title: A comparison of likelihood ratio tests and Rao's score test for three separable covariance matrix structures.
abstract: The problem of testing the separability of a covariance matrix against an unstructured variance-covariance matrix is studied in the context of multivariate repeated measures data using Rao's score test (RST). The RST statistic is developed with the first component of the separable structure as a first-order autoregressive (AR(1)) correlation matrix or an unstructured (UN) covariance matrix under the assumption of multivariate normality. It is shown that the distribution of the RST statistic under the null hypothesis of any separability does not depend on the true values of the mean or the unstructured components of the separable structure. A significant advantage of the RST is that it can be performed for small samples, even smaller than the dimension of the data, where the likelihood ratio test (LRT) cannot be used, and it outperforms the standard LRT in a number of contexts. Monte Carlo simulations are then used to study the comparative behavior of the null distribution of the RST statistic, as well as that of the LRT statistic, in terms of sample size considerations, and for the estimation of the empirical percentiles. Our findings are compared with existing results where the first component of the separable structure is a compound symmetry (CS) correlation matrix. It is also shown by simulations that the empirical null distribution of the RST statistic converges faster than the empirical null distribution of the LRT statistic to the limiting χ2distribution. The tests are implemented on a real dataset from medical studies.
authors: Institute of Mathematics, Poznań University of Technology, Piotrowo 3A, 60-965, Poznań, Poland.
authors: Katarzyna
authors: K
authors: Filipiak
authors: Institute of Mathematics, Faculty of Science, P. J. Šafárik University, 040 01, Košice, Slovakia.
authors: Daniel
authors: D
authors: Klein
authors: Department of Management Science and Statistics, The University of Texas at San Antonio, One UTSA Circle, San Antonio, TX, 78249, USA.
authors: Anuradha
authors: A
authors: Roy
mesh_terms: D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D016013:Likelihood Functions; D015233:Models, Statistical; D009010:Monte Carlo Method
keywords: Empirical null distribution; Likelihood ratio test; Maximum likelihood estimates; Rao’s score test; Separable covariance structure