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Regression modelling on stratified data with the lasso

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  • E. Ollier
  • V. Viallon

Abstract

SUMMARY We consider the estimation of regression models on strata defined using a categorical covariate, in order to identify interactions between this categorical covariate and the other predictors. A basic approach requires the choice of a reference stratum. We show that the performance of a penalized version of this approach depends on this arbitrary choice, and propose an approach that bypasses this at almost no additional computational cost. Regarding model selection consistency, our proposal mimics the strategy based on an optimal and covariate-specific choice for the reference stratum. An empirical study confirms that our proposal generally outperforms the basic approach in the identification and description of the interactions. An illustration on gene expression data is provided.

Suggested Citation

  • E. Ollier & V. Viallon, 2017. "Regression modelling on stratified data with the lasso," Biometrika, Biometrika Trust, vol. 104(1), pages 83-96.
    • Handle: RePEc:oup:biomet:v:104:y:2017:i:1:p:83-96.
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    File URL: http://hdl.handle.net/10.1093/biomet/asw065
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    References listed on IDEAS

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    1. Reid, Stephen & Tibshirani, Rob, 2014. "Regularization Paths for Conditional Logistic Regression: The clogitL1 Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 58(i12).
    2. Gross, Samuel M. & Tibshirani, Robert, 2016. "Data Shared Lasso: A novel tool to discover uplift," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 226-235.
    3. Qian, Junyang & Jia, Jinzhu, 2016. "On stepwise pattern recovery of the fused Lasso," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 221-237.
    4. Ollier, Edouard & Samson, Adeline & Delavenne, Xavier & Viallon, Vivian, 2016. "A SAEM algorithm for fused lasso penalized NonLinear Mixed Effect Models: Application to group comparison in pharmacokinetics," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 207-221.
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    Cited by:

    1. Zachary F. Fisher & Younghoon Kim & Barbara L. Fredrickson & Vladas Pipiras, 2022. "Penalized Estimation and Forecasting of Multiple Subject Intensive Longitudinal Data," Psychometrika, Springer;The Psychometric Society, vol. 87(2), pages 1-29, June.
    2. Rafael Blanquero & Emilio Carrizosa & Pepa Ramírez-Cobo & M. Remedios Sillero-Denamiel, 2021. "A cost-sensitive constrained Lasso," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 15(1), pages 121-158, March.

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