Analysis of multivariate repeated measures data using a MANOVA model and principal components
Mirosław Krzysko ; Tadeusz Smiałowski ; Waldemar Wołynski
Biometrical Letters, Tome 51 (2014), p. 103-114 / Harvested from The Polish Digital Mathematics Library

In this paper we consider a set of T repeated measurements on p characteristics on each of n individuals. The n individuals themselves may be divided and randomly assigned to K groups. These data are analyzed using a mixed effect MANOVA model, assuming that the data on an individual have a covariance matrix which is a Kronecker product of two positive definite matrices. Results are illustrated on a data set obtained from experiments with varieties of winter rye.

Publié le : 2014-01-01
EUDML-ID : urn:eudml:doc:268881
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     author = {Miros\l aw Krzysko and Tadeusz Smia\l owski and Waldemar Wo\l ynski},
     title = {Analysis of multivariate repeated measures data using a MANOVA model and principal components},
     journal = {Biometrical Letters},
     volume = {51},
     year = {2014},
     pages = {103-114},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_bile-2014-0008}
}
Mirosław Krzysko; Tadeusz Smiałowski; Waldemar Wołynski. Analysis of multivariate repeated measures data using a MANOVA model and principal components. Biometrical Letters, Tome 51 (2014) pp. 103-114. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_bile-2014-0008/

Arnold S. F. (1979): Linear models with exchangeably distributed errors. Journal of American Statistical Association 74: 194-199.[Crossref] | Zbl 0431.62044

Deregowski K., Krzysko M. (2009): Principal component analysis in the case of multivariate repeated measures data. Biometrical Letters 46: 163-172.

Florek K., Łukaszewicz J., Perkal J., Steinhaus H. and Zubrzycki S. (1951): Sur la liaison et la division des points d’un ensemble fini. Colloquium Mathematicum 2: 282-285.

Geisser S., Greenhouse S. (1958): An extension of Box’s results on the use of the F distribution in multivariate analysis. Annals of Mathematical Statistics 29: 885-891.[Crossref] | Zbl 0090.35804

Giri N. C. (1996): Multivariate Statistical Analysis. Marcel Dekker, Inc., New York. | Zbl 0846.62039

Khatri C. G. (1962): Conditions for Wishartness and independence of second degree polynomials in normal vector. Annals of Mathematical Statistics 33: 1002-1007.[Crossref] | Zbl 0108.32405

Kruskal J. B. (1956): On the shortest spanning subtree of a graph and the traveling salesman problem. Proc. Amer. Math. Soc. 7: 48âAS50. | Zbl 0070.18404

Lancaster P., Tismenetsky M. (1985): The Theory of Matrices, Second Edition: With Applications. Academic Press, Orlando. | Zbl 0558.15001

Mathew T. (1989): MANOVA in the multivariate components of variance model. Journal of Multivariate Analysis 29: 30-38.[Crossref] | Zbl 0667.62052

Naik D. N., Rao S. (2001): Analysis of multivariate repeated measures data with a Kronecker product structured covariance matrix. J. Appl. Statist. 28: 91-105.[Crossref] | Zbl 0991.62038

Ortega J. M. (1987): Matrix Theory: A Second Course. Plenum Press, New York. | Zbl 0654.15001

Reinsel G. (1982): Multivariate repeated measurements or growth curve models with multivariate random-effects covariance structure. Journal of American Statistical Association 77: 190-195.[Crossref] | Zbl 0489.62062

Roy A., Khattree R. (2005a): Discrimination and classification with repeated measures data under different covariance structures. Communications in Statistics - Simulation and Computation 34: 167-178.[Crossref] | Zbl 1061.62090

Roy A., Khattree R. (2005b): On discrimination and classification with multivariate repeated measures data. Journal of Statistical Planning and Inference 134: 462-485.[WoS] | Zbl 1066.62069

Roy A., Khattree R. (2008): Classification rules for repeated measures data from biomedical research. In: Khattree R., Naik D. N. (eds) Computational methods in biomedical research. Chapman and Hall/CRC: 323-370.

Srivastava M. S., von Rosen T., von Rosen D. (2008): Models with a Kronecker product covariance structure: estimation and testing. Math. Methods Stat. 17(4): 357-370.[Crossref] | Zbl 1231.62101

Ukalski K., Smiałowski T. (2011): Multivariate analysis of data from preliminary trials with winter rye. Biuletyn Instytutu Hodowli i Aklimatyzacji Roslin 260/261: 251-262.