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).
| Subjects: | Methodology (stat.ME) |
| Cite as: | arXiv:2605.24118 [stat.ME] |
| (or arXiv:2605.24118v1 [stat.ME] for this version) | |
| https://doi.org/10.48550/arXiv.2605.24118 arXiv-issued DOI via DataCite (pending registration) |
From: Yu Lu [view email]
[v1]
Fri, 22 May 2026 18:24:46 UTC (8,933 KB)
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