IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v134y2019icp17-35.html
   My bibliography  Save this article

Regression adjustment for treatment effect with multicollinearity in high dimensions

Author

Listed:
  • Yue, Lili
  • Li, Gaorong
  • Lian, Heng
  • Wan, Xiang

Abstract

Randomized experiment is an important tool for studying the Average Treatment Effect (ATE). This paper considers the regression adjustment estimation of the Sample Average Treatment Effect (SATE) in high-dimensional case, where the multicollinearity problem is often encountered and needs to be properly handled. Many existing regression adjustment methods fail to achieve satisfactory performances. To solve this issue, an Elastic-net adjusted estimator for SATE is proposed under the Rubin causal model of randomized experiments with multicollinearity in high dimensions. The asymptotic properties of the proposed SATE estimator are shown under some regularity conditions, and the asymptotic variance is proved to be not greater than that of the unadjusted estimator. Furthermore, Neyman-type conservative estimators for the asymptotic variance are proposed, which yields tighter confidence intervals than both the unadjusted and the Lasso-based adjusted estimators. Some simulation studies are carried out to show that the Elastic-net adjusted method is better in addressing collinearity problem than the existing methods. The advantages of our proposed method are also shown in analyzing the dataset of HER2 breast cancer patients.

Suggested Citation

  • Yue, Lili & Li, Gaorong & Lian, Heng & Wan, Xiang, 2019. "Regression adjustment for treatment effect with multicollinearity in high dimensions," Computational Statistics & Data Analysis, Elsevier, vol. 134(C), pages 17-35.
    • Handle: RePEc:eee:csdana:v:134:y:2019:i:c:p:17-35
    DOI: 10.1016/j.csda.2018.11.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947318302780
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2018.11.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Alexandre Belloni & Victor Chernozhukov & Christian Hansen, 2014. "Inference on Treatment Effects after Selection among High-Dimensional Controlsâ€," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 81(2), pages 608-650.
    2. Guido W. Imbens & Jeffrey M. Wooldridge, 2009. "Recent Developments in the Econometrics of Program Evaluation," Journal of Economic Literature, American Economic Association, vol. 47(1), pages 5-86, March.
    3. Guido W. Imbens, 2004. "Nonparametric Estimation of Average Treatment Effects Under Exogeneity: A Review," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 4-29, February.
    4. A. Belloni & V. Chernozhukov & I. Fernández‐Val & C. Hansen, 2017. "Program Evaluation and Causal Inference With High‐Dimensional Data," Econometrica, Econometric Society, vol. 85, pages 233-298, January.
    5. Luke W. Miratrix & Jasjeet S. Sekhon & Bin Yu, 2013. "Adjusting treatment effect estimates by post-stratification in randomized experiments," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(2), pages 369-396, March.
    6. Howard D. Bondell & Brian J. Reich, 2008. "Simultaneous Regression Shrinkage, Variable Selection, and Supervised Clustering of Predictors with OSCAR," Biometrics, The International Biometric Society, vol. 64(1), pages 115-123, March.
    7. Jianqing Fan & Jinchi Lv, 2008. "Sure independence screening for ultrahigh dimensional feature space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 849-911, November.
    8. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    9. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881.
    10. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
    11. Daye, Z. John & Jeng, X. Jessie, 2009. "Shrinkage and model selection with correlated variables via weighted fusion," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1284-1298, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Dridi, Ichrak & Boughrara, Adel, 2023. "Flexible inflation targeting and stock market volatility: Evidence from emerging market economies," Economic Modelling, Elsevier, vol. 126(C).
    2. Kimon Ntotsis & Alex Karagrigoriou & Andreas Artemiou, 2021. "Interdependency Pattern Recognition in Econometrics: A Penalized Regularization Antidote," Econometrics, MDPI, vol. 9(4), pages 1-13, December.
    3. Feng, Sanying & Kong, Kaidi & Kong, Yinfei & Li, Gaorong & Wang, Zhaoliang, 2022. "Statistical inference of heterogeneous treatment effect based on single-index model," Computational Statistics & Data Analysis, Elsevier, vol. 175(C).
