arXiv subjects

Nidhi Pai

Publications and source records attributed to Nidhi Pai.

3 recordsLinked to original sources

arXiv2026

Sparse Longitudinal Functional Principal Component Analysis for Episodic Ambulatory Behavioral Assessments

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.

stat.ME↗

arXiv2026

PCA score regression: the art of losing power

The regression of principal component scores (RPCS) on covariates is a widely used analytic approach to detect and test for associations between functional measurements and study participant characteristics. Here we show that: (1) RPCS loses power relative to Function on Scalar Regression (FoSR); (2) the amount of power loss depends on the correlation between the PCs and the true effect; (3) if not corrected for multiplicity, RPCS has inflated $α$-level; and (4) current RPCS methods do not provide valid inference for the true effect. In contrast, we show that Function on Scalar Regression (FoSR) can avoid these problems using a particular combination of modeling tools. We validate these theoretical findings through extensive simulations and illustrate their practical implications using minute-level accelerometry data from the National Health and Nutrition Examination Survey (NHANES).

stat.ME↗

arXiv2026

Quantifying Time-Varying Physical Activity Intervention Effects via Functional Regression

Physical activity (PA) intervention studies often collect repeated intensity measurements over long observation periods. Quantifying the variation in intervention effects over the study period is critical to evaluating and improving intervention strategies, yet many analyses reduce PA data into scalar summary measures, resulting in limited insights. We propose a functional regression framework, which captures time-varying intervention effects by modeling the entire PA trajectory as a functional observation. From both methodological and practical perspectives, we demonstrate the advantages of function-on-scalar regression (FoSR) over the traditional two-step approach of applying functional principal components analysis (FPCA) followed by regressing scores on covariates. The FoSR is further extended to a function-on-function regression (FoFR) for studying the association of PA across time periods. Methods are applied to daily step counts from the Social incentives to Encourage Physical Activity and Understand Predictors (STEP UP) study, revealing distinct and highly interpretable time-varying effects of three intervention strategies on PA and differences in their sustainability. Our case study highlights the feasibility of functional data analysis techniques for uncovering novel insights in intervention studies with high-dimensional endpoints.

stat.AP↗