Sparse Longitudinal Functional Principal Component Analysis for Episodic Ambulatory Behavioral Assessments

2026-06-06

AI Summary

This study addresses the challenge of analyzing sparsely observed keystroke timing trajectories from mobile typing to support real-time behavioral interventions for mental fatigue. The authors propose a sparse longitudinal functional principal component analysis method that extracts both inter-individual and day-to-day variation patterns. Their approach innovatively reformulates covariance structure estimation as a spline regression problem with structured penalties, enabling information sharing across time points within the functional domain and allowing simultaneous estimation and smoothing of multiple covariance components. This effectively handles sparse longitudinal functional data. Simulation studies demonstrate that the method accurately estimates eigenfunctions and yields well-calibrated predictions of latent curves, outperforming or matching existing approaches. Applied to real-world data, it uncovers previously undetected yet interpretable individual- and day-level patterns, providing a foundation for personalized intervention strategies.

Abstract

Accurately monitoring mental fatigue is critical for improving workplace safety and productivity. A recent study examined unobtrusively collected smartphone typing speed as a potential ambulatory proxy assessment of mental fatigue using data from the Intern Health Study (IHS). While population-level average typing speed patterns were found to be consistent with validated measures of mental fatigue, how these trajectories vary across participants and days may inform opportune moments for just-in-time interventions and remains an open question. Treating typing speed trajectories as sparsely observed functional data, we propose a novel sparse longitudinal functional principal component analysis (sparse LFPCA) method for decomposing variability and predicting individual curves. Specifically, sparse data are accommodated by casting covariance estimation as a structured penalized spline regression problem, enabling simultaneous estimation and smoothing of multiple covariance components while borrowing information across locations in the functional domain. Simulations show that sparse LFPCA (1) accurately estimates eigenfunctions and generates reasonable predictions for underlying curves, and (2) achieves similar or superior performance compared to existing alternatives. Our analysis of typing speed data collected from IHS reveals new and interpretable participant- and day-level patterns not captured by previous analyses and can be used to tailor behavioral interventions.

Problem

• sparse longitudinal data
• functional principal component analysis
• mental fatigue
• ambulatory assessment
• typing speed

Innovation

• sparse longitudinal functional data
• functional principal component analysis
• penalized spline regression
• covariance smoothing
• just-in-time intervention