Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2025-01-05T14:24:33.907Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  01 January 2025

Kai Wang Open the ORCID record for Kai Wang [Opens in a new window]
Kai Wang*
Affiliation:
The University of Iowa
*
Correspondence should bemade to Kai Wang, Department of Biostatistics, College of Public Health, The Universityof Iowa, Iowa City, IA 52242, USA. Email: [email protected]
Get access Rights & Permissions [Opens in a new window]

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.

Keywords

full-information likelihoodestimationidentificationmediation analysissensitivity analysis
Type
Original Paper
Information
Psychometrika , Volume 84 , Issue 3 , September 2019 , pp. 719 - 748
Copyright
Coyright © 2019 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Albert, J. M., & Wang, W. (2014). Sensitivity analyses for parametric causal mediation effect estimation. Biostatistics, 16 (2), 339–351.CrossRefGoogle ScholarPubMed
Arellano, M. (1989). An efficient GLS estimator of triangular models with covariance restrictions. Journal of Econometrics, 42 (2), 267–273.CrossRefGoogle Scholar
Baron, R. M., & Kenny, D. A (1986). The moderator–mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. Journal of Personality and Social Psychology, 51 (6), 1173–1182.CrossRefGoogle ScholarPubMed
Brito, C., & Pearl, J. (2002). A new identification condition for recursive models with correlated errors. Structural Equation Modeling, 9 (4), 459–474.CrossRefGoogle Scholar
Cotterman, R. F. (1981). A note on the consistency of the GLS estimator in triangular structural systems. Econometrica, 49 (6), 1589–1591.CrossRefGoogle Scholar
Cox, D. R. Planning of experiments, (1958). New York: Wiley.Google Scholar
Ding, P., & Vanderweele, T. J (2016). Sharp sensitivity bounds for mediation under unmeasured mediator-outcome confounding. Biometrika, 103 (2), 483–490.CrossRefGoogle ScholarPubMed
Drton, M.Eichler, M., & Richardson, T. S (2009). Computing maximum likelihood estimates in recursive linear models with correlated errors. Journal of Machine Learning Research, 10, 2329–2348.Google Scholar
Greene, W. H. Econometric analysis, (1993). 2 New York: Macmillan Publishing Company.Google Scholar
Imai, K.Keele, L., & Tingley, D. (2010). A general approach to causal mediation analysis. Psychological Methods, 15 (4), 309–334.CrossRefGoogle ScholarPubMed
Imai, K.Keele, L.Tingley, D., & Yamamoto, T. (2010). Causal mediation analysis using R. Advances in social science research using R, Berlin: Springer. 129–154.CrossRefGoogle Scholar
Imai, K.Keele, L., & Yamamoto, T. (2010). Identification, inference and sensitivity analysis for causal mediation effects. Statistical Science, 25 (1), 51–71.CrossRefGoogle Scholar
Lahiri, K., & Schmidt, P. (1978). On the estimation of triangular structural systems. Econometrica, 46, 1217–1221.CrossRefGoogle Scholar
le Cessie, S. (2016). Bias formulas for estimating direct and indirect effects when unmeasured confounding is present. Epidemiology, 27 (1), 125–132.CrossRefGoogle ScholarPubMed
MacKinnon, D. P. Introduction to statistical mediation analysis, (2008). New York: Taylor & Francis.Google Scholar
Preacher, K. J., & Hayes, A. F (2004). SPSS and SAS procedures for estimating indirect effects in simple mediation models. Behavior Research Methods, Instruments, & Computers, 36 (4), 717–731.CrossRefGoogle ScholarPubMed
Prucha, I. R. (1987). The variance–covariance matrix of the maximum likelihood estimator in triangular structural systems: Consistent estimation. Econometrica, 55 (4), 977–978.CrossRefGoogle Scholar
VanderWeele, T. Explanation in causal inference: Methods for mediation and interaction, (2015). New York: Oxford University Press.Google Scholar
VanderWeele, T. J., & Chiba, Y. (2014). Sensitivity analysis for direct and indirect effects in the presence of exposure-induced mediator-outcome confounders. Epidemiology, Biostatistics, and Public Health, 11 (2), e9027.Google ScholarPubMed
VanderWeele, T. J., & Vansteelandt, S. (2009). Conceptual issues concerning mediation, interventions and composition. Statistics and Its Interface, 2 (4), 457–468.CrossRefGoogle Scholar
Zellner, A. (1962). An efficient method of estimating seemingly unrelated regressions and tests for aggregation bias. Journal of the American Statistical Association, 57 (298), 348–368.CrossRefGoogle Scholar