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The use of vector bootstrapping to improve variable selection precision in Lasso models


  • Laurin Charles


  • Boomsma Dorret

    (Department of Biological Psychology, VU University Amsterdam, Amsterdam, 1081 HV, Netherlands)

  • Lubke Gitta


The Lasso is a shrinkage regression method that is widely used for variable selection in statistical genetics. Commonly, K-fold cross-validation is used to fit a Lasso model. This is sometimes followed by using bootstrap confidence intervals to improve precision in the resulting variable selections. Nesting cross-validation within bootstrapping could provide further improvements in precision, but this has not been investigated systematically. We performed simulation studies of Lasso variable selection precision (VSP) with and without nesting cross-validation within bootstrapping. Data were simulated to represent genomic data under a polygenic model as well as under a model with effect sizes representative of typical GWAS results. We compared these approaches to each other as well as to software defaults for the Lasso. Nested cross-validation had the most precise variable selection at small effect sizes. At larger effect sizes, there was no advantage to nesting. We illustrated the nested approach with empirical data comprising SNPs and SNP-SNP interactions from the most significant SNPs in a GWAS of borderline personality symptoms. In the empirical example, we found that the default Lasso selected low-reliability SNPs and interactions which were excluded by bootstrapping.

Suggested Citation

  • Laurin Charles & Boomsma Dorret & Lubke Gitta, 2016. "The use of vector bootstrapping to improve variable selection precision in Lasso models," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 15(4), pages 305-320, August.
  • Handle: RePEc:bpj:sagmbi:v:15:y:2016:i:4:p:305-320:n:3

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    References listed on IDEAS

    1. Jianqing Fan & Shaojun Guo & Ning Hao, 2012. "Variance estimation using refitted cross‐validation in ultrahigh dimensional regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(1), pages 37-65, January.
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    3. Robert Tibshirani, 2011. "Regression shrinkage and selection via the lasso: a retrospective," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(3), pages 273-282, June.
    4. Pötscher, Benedikt M. & Leeb, Hannes, 2009. "On the distribution of penalized maximum likelihood estimators: The LASSO, SCAD, and thresholding," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2065-2082, October.
    5. Freedman, David & Lane, David, 1983. "A Nonstochastic Interpretation of Reported Significance Levels," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(4), pages 292-298, October.
    6. Gareth M. James & Peter Radchenko, 2009. "A generalized Dantzig selector with shrinkage tuning," Biometrika, Biometrika Trust, vol. 96(2), pages 323-337.
    7. Chatterjee, A. & Lahiri, S. N., 2011. "Bootstrapping Lasso Estimators," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 608-625.
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