On implementation of a test for Kronecker product covariance structure for multivariate repeated measures data. (English) Zbl 1248.62092

Summary: Under the assumption of multivariate normality the likelihood ratio test is derived to test a hypothesis for Kronecker product structure on a covariance matrix in the context of multivariate repeated measures data. Although the proposed hypothesis testing can be computationally performed by indirect use of Proc Mixed of SAS, the Proc Mixed algorithm often fails to converge. We provide an alternative algorithm. The algorithm is illustrated with two real data sets. A simulation study is also conducted for the purpose of sample size consideration.


62H15 Hypothesis testing in multivariate analysis
65C60 Computational problems in statistics (MSC2010)


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[1] Boik, J.B., Scheffe’s mixed model for multivariate repeated measures: a relative efficiency evaluation, Communications in statistics-theory and methods, 20, 1233-1255, (1991) · Zbl 0751.62027
[2] Chaganty, N.R.; Naik, D.N., Analysis of multivariate longitudinal data using quasi-least squares, Journal of statistical planning and inference, 103, 421-436, (2002) · Zbl 1044.62059
[3] Galecki, A.T., General class of covariance structures for two or more repeated factors in longitudinal data analysis, Communications in statistics-theory and methods, 22, 3105-3120, (1994) · Zbl 0875.62274
[4] Khattree, R.; Naik, D.N., Applied multivariate statistics with SAS software, (1999), Wiley New York, NY
[5] Lu, N.; Zimmerman, D.L., The likelihood ratio test for a separable covariance matrix, Statistics and probability letters, 73, 449-457, (2005) · Zbl 1071.62052
[6] Naik, D.N.; Rao, S.S., Analysis of multivariate repeated measures data with a Kronecker product structured covariance matrix, Journal of applied statistics, 28, 1, 91-105, (2001) · Zbl 0991.62038
[7] A. Roy, Some contributions to discrimination and classification with repeated measures data with special emphasis on biomedical applications, Ph.D. Dissertation. Oakland University, Rochester, MI (unpublished)
[8] A. Roy, A New classification rule for incomplete doubly multivariate data using mixed effects model with performance comparisons on the imputed data, Statistics in Medicine (in press)
[9] Roy, A.; Khattree, R., Tests for Mean and covariance structures relevant in repeated measures based discriminant analysis, Journal of applied statistical sciences, 12, 2, 91-103, (2003) · Zbl 1064.62067
[10] Roy, A.; Khattree, R., On discrimination and classification with multivariate repeated measures data, Journal of statistical planning and inference, 134, 2, 462-485, (2005) · Zbl 1066.62069
[11] SAS Institute Inc, SAS/STAT user’s guide version 9, (2004), SAS Institute Inc. Cary, NC
[12] Self, S.G.; Liang, K., Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions, Journal of the American statistical association, 82, 398, 605-610, (1987) · Zbl 0639.62020
[13] Shults, J., Modeling the correlation structure of data that have multiple levels of association, Communications in statistics-theory and methods, 29, 1005-1015, (2000) · Zbl 1019.62058
[14] Shults, J.; Morrow, A.L., The use of quasi-least squares to adjust for two levels of correlation, Biometrics, 58, 521-530, (2002) · Zbl 1210.62074
[15] Shults, J.; Whitt, M.C.; Kumanyika, S., Analysis of data with multiple sources of correlation in the framework of generalized estimating equations, Statistics in medicine, 23, 3209-3226, (2004)
[16] Timm, N.H., Multivariate analysis of variance of repeated measurements, (), 41-87
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