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- Title
Testing Correlation in a Three-Level Model.
- Authors
Szczepańska-Álvarez, Anna; Álvarez, Adolfo; Szwengiel, Artur; von Rosen, Dietrich
- 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.
- Subjects
COVARIANCE matrices; SYMMETRIC matrices; KRONECKER products; TEST scoring; MAXIMUM likelihood statistics
- Publication
Journal of Agricultural, Biological & Environmental Statistics (JABES), 2024, Vol 29, Issue 2, p257
- ISSN
1085-7117
- Publication type
Article
- DOI
10.1007/s13253-023-00575-w