CANONICAL CORRELATION ANALYSIS IN THE CASE OF MULTIVARIATE REPEATED MEASURES DATA

Publications

Share / Export Citation / Email / Print / Text size:

Statistics in Transition New Series

Polish Statistical Association

Central Statistical Office of Poland

Subject: Economics , Statistics & Probability

GET ALERTS

ISSN: 1234-7655
eISSN: 2450-0291

DESCRIPTION

24
Reader(s)
54
Visit(s)
0
Comment(s)
0
Share(s)

SEARCH WITHIN CONTENT

FIND ARTICLE

Volume / Issue / page

Related articles

VOLUME 19 , ISSUE 1 (March 2018) > List of articles

CANONICAL CORRELATION ANALYSIS IN THE CASE OF MULTIVARIATE REPEATED MEASURES DATA

Mirosław Krzyśko / Wojciech Łukaszonek / Waldemar Wołyński

Keywords : canonical correlation analysis, repeated measures data (doubly multivariate data), Kronecker product covariance structure, maximum likelihood estimates

Citation Information : Statistics in Transition New Series. Volume 19, Issue 1, Pages 75-85, DOI: https://doi.org/10.21307/stattrans-2018-005

License : (CC BY-NC-ND 4.0)

Published Online: 27-May-2018

ARTICLE

ABSTRACT

In this paper, we present, in the real example, canonical variables applicable in the case of multivariate repeated measures data under the following assumptions: (1) multivariate normality for the vector of observations and (2) Kronecker product structure of the positive definite covariance matrix. These variables are especially useful when the number of observations is not large enough to estimate the covariance matrix, and thus the traditional canonical variables fail. Computational schemes for maximum likelihood estimates of required parameters are also given.

Content not available PDF Share

FIGURES & TABLES

REFERENCES

DERĘGOWSKI, K., KRZYŚKO, M., (2009). Principal component analysis in the case of multivariate repeated measures data, Biometrical Letters, 46 (2), pp. 163–172.

 

GALECKI, A. T., (1994). General class of covariance structures for two or more repeated factors in longitudinal data analysis, Communications in Statistics – Theory and Methods, 23, pp. 3105-3119.

 

GIRI, N. C., (1996). Multivariate Statistical Analysis, Marcel Dekker, New York.

 

HOTELLING, H., (1936). Relations between two sets of variates, Biometrika, 28, pp. 321–377.

 

KRZYŚKO, M., SKORZYBUT, M., (2009). Discriminant analysis of multivariate repeated measures data with a Kronecker product structured covariance matrices, Statistical papers, 50, 817-835.

 

KRZYŚKO, M., MĄDRY, W., PLUTA, S., SKORZYBUT, M., WOŁYŃSKI,W., (2010). Analysis of multivariate repeated measures data, Colloquium Biometricum, 40, pp. 117–133.

 

KRZYŚKO, M., SKORZYBUT, M., WOŁYŃSKI, W., (2011). Classifiers for doubly multivariate data, Discussiones Mathematicae. Probability and Statistics, 31, pp. 5–27.

 

KRZYŚKO, M., ŚMIAŁOWSKI, T., WOŁYŃSKI, W., (2014). Analysis of multivariate repeated measures data using a MANOVA model and principal components, Biometrical Letters, 51 (2), pp. 103–124.

 

LANCASTER, P., TISMENETSKY, M., (1985). The Theory of Matrices, Second Edition: With Applications. Academic Press, Orlando.

 

MCCOLLUM, R., (2010). Canonical correlation analysis for longitudinal data. Ph.D. thesis, Old Dominion University.

 

NAIK, D. N., RAO, S., (2001). Analysis of multivariate repeated measures data with a Kronecker product structured covariance matrix, J. Appl. Statist., 28, pp. 91–105.

 

ORTEGA, J. M., (1987). Matrix Theory: A Second Course. Plenum Press, New York.

 

R CORE TEAM (2017). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org/.

 

ROY, A., KHATTREE, R., (2005). On discrimination and classification with multivariate repeated measures data, Journal of Statistical Planning and Inference, 134, pp. 462–485.

 

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, pp. 323–370.

 

SRIVASTAVA, J., Naik, D. N., (2008). Canonical correlation analysis of longitudinal data, Denver JSM 2008 Proceedings, Biometrics Section, pp. 563–568.

 

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), pp. 357–370.

 

EXTRA FILES

COMMENTS