Testing Correlation in a Three-Level Model

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 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.

Keywords

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

SLU Authors

• von Rosen, Dietrich

  • Department of Energy and Technology, Swedish University of Agricultural Sciences
    

UKÄ Subject classification

Probability Theory and Statistics

Publication identifier

• DOI: https://doi.org/10.1007/s13253-023-00575-w

Permanent link to this page (URI)

https://res.slu.se/id/publ/127701