IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v86y2021i2d10.1007_s11336-021-09768-z.html
   My bibliography  Save this article

Robust Inference for Mediated Effects in Partially Linear Models

Author

Listed:
  • Oliver Hines

    (London School of Hygiene and Tropical Medicine)

  • Stijn Vansteelandt

    (London School of Hygiene and Tropical Medicine
    Ghent University)

  • Karla Diaz-Ordaz

    (London School of Hygiene and Tropical Medicine)

Abstract

We consider mediated effects of an exposure, X on an outcome, Y, via a mediator, M, under no unmeasured confounding assumptions in the setting where models for the conditional expectation of the mediator and outcome are partially linear. We propose G-estimators for the direct and indirect effects and demonstrate consistent asymptotic normality for indirect effects when models for the conditional means of M, or X and Y are correctly specified, and for direct effects, when models for the conditional means of Y, or X and M are correct. This marks an improvement, in this particular setting, over previous ‘triple’ robust methods, which do not assume partially linear mean models. Testing of the no-mediation hypothesis is inherently problematic due to the composite nature of the test (either X has no effect on M or M no effect on Y), leading to low power when both effect sizes are small. We use generalized methods of moments (GMM) results to construct a new score testing framework, which includes as special cases the no-mediation and the no-direct-effect hypotheses. The proposed tests rely on an orthogonal estimation strategy for estimating nuisance parameters. Simulations show that the GMM-based tests perform better in terms of power and small sample performance compared with traditional tests in the partially linear setting, with drastic improvement under model misspecification. New methods are illustrated in a mediation analysis of data from the COPERS trial, a randomized trial investigating the effect of a non-pharmacological intervention of patients suffering from chronic pain. An accompanying R package implementing these methods can be found at github.com/ohines/plmed.

Suggested Citation

  • Oliver Hines & Stijn Vansteelandt & Karla Diaz-Ordaz, 2021. "Robust Inference for Mediated Effects in Partially Linear Models," Psychometrika, Springer;The Psychometric Society, vol. 86(2), pages 595-618, June.
    • Handle: RePEc:spr:psycho:v:86:y:2021:i:2:d:10.1007_s11336-021-09768-z
    DOI: 10.1007/s11336-021-09768-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11336-021-09768-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11336-021-09768-z?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. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. Kai Wang, 2018. "Understanding Power Anomalies in Mediation Analysis," Psychometrika, Springer;The Psychometric Society, vol. 83(2), pages 387-406, June.
    3. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2018. "Double/debiased machine learning for treatment and structural parameters," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 1-68, February.
    4. Jean-Marie Dufour & Alain Trognon & Purevdorj Tuvaandorj, 2017. "Invariant tests based on M -estimators, estimating functions, and the generalized method of moments," Econometric Reviews, Taylor & Francis Journals, vol. 36(1-3), pages 182-204, March.
    5. Newey, Whitney K & West, Kenneth D, 1987. "Hypothesis Testing with Efficient Method of Moments Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(3), pages 777-787, October.
    6. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey, 2017. "Double/Debiased/Neyman Machine Learning of Treatment Effects," American Economic Review, American Economic Association, vol. 107(5), pages 261-265, May.
    7. Andrea Rotnitzky & Quanhong Lei & Mariela Sued & James M. Robins, 2012. "Improved double-robust estimation in missing data and causal inference models," Biometrika, Biometrika Trust, vol. 99(2), pages 439-456.
    8. Noud P.A. van Giersbergen, 2014. "Inference about the Indirect Effect: a Likelihood Approach," UvA-Econometrics Working Papers 14-10, Universiteit van Amsterdam, Dept. of Econometrics.
    9. E. J. Tchetgen Tchetgen & I. Shpitser, 2014. "Estimation of a semiparametric natural direct effect model incorporating baseline covariates," Biometrika, Biometrika Trust, vol. 101(4), pages 849-864.
    10. Karel Vermeulen & Stijn Vansteelandt, 2015. "Bias-Reduced Doubly Robust Estimation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1024-1036, September.
    11. Andrea Rotnitzky & Lingling Li & Xiaochun Li, 2010. "A note on overadjustment in inverse probability weighted estimation," Biometrika, Biometrika Trust, vol. 97(4), pages 997-1001.
    12. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2016. "Double/Debiased Machine Learning for Treatment and Causal Parameters," Papers 1608.00060, arXiv.org, revised Dec 2017.
    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. Cai, Xizhen & Zhu, Yeying & Huang, Yuan & Ghosh, Debashis, 2022. "High-dimensional causal mediation analysis based on partial linear structural equation models," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).

