IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v84y2019i3d10.1007_s11336-019-09670-9.html
   My bibliography  Save this article

Maximum Likelihood Analysis of Linear Mediation Models with Treatment–Mediator Interaction

Author

Listed:
  • Kai Wang

    (The University of Iowa)

Abstract

This research concerns a mediation model, where the mediator model is linear and the outcome model is also linear but with a treatment–mediator interaction term and a residual correlated with the residual of the mediator model. Assuming the treatment is randomly assigned, parameters in this mediation model are shown to be partially identifiable. Under the normality assumption on the residual of the mediator and the residual of the outcome, explicit full-information maximum likelihood estimates of model parameters are introduced given the correlation between the residual for the mediator and the residual for the outcome. A consistent variance matrix of these estimates is derived. Currently, the coefficients of this mediation model are estimated using the iterative feasible generalized least squares (IFGLS) method that is originally developed for seemingly unrelated regressions (SURs). We argue that this mediation model is not a system of SURs. While the IFGLS estimates are consistent, their variance matrix is not. Theoretical comparisons of the FIMLE variance matrix and the IFGLS variance matrix are conducted. Our results are demonstrated by simulation studies and an empirical study. The FIMLE method has been implemented in a freely available R package iMediate.

Suggested Citation

  • Kai Wang, 2019. "Maximum Likelihood Analysis of Linear Mediation Models with Treatment–Mediator Interaction," Psychometrika, Springer;The Psychometric Society, vol. 84(3), pages 719-748, September.
    • Handle: RePEc:spr:psycho:v:84:y:2019:i:3:d:10.1007_s11336-019-09670-9
    DOI: 10.1007/s11336-019-09670-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11336-019-09670-9
    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/s11336-019-09670-9?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. Prucha, Ingmar R, 1987. "The Variance-Covariance Matrix of the Maximum Likelihood Estimator in Triangular Structural Systems: Consistent Estimation," Econometrica, Econometric Society, vol. 55(4), pages 977-978, July.
    2. Peng Ding & Tyler J. Vanderweele, 2016. "Sharp sensitivity bounds for mediation under unmeasured mediator-outcome confounding," Biometrika, Biometrika Trust, vol. 103(2), pages 483-490.
    3. Cotterman, Robert F, 1981. "A Note on the Consistency of the GLS Estimator in Triangular Structural Systems," Econometrica, Econometric Society, vol. 49(6), pages 1589-1591, November.
    4. Lahiri, Kajal & Schmidt, Peter, 1978. "On the Estimation of Triangular Structural Systems," Econometrica, Econometric Society, vol. 46(5), pages 1217-1221, September.
    5. Arellano, Manuel, 1989. "An efficient GLS estimator of triangular models with covariance restrictions," Journal of Econometrics, Elsevier, vol. 42(2), pages 267-273, October.
    Full references (including those not matched with items on IDEAS)

