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Modelling nuisance parameters in linear models: Formal and empirical comparisons between the two-way Anova and Ancova — arXiv:2609.32085

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.32085
License (as archived): CC0-1.0
Archived: 2026-10-07T23:03:24.793Z
SHA-256 of the archived text: 287953188115b9b4dc31c189b1506f2fce8cf74d8a34768768e1ada6e952e5a8
Stable URL of this page: https://metraipolis.com/documento/dc_27e2b8a75fa7

How to cite

Modelling nuisance parameters in linear models: Formal and empirical comparisons between the two-way Anova and Ancova — arXiv:2609.32085 — arXiv (en), https://arxiv.org/abs/2609.32085 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_27e2b8a75fa7 (Metraipolis archive dc_27e2b8a75fa7, sha256 287953188115b9b4dc31c189b1506f2fce8cf74d8a34768768e1ada6e952e5a8)

BibTeX

@misc{dc27e2b8a75fa7,
  title = {Modelling nuisance parameters in linear models: Formal and empirical comparisons between the two-way Anova and Ancova — arXiv:2609.32085},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.32085},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_27e2b8a75fa7; sha256 287953188115b9b4dc31c189b1506f2fce8cf74d8a34768768e1ada6e952e5a8},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.32085. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

The analysis of experimental or observational data often requires controlling for the effects of variables of secondary interest. Two common approaches to account for such parameters are grouping experimental or observational units into homogeneous groups (blocking), and observing quantitative variables on each one of them (covariance analysis). Often, both can be used and; therefore, comparing their performance poses a research question. Specifically, under randomized complete block designs where the blocks are defined by quantitative variables, there is interest in comparing the two-way Anova (TWA) with analysis of covariance (Ancova) models. Motivated by real-life problems coming from statistical consulting, we compared the performance of linear models considering block effects and those considering covariate effects from analytical and empirical perspectives. Models assumed Gaussian errors and included the effects of T treatments. The formal comparison relied on the theory of orthogonal projections and vector spaces under containment relationships of column spaces of the design matrices induced by conditions on the experimental design or data structure. We found asymptotic and small-sample conditions for the TWA to be at least as precise as the Ancova, as well as for these models to be equivalent. As to the empirical perspective, models were compared through a simulation study motivated by agronomical experiments. The results suggested that when the covariates show complex heterogeneity patterns, the Ancova outperforms the TWA with blocks defined by traditional approaches in terms of precision of location parameters, but not in hypothesis testing accuracy.

Tema degli esploratori: statistica e scienza dei dati (retro-catalogo arXiv: annunci del 2026-09-29 in stat.ME).
Categorie arXiv: Methodology (stat.ME).
Pagina del lavoro: https://arxiv.org/abs/2609.32085 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-07T22:41:46.578Z dalla pagina https://arxiv.org/catchup/stat.ME/2026-09-29?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).