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

[Cameron McIntosh <cnm100@hotmail.com>]

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.http://www.ncbi.nlm.nih.gov/pubmed/21163849
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.http://arxiv.org/PS_cache/arxiv/pdf/1109/1109.1070v1.pdf
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. http://ftp.cs.ucla.edu/pub/stat_ser/r363.pdf
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.http://ftp.cs.ucla.edu/pub/stat_ser/r379.pdf
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.http://ftp.cs.ucla.edu/pub/stat_ser/r389.pdf
Gerring, J. (2010). Causal Mechanisms: Yes, But… Comparative Political Studies, 43(11), 1499-1526.http://sws1.bu.edu/jgerring/documents/CausalMechanisms.pdf
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.http://vote.research.yale.edu/pl504/mediation_psychology%205-2-09.pdfhttp://supp.apa.org/psycarticles/supplemental/psp_98_4_550/mediation_psychology_appendix.pdfhttp://bullock.research.yale.edu/papers/mediation_JPSP_appendix.pdf
Albert, J.M., & Nelson, S. (2011). Generalized Causal Mediation Analysis. Biometrics, 67(3), 1028-1038.http://onlinelibrary.wiley.com/doi/10.1111/j.1541-0420.2010.01547.x/fullhttp://www.biometrics.tibs.org/datasets/090828M_FINAL_supp_materials.pdf
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. http://www.bepress.com/ijb/vol7/iss1/16
VanderWeele, T.J.,  & Vansteelandt, S. (2009). Conceptual issues concerning mediation, interventions and composition. Statistics and Its Interface, 2, 457–468.http://www.math.mcgill.ca/~dstephens/dokuwiki/lib/exe/fetch.php?media=vanderweele_effect_decomposition_stats_interface_2009.pdf
VanderWeele, T.J. (2011). Controlled Direct and Mediated Effects: Definition, Identification and Bounds. Scandinavian Journal of Statistics, 38(3), 551–563. http://onlinelibrary.wiley.com/doi/10.1111/j.1467-9469.2010.00722.x/suppinfohttp://onlinelibrary.wiley.com/store/10.1111/j.1467-9469.2010.00722.x/asset/supinfo/SJOS_722_sm_AppendixS1.pdf?v=1&s=25efa14aa51c9a7d90ef2180a24c14a408f58e56
Glynn, A.N. (May 11, 2011). The Product and Difference Fallacies for Indirect Effects. http://scholar.harvard.edu/aglynn/files/mechanisms.pdf
Glynn, A.N. (July 14, 2008).Estimating and Bounding Mechanism Specific Causal Effectshttp://polmeth.wustl.edu/media/Paper/mse.pdf
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.http://www.personal.psu.edu/ljk20/mediationP.pdfhttp://dvn.iq.harvard.edu/dvn/dv/dtingley/faces/study/StudyPage.xhtml?studyId=71336&versionNumber=1
Imai, K., Keele, L., & Tingley, D. (2010). A general approach to causal mediation analysis. Psychological Methods, 15(4), 309-334.http://imai.princeton.edu/research/files/BaronKenny.pdf
Imai, K., Keele, L., & Yamamoto, T. (2010a). Identification, Inference and Sensitivity Analysis for Causal Mediation Effects. Statistical Science, 25(1), 51-71.http://imai.princeton.edu/research/files/mediation.pdf
Imai, K., Keele, L., & Yamamoto, T. (2010b). Replication data for: Identi?cation, inference, and sensitivity analysis for causal mediation effects. Available at http://hdl.handle.net/1902.1/14412.
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).http://imai.princeton.edu/research/files/mediationR.pdfhttp://cran.r-project.org/web/packages/mediation/vignettes/mediation.pdf
Keele, L., Tingley, D., Yamamoto, T., & Imai, K. (August 21, 2011). Package ‘mediation’: R Package for Causal Mediation Analysis, Version 3.1.http://cran.r-project.org/web/packages/mediation/mediation.pdfhttp://cran.r-project.org/web/packages/mediation/index.html
Tingley, D. (June 18, 2011). MEDIATION: Stata module for causal mediation analysis and sensitivity analysis.http://ideas.repec.org/c/boc/bocode/s457294.htmlhttp://scholar.harvard.edu/dtingley/files/mediationstata.pdf
Imai, K., Tingley, D., & Yamamoto, T. (Draft of August 10, 2011). Experimental designs for identifying causal mechanisms.http://imai.princeton.edu/research/files/Design.pdf
Imai, K., & Yamamoto, T. (Draft of June 29, 2011). Sensitivity analysis for causal mediation effects under alternative exogeneity assumptions.  http://imai.princeton.edu/research/files/medsens.pdf
Cam
> Date: Sat, 12 Nov 2011 17:24:13 +0100
> From: John.Antonakis@unil.ch
> To: statalist@hsphsun2.harvard.edu
> 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. 
> http://www.hec.unil.ch/jantonakis/Causal_Claims.pdf
> 
> 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
> http://www.hec.unil.ch/people/jantonakis
> 
> 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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