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A variable selection approach in the multivariate linear model: an application to LC-MS metabolomics data

Author

Listed:
  • Perrot-Dockès Marie
  • Lévy-Leduc Céline
  • Chiquet Julien
  • Sansonnet Laure
  • Brégère Margaux
  • Étienne Marie-Pierre
  • Robin Stéphane

    (UMR MIA-Paris, AgroParisTech, INRA – Université Paris-Saclay, 75005 Paris, France)

  • Genta-Jouve Grégory

    (UMR CNRS 8638 Comète – Université Paris-Descartes, CNRS, 75006 Paris, France)

Abstract

Omic data are characterized by the presence of strong dependence structures that result either from data acquisition or from some underlying biological processes. Applying statistical procedures that do not adjust the variable selection step to the dependence pattern may result in a loss of power and the selection of spurious variables. The goal of this paper is to propose a variable selection procedure within the multivariate linear model framework that accounts for the dependence between the multiple responses. We shall focus on a specific type of dependence which consists in assuming that the responses of a given individual can be modelled as a time series. We propose a novel Lasso-based approach within the framework of the multivariate linear model taking into account the dependence structure by using different types of stationary processes covariance structures for the random error matrix. Our numerical experiments show that including the estimation of the covariance matrix of the random error matrix in the Lasso criterion dramatically improves the variable selection performance. Our approach is successfully applied to an untargeted LC-MS (Liquid Chromatography-Mass Spectrometry) data set made of African copals samples. Our methodology is implemented in the R package MultiVarSel which is available from the Comprehensive R Archive Network (CRAN).

Suggested Citation

  • Perrot-Dockès Marie & Lévy-Leduc Céline & Chiquet Julien & Sansonnet Laure & Brégère Margaux & Étienne Marie-Pierre & Robin Stéphane & Genta-Jouve Grégory, 2018. "A variable selection approach in the multivariate linear model: an application to LC-MS metabolomics data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 17(5), pages 1-14, October.
    • Handle: RePEc:bpj:sagmbi:v:17:y:2018:i:5:p:14:n:3
    DOI: 10.1515/sagmb-2017-0077
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    References listed on IDEAS

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    1. Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2010. "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i01).
    2. Perrot-Dockès, Marie & Lévy-Leduc, Céline & Sansonnet, Laure & Chiquet, Julien, 2018. "Variable selection in multivariate linear models with high-dimensional covariance matrix estimation," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 78-97.
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