Multivariate Functional Principal Component Analysis for Mixed-Type mHealth Data: An Application to Mood Disorders

TL;DR

This paper introduces M^2FPCA, a novel multivariate functional principal component analysis method for mixed-type mHealth data, enabling the extraction of interpretable digital biomarkers for mood disorder analysis.

Contribution

The paper develops a semiparametric Gaussian copula-based M^2FPCA method for mixed-type data, including continuous, ordinal, and binary variables, with applications to mood disorder research.

Findings

Identifies shared time-of-day patterns across multiple health domains.

Effectively stratifies mood disorder subtypes using latent principal components.

Demonstrates competitive performance in simulation studies.

Abstract

Modern mobile health (mHealth) assessment combines self-reported measures of participants' health experiences with passively collected health behavior data throughout the day. These data are collected across multiple measurement scales, including continuous (physical activity), truncated (pain), ordinal (mood), and binary (daily life events). When indexed by time of day and stacked across assessment domains, these data structures can be treated as multivariate functional data comprising continuous, truncated, ordinal, and binary variables. Motivated by these applications, we propose a multivariate functional principal component analysis for mixed-type data ($M^2$FPCA). The approach is based on a semiparametric Gaussian copula model and assumes that the observed data arise from an underlying multivariate generalized latent nonparanormal functional process. Latent temporal and inter-variable dependence are estimated semiparametrically through Kendall's tau bridging method. Two covariance estimation procedures are developed: a fully multivariate block-wise estimator and a computationally efficient alternative based on partial separability that assumes shared principal components across domains. The proposed method yields interpretable latent functional principal component scores that can serve as participant-specific digital biomarkers. Simulation studies demonstrate the method's competitive performance under various complex dependence structures. The method is applied to mHealth data from 307 participants in the National Institute of Mental Health Family Study of Mood and Affective Spectrum Disorders. Our approach identifies time-of-day patterns shared across mood, anxiety, energy, and physical activity that meaningfully stratify mood disorder subtypes.