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

2026-03-11

AI Summary

This study addresses the analysis of multimodal mobile health time-series data comprising continuous, truncated, ordinal, and binary variables by proposing Mixed-type Multivariate Functional Principal Component Analysis (M²FPCA). Built upon a semiparametric Gaussian copula framework, M²FPCA assumes observations arise from an underlying multivariate generalized nonparametric normal functional process. It employs Kendall’s tau bridging to estimate both cross-variable and temporal dependence structures and incorporates a partial separability assumption on the covariance operator to enhance computational efficiency. As the first extension of multivariate functional principal component analysis to mixed data types, M²FPCA yields interpretable latent digital biomarkers. Applied to data from 307 participants, it successfully identifies shared diurnal patterns across mood, anxiety, energy, and physical activity, effectively differentiating subtypes of mood disorders; simulation studies further confirm its superior performance under complex dependency structures.

Technology Category

• Machine Learning: Multimodal Learning
• Computer Vision: Multi-modal Vision
• Data Mining & Knowledge Management: Mining of Visual, Multimedia & Multimodal Data

Application Category

• Web Mining and Content Analysis: Mining multimedia, multimodal, multilingual, cross-lingual Web data
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience

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.

Problem

• multivariate functional data
• mixed-type data
• mHealth
• principal component analysis
• mood disorders

Innovation

• Multivariate Functional PCA
• Mixed-type Data
• Gaussian Copula
• Nonparanormal Process
• Digital Biomarkers