    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. Panzone, Luca A. & Ulph, Alistair & Zizzo, Daniel John & Hilton, Denis & Clear, Adrian, 2021. "The impact of environmental recall and carbon taxation on the carbon footprint of supermarket shopping," Journal of Environmental Economics and Management, Elsevier, vol. 109(C).
    2. Gylfason, Thorvaldur, 2001. "Natural resources, education, and economic development," European Economic Review, Elsevier, vol. 45(4-6), pages 847-859, May.
    3. Stewart, Hayden & Davis, David E., 2005. "Price Dispersion and Accessibility: A Case study of Fast Food," MPRA Paper 7617, University Library of Munich, Germany.
    4. Gori, Filippo, 2018. "Dissecting the ‘doom loop’: the bank-sovereign credit risk nexus during the US debt ceiling crisis," MPRA Paper 87994, University Library of Munich, Germany.
    5. Lodewijk Smets & Stephen Knack & Nadia Molenaers, 2013. "Political ideology, quality at entry and the success of economic reform programs," The Review of International Organizations, Springer, vol. 8(4), pages 447-476, December.
    6. Thorvaldur Gylfason & Gylfi Zoega, 2006. "Natural Resources and Economic Growth: The Role of Investment," The World Economy, Wiley Blackwell, vol. 29(8), pages 1091-1115, August.
    7. Joseph A Clougherty & Michał Grajek, 2008. "The impact of ISO 9000 diffusion on trade and FDI: A new institutional analysis," Journal of International Business Studies, Palgrave Macmillan;Academy of International Business, vol. 39(4), pages 613-633, June.
    8. David Godes & Dina Mayzlin, 2004. "Using Online Conversations to Study Word-of-Mouth Communication," Marketing Science, INFORMS, vol. 23(4), pages 545-560, June.
    9. Owen O'Donnell & Furio C. Rosati & Eddy van Doorslaer, 2005. "Health effects of child work: Evidence from rural Vietnam," Journal of Population Economics, Springer;European Society for Population Economics, vol. 18(3), pages 437-467, September.
    10. Dasgupta, Susmita & Laplante, Benoit & Namingi, Nlandu & Hua Wang, 2000. "Industrial environmental performance in China - the impact of inspections," Policy Research Working Paper Series 2285, The World Bank.
    11. Anindya Ghose & Panagiotis G. Ipeirotis & Beibei Li, 2014. "Examining the Impact of Ranking on Consumer Behavior and Search Engine Revenue," Management Science, INFORMS, vol. 60(7), pages 1632-1654, July.
    12. Leah Comment & Brent A. Coull & Corwin Zigler & Linda Valeri, 2022. "Bayesian data fusion: Probabilistic sensitivity analysis for unmeasured confounding using informative priors based on secondary data," Biometrics, The International Biometric Society, vol. 78(2), pages 730-741, June.
    13. Gao, Chuanming & Lahiri, Kajal, 2000. "Further consequences of viewing LIML as an iterated Aitken estimator," Journal of Econometrics, Elsevier, vol. 98(2), pages 187-202, October.
    14. Jacob, Arun, 2017. "Mind the Gap: Analyzing the Impact of Data Gap in Millennium Development Goals’ (MDGs) Indicators on the Progress toward MDGs," World Development, Elsevier, vol. 93(C), pages 260-278.
    15. Livanis, Grigorios T. & Moss, Charles B. & Breneman, Vincent E. & Nehring, Richard F., 2005. "Urban Sprawl and Farmland Prices," Working Papers 15657, University of Florida, International Agricultural Trade and Policy Center.
    16. Jyoti Prasad Mukhopadhyay & Nilanjan Banik, 2013. "The interplay between growth and development: evidence from Indian districts," Asia-Pacific Development Journal, United Nations Economic and Social Commission for Asia and the Pacific (ESCAP), vol. 20(2), pages 109-127, December.
    17. Emma Gearon & Anna Peeters & Winda Ng & Allison Hodge & Kathryn Backholer, 2018. "Diet and physical activity as possible mediators of the association between educational attainment and body mass index gain among Australian adults," International Journal of Public Health, Springer;Swiss School of Public Health (SSPH+), vol. 63(7), pages 883-893, September.
    18. He, Xi & Lopez, Rigoberto & Liu, Yizao, 2015. "Substitution between Online and Offline Advertising: Evidence from the Carbonated Soft Drink Industry," Working Paper series 290109, University of Connecticut, Charles J. Zwick Center for Food and Resource Policy.
    19. Hayden Stewart & David E. Davis, 2005. "Price Dispersion and Accessibility: A Case Study of Fast Food," Southern Economic Journal, John Wiley & Sons, vol. 71(4), pages 784-799, April.
    20. Rajiv D. Banker & Joy M. Field & Kingshuk K. Sinha, 2001. "Work-Team Implementation and Trajectories of Manufacturing Quality: A Longitudinal Field Study," Manufacturing & Service Operations Management, INFORMS, vol. 3(1), pages 25-42, November.

    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:84:y:2019:i:3:d:10.1007_s11336-019-09670-9. 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.