1. Testing Correlation in a Three-Level Model.
- Author
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Szczepańska-Álvarez, Anna, Álvarez, Adolfo, Szwengiel, Artur, and von Rosen, Dietrich
- Subjects
- *
COVARIANCE matrices , *SYMMETRIC matrices , *KRONECKER products , *TEST scoring , *MAXIMUM likelihood statistics - 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 Σ ⊗ Ψ 1 ⊗ Ψ 2 , where Σ is an arbitrary positive definite covariance matrix, and Ψ 1 and 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. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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