PCA score regression: the art of losing power

2026-05-22

AI Summary

This study addresses critical limitations of regression on principal component scores (RPCS) in associating functional data with scalar covariates, including loss of statistical power, poor control of Type I error, and lack of valid inference. Through a systematic comparison with function-on-scalar regression (FoSR), the work quantifies for the first time the mechanism underlying RPCS’s power loss, demonstrating its dependence on the correlation between principal components and the true effect function. The authors further establish that existing RPCS approaches generally fail to yield reliable statistical inference. Extensive simulations and an analysis of minute-level accelerometer data from NHANES confirm that FoSR consistently outperforms RPCS in terms of power, Type I error control, and estimation accuracy, thereby establishing FoSR as a more robust and trustworthy alternative for functional data analysis.

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).

Problem

• PCA score regression
• power loss
• Function on Scalar Regression
• inference validity
• multiple testing

Innovation

• Function on Scalar Regression
• Principal Component Score Regression
• Statistical Power
• Multiplicity Correction
• Functional Data Analysis