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2014 | 51 | 2 | 103-114
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Wydawca
Czasopismo
Rocznik
Tom
51
Numer
2
Strony
103-114
Opis fizyczny
Daty
wydano
2014-12-01
online
2014-12-20
Twórcy
  • Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznan, Poland, mkrzysko@amu.edu.pl
  • Plant Breeding and Acclimatization Institute, National Research Institute, Radzików, 05-870 Błonie, Poland, zhsmialo@cyf-kr.edu.pl
  • Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznan, Poland
Bibliografia
  • Arnold S. F. (1979): Linear models with exchangeably distributed errors. Journal of American Statistical Association 74: 194-199.[Crossref]
  • 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]
  • Giri N. C. (1996): Multivariate Statistical Analysis. Marcel Dekker, Inc., New York.
  • Khatri C. G. (1962): Conditions for Wishartness and independence of second degree polynomials in normal vector. Annals of Mathematical Statistics 33: 1002-1007.[Crossref]
  • Kruskal J. B. (1956): On the shortest spanning subtree of a graph and the traveling salesman problem. Proc. Amer. Math. Soc. 7: 48âAS50.
  • Lancaster P., Tismenetsky M. (1985): The Theory of Matrices, Second Edition: With Applications. Academic Press, Orlando.
  • Mathew T. (1989): MANOVA in the multivariate components of variance model. Journal of Multivariate Analysis 29: 30-38.[Crossref]
  • 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]
  • Ortega J. M. (1987): Matrix Theory: A Second Course. Plenum Press, New York.
  • 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]
  • 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]
  • Roy A., Khattree R. (2005b): On discrimination and classification with multivariate repeated measures data. Journal of Statistical Planning and Inference 134: 462-485.[WoS]
  • 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]
  • 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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_bile-2014-0008
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