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Determining the number of components in PLS regression on incomplete data set

Author

Listed:
  • Nengsih Titin Agustin

    (IRMA, CNRS UMR 7501, Université de Strasbourg, 67084 Strasbourg, Cedex, France)

  • Bertrand Frédéric

    (IRMA, CNRS UMR 7501, Université de Strasbourg, 67084 Strasbourg, Cedex, France)

  • Maumy-Bertrand Myriam

    (IRMA, CNRS UMR 7501, Université de Strasbourg, 67084 Strasbourg, Cedex, France)

  • Meyer Nicolas

    (iCUBE, CNRS UMR 7357, Université de Strasbourg, 67400 Strasbourg, France)

Abstract

Partial least squares regression – or PLS regression – is a multivariate method in which the model parameters are estimated using either the SIMPLS or NIPALS algorithm. PLS regression has been extensively used in applied research because of its effectiveness in analyzing relationships between an outcome and one or several components. Note that the NIPALS algorithm can provide estimates parameters on incomplete data. The selection of the number of components used to build a representative model in PLS regression is a central issue. However, how to deal with missing data when using PLS regression remains a matter of debate. Several approaches have been proposed in the literature, including the Q2 criterion, and the AIC and BIC criteria. Here we study the behavior of the NIPALS algorithm when used to fit a PLS regression for various proportions of missing data and different types of missingness. We compare criteria to select the number of components for a PLS regression on incomplete data set and on imputed data set using three imputation methods: multiple imputation by chained equations, k-nearest neighbour imputation, and singular value decomposition imputation. We tested various criteria with different proportions of missing data (ranging from 5% to 50%) under different missingness assumptions. Q2-leave-one-out component selection methods gave more reliable results than AIC and BIC-based ones.

Suggested Citation

  • Nengsih Titin Agustin & Bertrand Frédéric & Maumy-Bertrand Myriam & Meyer Nicolas, 2019. "Determining the number of components in PLS regression on incomplete data set," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 18(6), pages 1-28, December.
    • Handle: RePEc:bpj:sagmbi:v:18:y:2019:i:6:p:28:n:2
    DOI: 10.1515/sagmb-2018-0059
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    References listed on IDEAS

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    1. Kowarik, Alexander & Templ, Matthias, 2016. "Imputation with the R Package VIM," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 74(i07).
    2. van Buuren, Stef & Groothuis-Oudshoorn, Karin, 2011. "mice: Multivariate Imputation by Chained Equations in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 45(i03).
    3. Patrick Royston, 2004. "Multiple imputation of missing values," Stata Journal, StataCorp LP, vol. 4(3), pages 227-241, September.
    4. Nguyen, Danh V. & Rocke, D.M.David M., 2004. "On partial least squares dimension reduction for microarray-based classification: a simulation study," Computational Statistics & Data Analysis, Elsevier, vol. 46(3), pages 407-425, June.
    5. Horton N. J. & Lipsitz S. R., 2001. "Multiple Imputation in Practice: Comparison of Software Packages for Regression Models With Missing Variables," The American Statistician, American Statistical Association, vol. 55, pages 244-254, August.
    6. Royston, Patrick & White, Ian R., 2011. "Multiple Imputation by Chained Equations (MICE): Implementation in Stata," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 45(i04).
    7. Hirotugu Akaike, 1969. "Fitting autoregressive models for prediction," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 21(1), pages 243-247, December.
    8. Serneels, Sven & Verdonck, Tim, 2008. "Principal component analysis for data containing outliers and missing elements," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1712-1727, January.
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