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Regression based thresholds in principal loading analysis

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  • Bauer, Jan O.
  • Drabant, Bernhard

Abstract

Principal loading analysis is a dimension reduction method that discards variables which have only a small distorting effect on the covariance matrix. As a special case, principal loading analysis discards variables that are not correlated with the remaining ones. In multivariate linear regression on the other hand, predictors that are neither correlated with both the remaining predictors nor with the dependent variables have a regression coefficients equal to zero. Hence, if the goal is to select a number of predictors, variables that do not correlate are discarded as it is also done in principal loading analysis. That both methods select the same variables occurs not only for the special case of zero correlation however. We contribute conditions under which both methods share the same variable selection. Further, we extend those conditions to provide a choice for the threshold in principal loading analysis which only follows recommendations based on simulation results so far.

Suggested Citation

  • Bauer, Jan O. & Drabant, Bernhard, 2023. "Regression based thresholds in principal loading analysis," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
    • Handle: RePEc:eee:jmvana:v:193:y:2023:i:c:s0047259x2200094x
    DOI: 10.1016/j.jmva.2022.105103
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    References listed on IDEAS

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    1. E. R. Mansfield & J. T. Webster & R. F. Gunst, 1977. "An Analytic Variable Selection Technique for Principal Component Regression," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 26(1), pages 34-40, March.
    2. Douglas M. Hawkins, 1973. "On the Investigation of Alternative Regressions by Principal Component Analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 22(3), pages 275-286, November.
    3. Bauer, Jan O. & Drabant, Bernhard, 2021. "Principal loading analysis," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    4. Muller, Keith E. & Peterson, Bercedis L., 1984. "Practical methods for computing power in testing the multivariate general linear hypothesis," Computational Statistics & Data Analysis, Elsevier, vol. 2(2), pages 143-158, August.
    5. Vichi, Maurizio & Saporta, Gilbert, 2009. "Clustering and disjoint principal component analysis," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 3194-3208, June.
    6. Kollo, T. & Neudecker, H., 1993. "Asymptotics of Eigenvalues and Unit-Length Eigenvectors of Sample Variance and Correlation Matrices," Journal of Multivariate Analysis, Elsevier, vol. 47(2), pages 283-300, November.
    7. Dauxois, J. & Pousse, A. & Romain, Y., 1982. "Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference," Journal of Multivariate Analysis, Elsevier, vol. 12(1), pages 136-154, March.
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