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Partial least squares for simultaneous reduction of response and predictor vectors in regression

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  • Cook, R. Dennis
  • Forzani, Liliana
  • Liu, Lan

Abstract

We study and establish a foundation for dimension reduction methods that compress the response and predictor vectors in multivariate regression. While all of the methods studied can perform competitively, depending on the characteristics of the regression, using partial least squares to compress the response and predictor vectors was judged to be the best for prediction and parameter estimation.

Suggested Citation

  • Cook, R. Dennis & Forzani, Liliana & Liu, Lan, 2023. "Partial least squares for simultaneous reduction of response and predictor vectors in regression," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
    • Handle: RePEc:eee:jmvana:v:196:y:2023:i:c:s0047259x2300009x
    DOI: 10.1016/j.jmva.2023.105163
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    References listed on IDEAS

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    1. Cook, R. Dennis, 2022. "A slice of multivariate dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    2. Lexin Li & R. Dennis Cook & Chih-Ling Tsai, 2007. "Partial inverse regression," Biometrika, Biometrika Trust, vol. 94(3), pages 615-625.
    3. Mevik, Björn-Helge & Wehrens, Ron, 2007. "The pls Package: Principal Component and Partial Least Squares Regression in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 18(i02).
    4. Yin, Xiangrong & Li, Bing & Cook, R. Dennis, 2008. "Successive direction extraction for estimating the central subspace in a multiple-index regression," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1733-1757, September.
    5. R. D. Cook & I. S. Helland & Z. Su, 2013. "Envelopes and partial least squares regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(5), pages 851-877, November.
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    Cited by:

    1. Dennis Cook, R. & Forzani, Liliana, 2023. "On the role of partial least squares in path analysis for the social sciences," Journal of Business Research, Elsevier, vol. 167(C).

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