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.

翻译：准确监测精神疲劳对提升工作场所安全性与生产力至关重要。近期一项研究利用实习医生健康研究数据，将非侵入性采集的智能手机打字速度作为精神疲劳的潜在动态替代指标。尽管群体层面的平均打字速度模式与已验证的精神疲劳测量结果一致，但这些轨迹在不同参与者和日期间的变化可能为即时干预提供最佳时机，目前仍是一个未解问题。将打字速度轨迹视为稀疏观测的函数数据，本文提出一种新型稀疏纵向函数主成分分析方法，用于分解变异性并预测个体曲线。具体而言，通过将协方差估计构建为结构化惩罚样条回归问题来处理稀疏数据，该方法可在函数域内跨位置借用信息的同时，实现对多个协方差成分的同步估计与平滑。模拟实验表明，稀疏LFPCA能够（1）准确估计本征函数并生成合理的基础曲线预测，（2）在性能上达到或优于现有替代方法。我们对IHS收集的打字速度数据进行分析，揭示了既往分析未捕捉到的、可解释的新参与者水平与日水平模式，并为定制化行为干预提供依据。