title: An Optimal Test for Variance Components of Multivariate Mixed-Effects Linear Models.
abstract: In this article we derive an optimal test for testing the significance of covariance matrices of random-effects of two multivariate mixed-effects linear models. We compute the power of this newly derived test via simulation for various alternative hypotheses in a bivariate set up for unbalanced designs and observe that power responds sharply when sample size and alternative hypotheses are changed. For some balanced designs we compare power of the optimal test to that of the likelihood ratio test via simulation, and find that the proposed test has greater power than the likelihood ratio test. The results are illustrated using real data on human growth. Other relevant applications of the model are highlighted.
authors.affiliation: Department of Biostatistics and The Osteopathic Research Center, UNT Health Science Center.
authors.forename: Subhash
authors.initials: S
authors.lastname: Aryal
authors.affiliation: Departments of Biostatistics and Psychiatry, University of Illinois at Chicago.
authors.forename: Dulal K
authors.initials: DK
authors.lastname: Bhaumik
authors.affiliation: Department of Statistics, University of Maryland, Baltimore County.
authors.forename: Thomas
authors.initials: T
authors.lastname: Mathew
authors.affiliation: Center for Health Statistics, University of Chicago.
authors.forename: Robert D
authors.initials: RD
authors.lastname: Gibbons
keywords: Likelihood ratio test (LRT); growth curve models; locally best invariant test (LBI); unbalanced designs