Testing of a Structures Covariance Matrix for Three-Level Repeated Measures Data.

This paper considers the problem of estimating, and testing for, a Kronecker product covariance structure of three-level (multiple time points (p), multiple sites (u), and multiple response variables (q)) multivariate data. Testing of such covariance structures is potentially important when not enough samples are available to estimate the unstructures variance-covariance matrix. This hypothesis procedure not only can test the hypothesis on three-level multivariate data, but also can test the hypotheses on two-level multivariate data as special cases. We provide the maximum likelihood estimates of the unknown population parameters. The test is implemented with a real data set.