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Testing Correlation in a Three-Level Model

cris.lastimport.scopus2025-10-23T06:58:10Z
cris.virtual.author-orcid0000-0001-9428-8938
cris.virtual.author-orcid0000-0003-4570-7221
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cris.virtualsource.author-orciddafe00c4-99bb-45f5-8886-d6f261ff6cb3
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dc.abstract.enIn this paper, we present a statistical approach to evaluate the relationship between variables observed in a two-factors experiment. We consider a three-level model with covariance structure Σ ⊗ ψ1 ⊗ ψ2, where Σ is an arbitrary positive definite covariance matrix, and ψ1 and ψ2 are both correlation matrices with a compound symmetric structure corresponding to two different factors. The Rao’s score test is used to test the hypotheses that observations grouped by one or two factors are uncorrelated. We analyze a fermentation process to illustrate the results. Supplementary materials accompanying this paper appear online
dc.affiliationWydział Rolnictwa, Ogrodnictwa i Biotechnologii
dc.affiliationWydział Nauk o Żywności i Żywieniu
dc.affiliation.instituteKatedra Metod Matematycznych i Statystycznych
dc.affiliation.instituteKatedra Technologii Żywności Pochodzenia Roślinnego
dc.contributor.authorSzczepańska-Alvarez, Anna
dc.contributor.authorÁlvarez, Adolfo
dc.contributor.authorSzwengiel, Artur
dc.contributor.authorvon Rosen, Dietrich
dc.date.access2025-05-07
dc.date.accessioned2025-08-26T12:15:55Z
dc.date.available2025-08-26T12:15:55Z
dc.date.copyright2023-11
dc.date.issued2023
dc.description.abstract<jats:title>Abstract</jats:title><jats:p>In this paper, we present a statistical approach to evaluate the relationship between variables observed in a two-factors experiment. We consider a three-level model with covariance structure <jats:inline-formula><jats:alternatives><jats:tex-math>$${\varvec{\Sigma }} \otimes {\varvec{\Psi }}_1 \otimes {\varvec{\Psi }}_2$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:mi>Σ</mml:mi> </mml:mrow> <mml:mo>⊗</mml:mo> <mml:msub> <mml:mrow> <mml:mi>Ψ</mml:mi> </mml:mrow> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>⊗</mml:mo> <mml:msub> <mml:mrow> <mml:mi>Ψ</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula>, where <jats:inline-formula><jats:alternatives><jats:tex-math>$${\varvec{\Sigma }}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Σ</mml:mi> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> is an arbitrary positive definite covariance matrix, and <jats:inline-formula><jats:alternatives><jats:tex-math>$${\varvec{\Psi }}_1$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>Ψ</mml:mi> </mml:mrow> <mml:mn>1</mml:mn> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:tex-math>$${\varvec{\Psi }}_2$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>Ψ</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula> are both correlation matrices with a compound symmetric structure corresponding to two different factors. The Rao’s score test is used to test the hypotheses that observations grouped by one or two factors are uncorrelated. We analyze a fermentation process to illustrate the results. Supplementary materials accompanying this paper appear online. </jats:p>
dc.description.accesstimeat_publication
dc.description.bibliographyil., bibliogr.
dc.description.financepublication_nocost
dc.description.financecost0,00
dc.description.if1,4
dc.description.number2 June 2024
dc.description.points70
dc.description.versionfinal_published
dc.description.volume29
dc.identifier.doi10.1007/s13253-023-00575-w
dc.identifier.eissn1537-2693
dc.identifier.issn1085-7117
dc.identifier.urihttps://sciencerep.up.poznan.pl/handle/item/4388
dc.identifier.weblinkhttps://link.springer.com/article/10.1007/s13253-023-00575-w
dc.languageen
dc.relation.ispartofJournal of Agricultural, Biological, and Environmental Statistics
dc.relation.pages257-276
dc.rightsCC-BY
dc.sciencecloudnosend
dc.share.typeOTHER
dc.subject.enThree-level model
dc.subject.enRao’s score test
dc.subject.enMaximum likelihood estimation
dc.subject.enIndependence test
dc.subject.enFactorial design
dc.subject.enKronecker product structured covariance matrix
dc.titleTesting Correlation in a Three-Level Model
dc.typeJournalArticle
dspace.entity.typePublication
oaire.citation.issue2
oaire.citation.volume29