# Analysis of multivariate repeated measures data using a MANOVA model and principal components

Mirosław Krzysko; Tadeusz Smiałowski; Waldemar Wołynski

Biometrical Letters (2014)

- Volume: 51, Issue: 2, page 103-114
- ISSN: 1896-3811

## Access Full Article

top## Abstract

top## How to cite

topMirosław Krzysko, Tadeusz Smiałowski, and Waldemar Wołynski. "Analysis of multivariate repeated measures data using a MANOVA model and principal components." Biometrical Letters 51.2 (2014): 103-114. <http://eudml.org/doc/268881>.

@article{MirosławKrzysko2014,

abstract = {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.},

author = {Mirosław Krzysko, Tadeusz Smiałowski, Waldemar Wołynski},

journal = {Biometrical Letters},

keywords = {multivariate repeated measures data (doubly multivariate data); Kronecker product covariance structure; maximum likelihood estimates; mixed MANOVA model; principal component analysis},

language = {eng},

number = {2},

pages = {103-114},

title = {Analysis of multivariate repeated measures data using a MANOVA model and principal components},

url = {http://eudml.org/doc/268881},

volume = {51},

year = {2014},

}

TY - JOUR

AU - Mirosław Krzysko

AU - Tadeusz Smiałowski

AU - Waldemar Wołynski

TI - Analysis of multivariate repeated measures data using a MANOVA model and principal components

JO - Biometrical Letters

PY - 2014

VL - 51

IS - 2

SP - 103

EP - 114

AB - 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.

LA - eng

KW - multivariate repeated measures data (doubly multivariate data); Kronecker product covariance structure; maximum likelihood estimates; mixed MANOVA model; principal component analysis

UR - http://eudml.org/doc/268881

ER -

## References

top- Arnold S. F. (1979): Linear models with exchangeably distributed errors. Journal of American Statistical Association 74: 194-199.[Crossref] Zbl0431.62044
- 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] Zbl0090.35804
- Giri N. C. (1996): Multivariate Statistical Analysis. Marcel Dekker, Inc., New York. Zbl0846.62039
- Khatri C. G. (1962): Conditions for Wishartness and independence of second degree polynomials in normal vector. Annals of Mathematical Statistics 33: 1002-1007.[Crossref] Zbl0108.32405
- Kruskal J. B. (1956): On the shortest spanning subtree of a graph and the traveling salesman problem. Proc. Amer. Math. Soc. 7: 48âAS50. Zbl0070.18404
- Lancaster P., Tismenetsky M. (1985): The Theory of Matrices, Second Edition: With Applications. Academic Press, Orlando. Zbl0558.15001
- Mathew T. (1989): MANOVA in the multivariate components of variance model. Journal of Multivariate Analysis 29: 30-38.[Crossref] Zbl0667.62052
- 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] Zbl0991.62038
- Ortega J. M. (1987): Matrix Theory: A Second Course. Plenum Press, New York. Zbl0654.15001
- 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] Zbl0489.62062
- 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] Zbl1061.62090
- Roy A., Khattree R. (2005b): On discrimination and classification with multivariate repeated measures data. Journal of Statistical Planning and Inference 134: 462-485.[WoS] Zbl1066.62069
- 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] Zbl1231.62101
- 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.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.