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RE: reL Re: st: Interpreting mediation model sobel goodman test

From   Cameron McIntosh <>
Subject   RE: reL Re: st: Interpreting mediation model sobel goodman test
Date   Sat, 12 Nov 2011 15:12:05 -0500

Hi Ariel,
John's response is part of the iceberg (not necessarily only the tip, perhaps somewhere nearer the foundation) that is showing the deficiencies in the traditional statistical approaches to mediation. There is a large literature on causal mediation that you really should look into: 
Ten Have, T.R., & Joffe, M. (2010). A review of causal estimation of effects in mediation analyses. Statistical Methods in Medical Research, Epub ahead of print.
Small, D.S. (September 7, 2011). Mediation Analysis Without Sequential Ignorability: Using Baseline Covariates Interacted with Random Assignment as Instrumental Variables.Philadelphia, PA: Department of Statistics, The Wharton School of the University of Pennsylvania.
Pearl, J. (2011a). The mediation formula: A guide to the assessment of causal pathways in non-linear models. Tech. Rep. R-363. Los Angeles, CA: Department of Computer Science, University of California. To appear in C. Berzuini, P. Dawid, and L. Bernardinelli (Eds.), Causality: Statistical Perspectives and Applications. Forthcoming, 2011.
Pearl, J. (2011b). The Causal Mediation Formula – A Guide to the Assessment of Pathways and Mechanisms. Tech. Rep. R-363. Los Angeles, CA: Department of Computer Science,University of California. Forthcoming, Preventive Science.
Judea Pearl and possibly others. (November, 2011).  Interpretable conditions for identifying natural direct effects. Technical Report R-389. Los Angeles, CA: Department of Computer Science, UCLA.
Gerring, J. (2010). Causal Mechanisms: Yes, But… Comparative Political Studies, 43(11), 1499-1526.
Bullock J.G., Green, D.P., & Han, S.E. (2010). Yes, but what's the mechanism? (don't expect an easy answer). Journal of Personality and Social Psychology, 98(4), 550-558.
Albert, J.M., & Nelson, S. (2011). Generalized Causal Mediation Analysis. Biometrics, 67(3), 1028-1038.
Shpitser, I., & VanderWeele, T.J. (2011). A Complete Graphical Criterion for the Adjustment Formula in Mediation Analysis. The International Journal of Biostatistics, 7(1), Article 16.
VanderWeele, T.J.,  & Vansteelandt, S. (2009). Conceptual issues concerning mediation, interventions and composition. Statistics and Its Interface, 2, 457–468.
VanderWeele, T.J. (2011). Controlled Direct and Mediated Effects: Definition, Identification and Bounds. Scandinavian Journal of Statistics, 38(3), 551–563.
Glynn, A.N. (May 11, 2011). The Product and Difference Fallacies for Indirect Effects.
Glynn, A.N. (July 14, 2008).Estimating and Bounding Mechanism Specific Causal Effects
Imai, K., Keele, L., Tingley, D., & Yamamoto, T. (2011). Unpacking the Black Box of Causality: Learning about Causal Mechanisms from Experimental and Observational Studies. Forthcoming in American Political Science Review.
Imai, K., Keele, L., & Tingley, D. (2010). A general approach to causal mediation analysis. Psychological Methods, 15(4), 309-334.
Imai, K., Keele, L., & Yamamoto, T. (2010a). Identification, Inference and Sensitivity Analysis for Causal Mediation Effects. Statistical Science, 25(1), 51-71.
Imai, K., Keele, L., & Yamamoto, T. (2010b). Replication data for: Identi?cation, inference, and sensitivity analysis for causal mediation effects. Available at
Imai, K., Keele, L., & Tingley, D., & Yamamoto, T. (2010). Causal Mediation Analysis Using R. In H. D. Vinod (Ed.), Advances in Social Science Research Using R (pp. 129-154). New York: Springer (Lecture Notes in Statistics).
Keele, L., Tingley, D., Yamamoto, T., & Imai, K. (August 21, 2011). Package ‘mediation’: R Package for Causal Mediation Analysis, Version 3.1.
Tingley, D. (June 18, 2011). MEDIATION: Stata module for causal mediation analysis and sensitivity analysis.
Imai, K., Tingley, D., & Yamamoto, T. (Draft of August 10, 2011). Experimental designs for identifying causal mechanisms.
Imai, K., & Yamamoto, T. (Draft of June 29, 2011). Sensitivity analysis for causal mediation effects under alternative exogeneity assumptions.
> Date: Sat, 12 Nov 2011 17:24:13 +0100
> From:
> To:
> Subject: Re: reL Re: st: Interpreting mediation model sobel goodman test
> Hi:
> In the case of the following code:
> clear
> set seed 123
> set obs 1000
> gen x = rnormal()
> gen e = rnormal()
> gen m = e + .5*x + rnormal()
> gen y = .5*m - e + rnormal()
> reg3 (y = m) (m = x), 2sls
> nlcom [m]x*[y]m
> sgmediation y, mv(m) iv(x)
> What you want is not possible; to be clear once more, what you want is 
> what sgmediation gives. However, it cannot recover the correct indirect 
> effect because m is endogenous. One needs to instrument m with x so one 
> cannot regress y on x and control for m because both the coefficients of 
> x and m will be biased (because m is endogenous and this endogeneity 
> problem will be transmitted to x because x and m correlate). See the 
> discussion around Figure 1C and Section 3.1.1 regarding omitting a 
> regressor (in this case "e") in the following paper to get a handle on 
> the problem:
> Antonakis, J., Bendahan, S., Jacquart, P., & Lalive, R. (2010). On 
> making causal claims: A review and recommendations. The Leadership 
> Quarterly, 21(6). 1086-1120. 
> When using 2SLS the direct effect of x on y is simply the reduced form 
> of the model:
> reg y x
> This gives a coefficient of .2373032, which is the same as the indirect 
> effect. It is not possible to get what you want when the mediator is 
> endogenous.
> HTH,
> John.
> __________________________________________
> Prof. John Antonakis
> Faculty of Business and Economics
> Department of Organizational Behavior
> University of Lausanne
> Internef #618
> CH-1015 Lausanne-Dorigny
> Switzerland
> Tel ++41 (0)21 692-3438
> Fax ++41 (0)21 692-3305
> Associate Editor
> The Leadership Quarterly
> __________________________________________
> On 10.11.2011 16:56, Ariel Linden, DrPH wrote:
>  > Hi John,
>  >
>  > While this is a relatively old thread (in statalist time a month is 
> like a
>  > century), I am revisiting your code below and have a question. In your
>  > -reg3- equation and subsequent nlcom, you recover the "total effect". How
>  > would you recover the direct and indirect effects using -reg3-?
>  >
>  > In a separate set of postings dated Feb 2009, Maarten laid out an 
> approach
>  > using -sureg-, but it doesn't appear that the thread ever came back to
>  > -reg3- . The primary issue here is that one would need to have an outcome
>  > model containing both the mediator (m) and treatment variable (x), in 
> order
>  > to derive the direct effect of x on y. The -reg3- model below for the
>  > outcome does not contain the x variable (x is treated as exogenous).
>  >
>  > Thanks
>  >
>  > Ariel

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