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Generalized canonical correlation analysis with missing values

Author

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  • Michel Velden

    ()

  • Yoshio Takane

    ()

Abstract

Generalized canonical correlation analysis is a versatile technique that allows the joint analysis of several sets of data matrices. The generalized canonical correlation analysis solution can be obtained through an eigenequation and distributional assumptions are not required. When dealing with multiple set data, the situation frequently occurs that some values are missing. In this paper, two new methods for dealing with missing values in generalized canonical correlation analysis are introduced. The first approach, which does not require iterations, is a generalization of the Test Equating method available for principal component analysis. In the second approach, missing values are imputed in such a way that the generalized canonical correlation analysis objective function does not increase in subsequent steps. Convergence is achieved when the value of the objective function remains constant. By means of a simulation study, we assess the performance of the new methods. We compare the results with those of two available methods; the missing-data passive method, introduced in Gifi’s homogeneity analysis framework, and the GENCOM algorithm developed by Green and Carroll. An application using world bank data is used to illustrate the proposed methods. Copyright The Author(s) 2012

Suggested Citation

  • Michel Velden & Yoshio Takane, 2012. "Generalized canonical correlation analysis with missing values," Computational Statistics, Springer, vol. 27(3), pages 551-571, September.
  • Handle: RePEc:spr:compst:v:27:y:2012:i:3:p:551-571
    DOI: 10.1007/s00180-011-0276-y
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    File URL: http://hdl.handle.net/10.1007/s00180-011-0276-y
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    References listed on IDEAS

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    1. Michel Velden & Tammo Bijmolt, 2006. "Generalized canonical correlation analysis of matrices with missing rows: a simulation study," Psychometrika, Springer;The Psychometric Society, vol. 71(2), pages 323-331, June.
    2. Casper Albers & John Gower, 2010. "A general approach to handling missing values in Procrustes analysis," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 4(4), pages 223-237, December.
    3. Zanakis, Stelios H. & Alvarez, Cecilia & Li, Vivian, 2007. "Socio-economic determinants of HIV/AIDS pandemic and nations efficiencies," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1811-1838, February.
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    Citations

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    Cited by:

    1. M. Velden & A. Iodice D’Enza & F. Palumbo, 2017. "Cluster Correspondence Analysis," Psychometrika, Springer;The Psychometric Society, vol. 82(1), pages 158-185, March.
    2. van de Velden, M. & Iodice D' Enza, A. & Palumbo, F., 2014. "Cluster Correspondence Analysis," Econometric Institute Research Papers EI 2014-24, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    3. Kohei Adachi, 2013. "Generalized joint Procrustes analysis," Computational Statistics, Springer, vol. 28(6), pages 2449-2464, December.

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