Testing Correlation in a Three-Level Model

Anna Szczepańska-Álvarez (), Adolfo Álvarez (), Artur Szwengiel () and Dietrich Rosen ()
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Anna Szczepańska-Álvarez: Poznań University of Life Sciences
Adolfo Álvarez: O-I Business Service Center
Artur Szwengiel: Poznań University of Life Sciences
Dietrich Rosen: Linköping University

Journal of Agricultural, Biological and Environmental Statistics, 2024, vol. 29, issue 2, No 4, 257-276

Abstract: Abstract 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 $${\varvec{\Sigma }} \otimes {\varvec{\Psi }}_1 \otimes {\varvec{\Psi }}_2$$ Σ ⊗ Ψ 1 ⊗ Ψ 2 , where $${\varvec{\Sigma }}$$ Σ is an arbitrary positive definite covariance matrix, and $${\varvec{\Psi }}_1$$ Ψ 1 and $${\varvec{\Psi }}_2$$ Ψ 2 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.

Keywords: Three-level model; Rao’s score test; Maximum likelihood estimation; Independence test; Factorial design; Kronecker product structured covariance matrix (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13253-023-00575-w

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