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arXiv · 2605.24118

PCA score regression: the art of losing power

Yu Lu·Nidhi Pai·Erjia Cui·Ciprian Crainiceanu
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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 $\alpha$-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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Yu Lu, Nidhi Pai, Erjia Cui, Ciprian Crainiceanu. 2026-05-22. PCA score regression: the art of losing power. https://arxiv.org/abs/2605.24118

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