    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. Jiaming Mao & Jingzhi Xu, 2020. "Ensemble Learning with Statistical and Structural Models," Papers 2006.05308, arXiv.org.
    2. Sant’Anna, Pedro H.C. & Zhao, Jun, 2020. "Doubly robust difference-in-differences estimators," Journal of Econometrics, Elsevier, vol. 219(1), pages 101-122.
    3. Jushan Bai & Sung Hoon Choi & Yuan Liao, 2021. "Feasible generalized least squares for panel data with cross-sectional and serial correlations," Empirical Economics, Springer, vol. 60(1), pages 309-326, January.
    4. Jiaming Mao & Zhesheng Zheng, 2020. "Structural Regularization," Papers 2004.12601, arXiv.org, revised Jun 2020.
    5. Ruoxuan Xiong & Allison Koenecke & Michael Powell & Zhu Shen & Joshua T. Vogelstein & Susan Athey, 2021. "Federated Causal Inference in Heterogeneous Observational Data," Papers 2107.11732, arXiv.org, revised Apr 2023.
    6. Yoganathan, Vignesh & Osburg, Victoria-Sophie, 2024. "The mind in the machine: Estimating mind perception's effect on user satisfaction with voice-based conversational agents," Journal of Business Research, Elsevier, vol. 175(C).
    7. Waverly Wei & Maya Petersen & Mark J van der Laan & Zeyu Zheng & Chong Wu & Jingshen Wang, 2023. "Efficient targeted learning of heterogeneous treatment effects for multiple subgroups," Biometrics, The International Biometric Society, vol. 79(3), pages 1934-1946, September.
    8. Huber Martin & Wüthrich Kaspar, 2019. "Local Average and Quantile Treatment Effects Under Endogeneity: A Review," Journal of Econometric Methods, De Gruyter, vol. 8(1), pages 1-27, January.
    9. Miquel Oliu-Barton & Bary S. R. Pradelski & Nicolas Woloszko & Lionel Guetta-Jeanrenaud & Philippe Aghion & Patrick Artus & Arnaud Fontanet & Philippe Martin & Guntram B. Wolff, 2022. "The effect of COVID certificates on vaccine uptake, health outcomes, and the economy," Nature Communications, Nature, vol. 13(1), pages 1-13, December.
    10. Sander Gerritsen & Mark Kattenberg & Sonny Kuijpers, 2019. "The impact of age at arrival on education and mental health," CPB Discussion Paper 389.rdf, CPB Netherlands Bureau for Economic Policy Analysis.
    11. Elliott Ash & Daniel L. Chen & Sergio Galletta, 2022. "Measuring Judicial Sentiment: Methods and Application to US Circuit Courts," Economica, London School of Economics and Political Science, vol. 89(354), pages 362-376, April.
    12. Pradhi Aggarwal & Alec Brandon & Ariel Goldszmidt & Justin Holz & John List & Ian Muir & Gregory Sun & Thomas Yu, 2022. "High-frequency location data shows that race affects the likelihood of being stopped and fined for speeding," Natural Field Experiments 00764, The Field Experiments Website.
    13. Songul Cinaroglu, 2020. "Modelling unbalanced catastrophic health expenditure data by using machine‐learning methods," Intelligent Systems in Accounting, Finance and Management, John Wiley & Sons, Ltd., vol. 27(4), pages 168-181, October.
    14. Miruna Oprescu & Vasilis Syrgkanis & Zhiwei Steven Wu, 2018. "Orthogonal Random Forest for Causal Inference," Papers 1806.03467, arXiv.org, revised Sep 2019.
    15. Sander Gerritsen & Mark Kattenberg & Sonny Kuijpers, 2019. "The impact of age at arrival on education and mental health," CPB Discussion Paper 389, CPB Netherlands Bureau for Economic Policy Analysis.
    16. Mark Kattenberg & Bas Scheer & Jurre Thiel, 2023. "Causal forests with fixed effects for treatment effect heterogeneity in difference-in-differences," CPB Discussion Paper 452, CPB Netherlands Bureau for Economic Policy Analysis.
    17. Jonas Metzger, 2022. "Adversarial Estimators," Papers 2204.10495, arXiv.org, revised Jun 2022.
    18. Yuya Sasaki & Takuya Ura & Yichong Zhang, 2022. "Unconditional quantile regression with high‐dimensional data," Quantitative Economics, Econometric Society, vol. 13(3), pages 955-978, July.
    19. S Klaassen & J Kueck & M Spindler & V Chernozhukov, 2023. "Uniform inference in high-dimensional Gaussian graphical models," Biometrika, Biometrika Trust, vol. 110(1), pages 51-68.
    20. Victor Chernozhukov & Carlos Cinelli & Whitney Newey & Amit Sharma & Vasilis Syrgkanis, 2021. "Long Story Short: Omitted Variable Bias in Causal Machine Learning," Papers 2112.13398, arXiv.org, revised May 2024.

    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:spr:psycho:v:86:y:2021:i:2:d:10.1007_s11336-021-09768-z. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.