PCA score regression: the art of losing power
Abstract
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).
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BibTeX
@misc{lu2026score,
title = {{PCA score regression: the art of losing power}},
author = {Yu Lu and Nidhi Pai and Erjia Cui and Ciprian Crainiceanu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.24118},
eprint = {2605.24118},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.24118},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - PCA score regression: the art of losing power
AU - Yu Lu
AU - Nidhi Pai
AU - Erjia Cui
AU - Ciprian Crainiceanu
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2605.24118
UR - https://arxiv.org/abs/2605.24118
AB - 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).
ER -