynamic factor model for analyzing intensive longitudinal data from mobile health studies, capturing short-term and long-term emotional dynamics to understand behavior change.

Contribution

It develops a novel model combining a factor analysis with an Ornstein-Uhlenbeck process, providing a new way to analyze complex ILD in mobile health research.

Findings

Successfully summarized 18 emotions into two latent processes.

Interpreted latent processes as positive and negative affect.

Applied model to smoking cessation data, revealing psychological constructs.

Abstract

Intensive longitudinal data (ILD) collected in mobile health (mHealth) studies contain rich information on multiple outcomes measured frequently over time that have the potential to capture short-term and long-term dynamics. Motivated by an mHealth study of smoking cessation in which participants self-report the intensity of many emotions multiple times per day, we describe a dynamic factor model that summarizes the ILD as a low-dimensional, interpretable latent process. This model consists of two submodels: (i) a measurement submodel--a factor model--that summarizes the multivariate longitudinal outcome as lower-dimensional latent variables and (ii) a structural submodel--an Ornstein-Uhlenbeck (OU) stochastic process--that captures the temporal dynamics of the multivariate latent process in continuous time. We derive a closed-form likelihood for the marginal distribution of the outcome and the computationally-simpler sparse precision matrix for the OU process. We propose a block coordinate descent algorithm for estimation. Finally, we apply our method to the mHealth data to summarize the dynamics of 18 different emotions as two latent processes. These latent processes are interpreted by behavioral scientists as the psychological constructs of positive and negative affect and are key in understanding vulnerability to lapsing back to tobacco use among smokers attempting to quit.