{
  "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).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.24118",
  "author_total": 4,
  "authors": [
    {
      "name": "Yu Lu"
    },
    {
      "name": "Nidhi Pai"
    },
    {
      "name": "Erjia Cui"
    },
    {
      "name": "Ciprian Crainiceanu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0hv0tj28mwt1p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.24118",
  "fulltext_url": null,
  "id": "0hv0tj28mwt1p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.24118",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "openalex",
      "2613|Statistical Methods and Applications"
    ]
  ],
  "openalex": "W7162403069",
  "pdf_url": "https://arxiv.org/pdf/2605.24118",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0hv0tj28mwt1p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:43Z",
      "native_id": "2605.24118",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.24118"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "PCA score regression: the art of losing power",
  "title_text": "PCA score regression: the art of losing power",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:43Z",
  "url": "https://research.draconitic.com/paper/0hv0tj28mwt1p",
  "venue": "arXiv",
  "versions": []
}