    4. Zeyu Diao & Lili Yue & Fanrong Zhao & Gaorong Li, 2022. "High-Dimensional Regression Adjustment Estimation for Average Treatment Effect with Highly Correlated Covariates," Mathematics, MDPI, vol. 10(24), pages 1-18, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zeyu Diao & Lili Yue & Fanrong Zhao & Gaorong Li, 2022. "High-Dimensional Regression Adjustment Estimation for Average Treatment Effect with Highly Correlated Covariates," Mathematics, MDPI, vol. 10(24), pages 1-18, December.
    2. Gabriel Okasa, 2022. "Meta-Learners for Estimation of Causal Effects: Finite Sample Cross-Fit Performance," Papers 2201.12692, arXiv.org.
    3. Alexandre Belloni & Victor Chernozhukov & Denis Chetverikov & Christian Hansen & Kengo Kato, 2018. "High-dimensional econometrics and regularized GMM," CeMMAP working papers CWP35/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. Susan Athey & Guido W. Imbens & Stefan Wager, 2018. "Approximate residual balancing: debiased inference of average treatment effects in high dimensions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(4), pages 597-623, September.
    5. Zhengyuan Zhou & Susan Athey & Stefan Wager, 2023. "Offline Multi-Action Policy Learning: Generalization and Optimization," Operations Research, INFORMS, vol. 71(1), pages 148-183, January.
    6. Michael Lechner, 2023. "Causal Machine Learning and its use for public policy," Swiss Journal of Economics and Statistics, Springer;Swiss Society of Economics and Statistics, vol. 159(1), pages 1-15, December.
    7. Lee, Ji Hyung & Shi, Zhentao & Gao, Zhan, 2022. "On LASSO for predictive regression," Journal of Econometrics, Elsevier, vol. 229(2), pages 322-349.
    8. Denis Fougère & Nicolas Jacquemet, 2020. "Policy Evaluation Using Causal Inference Methods," SciencePo Working papers Main hal-03455978, HAL.
    9. Ricardo P. Masini & Marcelo C. Medeiros & Eduardo F. Mendes, 2023. "Machine learning advances for time series forecasting," Journal of Economic Surveys, Wiley Blackwell, vol. 37(1), pages 76-111, February.
    10. Zongwu Cai & Ying Fang & Ming Lin & Shengfang Tang, 2020. "Testing Unconfoundedness Assumption Using Auxiliary Variables," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202004, University of Kansas, Department of Economics, revised Feb 2020.
    11. Philip Kostov & Thankom Arun & Samuel Annim, 2014. "Financial Services to the Unbanked: the case of the Mzansi intervention in South Africa," Contemporary Economics, University of Economics and Human Sciences in Warsaw., vol. 8(2), June.
    12. Huber, Martin, 2019. "An introduction to flexible methods for policy evaluation," FSES Working Papers 504, Faculty of Economics and Social Sciences, University of Freiburg/Fribourg Switzerland.
    13. Athey, Susan & Imbens, Guido W., 2019. "Machine Learning Methods Economists Should Know About," Research Papers 3776, Stanford University, Graduate School of Business.
    14. Christis Katsouris, 2023. "High Dimensional Time Series Regression Models: Applications to Statistical Learning Methods," Papers 2308.16192, arXiv.org.
    15. Jonathan Fuhr & Philipp Berens & Dominik Papies, 2024. "Estimating Causal Effects with Double Machine Learning -- A Method Evaluation," Papers 2403.14385, arXiv.org.
    16. Shengfang Tang & Zongwu Cai & Ying Fang & Ming Lin, 2019. "Testing Unconfoundedness Assumption Using Auxiliary Variables," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201905, University of Kansas, Department of Economics, revised Mar 2019.
    17. Michael Pollmann, 2020. "Causal Inference for Spatial Treatments," Papers 2011.00373, arXiv.org, revised Jan 2023.
    18. Nicolaj N. Mühlbach, 2020. "Tree-based Synthetic Control Methods: Consequences of moving the US Embassy," CREATES Research Papers 2020-04, Department of Economics and Business Economics, Aarhus University.
    19. Sant’Anna, Pedro H.C. & Zhao, Jun, 2020. "Doubly robust difference-in-differences estimators," Journal of Econometrics, Elsevier, vol. 219(1), pages 101-122.
    20. Mkhadri, Abdallah & Ouhourane, Mohamed, 2013. "An extended variable inclusion and shrinkage algorithm for correlated variables," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 631-644.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:134:y:2019:i:c:p:17-35. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.