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Bootstrap-Based LASSO-Type Selection to Build Generalized Additive Partially Linear Models for High-Dimensional Data

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Monte-Carlo Simulation-Based Statistical Modeling

Part of the book series: ICSA Book Series in Statistics ((ICSABSS))

Abstract

Generalized additive partially linear model (GAPLM) is a flexible option to model the effects of covariates on the response by allowing nonlinear effects of some covariates and linear effects of the other covariates. To address the practical needs of applying GAPLM to high-dimensional data, we propose a procedure to select variables and therefore to build a GAPLM by using the bootstrap technique with the penalized regression. We demonstrate the proposed procedure by applying it to analyze data from a breast cancer study and an HIV study. The two examples show that the procedure is useful in practice. A simulation study also shows that the proposed procedure has a better performance of variable selection than the penalized regression.

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Acknowledgements

Material has been reviewed by the Walter Reed Army Institute of Research. There is no objection to its presentation and/or publication. The opinions or assertions contained herein are the private views of the author, and are not to be construed as official, or as reflecting true views of the Department of the Army, the Agency for Healthcare Research and Quality, the Department of Defense or the Department of Health and Human Services. Liang’s research was partially supported by NSF grants DMS-1418042 and DMS-1620898, and by Award Number 11529101, made by National Natural Science Foundation of China.

Author information

Authors and Affiliations

  1. Health Informatics Institute, University of South Florida, Tampa, FL, 33612, USA

    Xiang Liu

  2. Department of Mathematics and Statistics, University of Toledo, Toledo, OH, 43606, USA

    Tian Chen

  3. Division of Preventive Medicine, Walter Reed Army Institute of Research, Silver Spring, MD, 20910, USA

    Yuanzhang Li

  4. Department of Statistics, George Washington University, Washington, DC, 20052, USA

    Hua Liang

Authors
  1. Xiang Liu
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  2. Tian Chen
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  3. Yuanzhang Li
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  4. Hua Liang
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Corresponding authors

Correspondence to Xiang Liu or Hua Liang .

Editor information

Editors and Affiliations

  1. Gillings School of Global Public Health, University of North Carolina, Chapel Hill, North Carolina, USA

    Ding-Geng (Din) Chen

  2. Risk Management, Credit Suisse Risk Management, New York, New York, USA

    John Dean Chen

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Liu, X., Chen, T., Li, Y., Liang, H. (2017). Bootstrap-Based LASSO-Type Selection to Build Generalized Additive Partially Linear Models for High-Dimensional Data. In: Chen, DG., Chen, J. (eds) Monte-Carlo Simulation-Based Statistical Modeling . ICSA Book Series in Statistics. Springer, Singapore. https://doi.org/10.1007/978-981-10-3307-0_18

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