Testing Correlation in a Three-Level Model

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 ⊗ ψ1 ⊗ ψ2, where Σ is an arbitrary positive definite covariance matrix, and ψ1 and ψ2 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