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Principal Component Analysis in the Presence of Group Structure

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  • W. J. Krzanowski

Abstract

A nested series of hypotheses on dispersion structure is identified when observations are grouped in a multivariate sample. A simple method of estimation is suggested for one of these hypotheses, and results using this method are compared with those previously obtained by maximum likelihood methods. Using these hypotheses, an analogy may be drawn between comparison of principal components between groups and comparison of regressions between groups.

Suggested Citation

  • W. J. Krzanowski, 1984. "Principal Component Analysis in the Presence of Group Structure," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 33(2), pages 164-168, June.
    • Handle: RePEc:bla:jorssc:v:33:y:1984:i:2:p:164-168
    DOI: 10.2307/2347442
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    Cited by:

    1. Bingkai Wang & Xi Luo & Yi Zhao & Brian Caffo, 2021. "Semiparametric partial common principal component analysis for covariance matrices," Biometrics, The International Biometric Society, vol. 77(4), pages 1175-1186, December.
    2. Trendafilov, Nickolay T., 2010. "Stepwise estimation of common principal components," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3446-3457, December.
    3. Kyusoon Kim & Hee‐Seok Oh & Minsu Park, 2023. "Principal component analysis for river network data: Use of spatiotemporal correlation and heterogeneous covariance structure," Environmetrics, John Wiley & Sons, Ltd., vol. 34(4), June.
    4. Luca Bagnato & Antonio Punzo, 2021. "Unconstrained representation of orthogonal matrices with application to common principal components," Computational Statistics, Springer, vol. 36(2), pages 1177-1195, June.
    5. Schott, James R., 1998. "Estimating correlation matrices that have common eigenvectors," Computational Statistics & Data Analysis, Elsevier, vol. 27(4), pages 445-459, June.
    6. Pourahmadi, Mohsen & Daniels, Michael J. & Park, Trevor, 2007. "Simultaneous modelling of the Cholesky decomposition of several covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 98(3), pages 568-587, March.
    7. Nickolay T. Trendafilov & Tsegay Gebrehiwot Gebru, 2016. "Recipes for sparse LDA of horizontal data," METRON, Springer;Sapienza Università di Roma, vol. 74(2), pages 207-221, August.
    8. Tenenhaus, Arthur & Tenenhaus, Michel, 2014. "Regularized generalized canonical correlation analysis for multiblock or multigroup data analysis," European Journal of Operational Research, Elsevier, vol. 238(2), pages 391-403.

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