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Testing Correlation in a Three-Level Model

Author

Listed:
  • 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)

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.

Suggested Citation

  • Anna Szczepańska-Álvarez & Adolfo Álvarez & Artur Szwengiel & Dietrich Rosen, 2024. "Testing Correlation in a Three-Level Model," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 29(2), pages 257-276, June.
    • Handle: RePEc:spr:jagbes:v:29:y:2024:i:2:d:10.1007_s13253-023-00575-w
    DOI: 10.1007/s13253-023-00575-w
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    References listed on IDEAS

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    1. Soloveychik, I. & Trushin, D., 2016. "Gaussian and robust Kronecker product covariance estimation: Existence and uniqueness," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 92-113.
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    3. L. Rob Verdooren, 2020. "History of the Statistical Design of Agricultural Experiments," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(4), pages 457-486, December.
    4. Roy, Anuradha & Leiva, Ricardo, 2008. "Likelihood ratio tests for triply multivariate data with structured correlation on spatial repeated measurements," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1971-1980, September.
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