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Estimation and Sufficiency Under the Mixed Effects Extended Growth Curve Model with Compound Symmetry Covariance Structure

cris.virtual.author-orcid0000-0001-5473-3419
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dc.abstract.enAn extended growth curve model with fixed and random effects is considered. Under the assumption of multivariate normality, the maximum likelihood estimators of the fixed effects and the dispersion matrix are determined in a model with random nuisance param-eters, both without any assumption on the covariance structure and under the assumption of compound symmetry. For this purpose, rules for differentiation of symmetric matrices are applied. Furthermore, when the experiments are designed in balanced complete blocks, particular symmetric matrices appear in the likelihood equations, allowing closed-form expressions for the estimators. It is also shown that the vector of sufficient statistics for the fixed effects extended growth curve model is also sufficient for the model with random nuisance parameters. The presented results are illustrated using a real data example.
dc.affiliationWydział Rolnictwa, Ogrodnictwa i Biotechnologii
dc.affiliation.instituteKatedra Metod Matematycznych i Statystycznych
dc.contributor.authorFilipiak, Katarzyna
dc.contributor.authorMarkiewicz, Augustyn
dc.contributor.authorKrajewski, Paweł
dc.contributor.authorĆwiek-Kupczyńska, Hanna
dc.date.access2025-11-12
dc.date.accessioned2025-11-12T12:24:23Z
dc.date.available2025-11-12T12:24:23Z
dc.date.copyright2025-11-07
dc.date.issued2025
dc.description.abstract<jats:p>An extended growth curve model with fixed and random effects is considered. Under the assumption of multivariate normality, the maximum likelihood estimators of the fixed effects and the dispersion matrix are determined in a model with random nuisance parameters, both without any assumption on the covariance structure and under the assumption of compound symmetry. For this purpose, rules for differentiation of symmetric matrices are applied. Furthermore, when the experiments are designed in balanced complete blocks, particular symmetric matrices appear in the likelihood equations, allowing closed-form expressions for the estimators. It is also shown that the vector of sufficient statistics for the fixed effects extended growth curve model is also sufficient for the model with random nuisance parameters. The presented results are illustrated using a real data example.</jats:p>
dc.description.accesstimeat_publication
dc.description.bibliographyil., bibliogr.
dc.description.financepublication_nocost
dc.description.financecost0,00
dc.description.if2,2
dc.description.number11
dc.description.points70
dc.description.versionfinal_published
dc.description.volume17
dc.identifier.doi10.3390/sym17111901
dc.identifier.issn2073-8994
dc.identifier.urihttps://sciencerep.up.poznan.pl/handle/item/5846
dc.identifier.weblinkhttps://www.mdpi.com/2073-8994/17/11/1901
dc.languageen
dc.relation.ispartofSymmetry
dc.relation.pagesart. 1901
dc.rightsCC-BY
dc.sciencecloudnosend
dc.share.typeOPEN_JOURNAL
dc.subject.enextended growth curve model
dc.subject.enfixed effects
dc.subject.enrandom effects
dc.subject.endispersion matrix
dc.subject.enestimation
dc.subject.ensufficiency
dc.subject.encompound symmetry
dc.subject.enbalanced incomplete block design
dc.titleEstimation and Sufficiency Under the Mixed Effects Extended Growth Curve Model with Compound Symmetry Covariance Structure
dc.title.volumeSpecial Issue Symmetrical and Asymmetrical Distributions in Statistics and Data Science II
dc.typeJournalArticle
dspace.entity.typePublication
oaire.citation.issue11
oaire.citation.volume17