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Latent models for cross-covariance


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  • Wegelin, Jacob A.
  • Packer, Asa
  • Richardson, Thomas S.
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    We consider models for the covariance between two blocks of variables. Such models are often used in situations where latent variables are believed to present. In this paper we characterize exactly the set of distributions given by a class of models with one-dimensional latent variables. These models relate two blocks of observed variables, modeling only the cross-covariance matrix. We describe the relation of this model to the singular value decomposition of the cross-covariance matrix. We show that, although the model is underidentified, useful information may be extracted. We further consider an alternative parameterization in which one latent variable is associated with each block, and we extend the result to models with r-dimensional latent variables.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 97 (2006)
    Issue (Month): 1 (January)
    Pages: 79-102

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    Handle: RePEc:eee:jmvana:v:97:y:2006:i:1:p:79-102

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    Keywords: Canonical correlation Latent variables Partial least squares Reduced-rank regression Singular value decomposition;


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    Cited by:
    1. Haruhiko Ogasawara, 2009. "Asymptotic expansions in the singular value decomposition for cross covariance and correlation under nonnormality," Annals of the Institute of Statistical Mathematics, Springer, vol. 61(4), pages 995-1017, December.
    2. Ogasawara, Haruhiko, 2007. "Asymptotic expansions of the distributions of estimators in canonical correlation analysis under nonnormality," Journal of Multivariate Analysis, Elsevier, vol. 98(9), pages 1726-1750, October.
    3. Philip Yu & Paul Lee & W. Wan, 2013. "Factor analysis for paired ranked data with application on parent–child value orientation preference data," Computational Statistics, Springer, vol. 28(5), pages 1915-1945, October.


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