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

Abstract

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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.

How to cite

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Mirosław 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

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  11. Ortega J. M. (1987): Matrix Theory: A Second Course. Plenum Press, New York. Zbl0654.15001
  12. 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
  13. 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
  14. 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
  15. 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. 
  16. 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
  17. 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. 

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