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Research article2024Peer reviewedOpen access

Testing Correlation in a Three-Level Model

Szczepanska-Alvarez, Anna; Alvarez, Adolfo; Szwengiel, Artur; von Rosen, Dietrich


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 Sigma circle times psi(1) circle times psi(2), where Sigma is an arbitrary positive definite covariance matrix, and psi(1) and psi(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.


Three-level model; Rao's score test; Maximum likelihood estimation; Independence test; Factorial design; Kronecker product structured covariance matrix

Published in

Journal of Agricultural, Biological, and Environmental Statistics
2024, Volume: 29, number: 2, pages: 257–276
Publisher: SPRINGER

    UKÄ Subject classification

    Probability Theory and Statistics

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