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Re: st: Interpreting mediation model sobel goodman test


From   John Antonakis <John.Antonakis@unil.ch>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Interpreting mediation model sobel goodman test
Date   Tue, 18 Oct 2011 21:11:28 +0200

Hi Meredith:

I assume you used the -sgmediation- package; I would not use this routine UNLESS your mediator is exogenous (and you are sure of this). If it is endogenous sgmedation will give you inconsistent estimates (it estimates the system of equations with OLS, and uses the dated Baron-Kenny methods); you do not tackle the endogeneity problem with sgmediation. You need to estimate your system of equations with an instrumental-variable estimator (e.g., 2SLS).

Take a look at this podcast, where I discuss this problem in detail:

Endogeneity: An inconvenient truth (full version) (about 32 minutes in length)
http://www.youtube.com/watch?v=dLuTjoYmfXs

If you just want the nitty gritty see:

Endogeneity: An inconvenient truth (for researchers)
(Excludes the "gentle introduction" content and discusses the two-stage least squares estimator straight away; about 16 minutes in length)
http://www.youtube.com/watch?v=yi_5M7oUceE

See also:

Antonakis, J., Bendahan, S., Jacquart, P., & Lalive, R. (submitted). Causality and endogeneity: Problems and solutions. In D.V. Day (Ed.), The Oxford Handbook of Leadership and Organizations.
http://www.hec.unil.ch/jantonakis/Causality_and_endogeneity_final.pdf

To understand exactly the nature of the problem run the following code, where x is endogenous with respect to y:

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)

From the above model, we have an instrument x, an endogenous regressor m, and omitted cause e, and a dependent variable y. We know that the indirect effect of x on y is .5*.5=.25. 2SLS recovers this parameter well (.24, p>.001). However, the sgmediation program gives .03 (and p = .04).


Now, let's rerun this to see when you'd get the same results with sgmediation (if x is exogenous with respect to y):

clear
set seed 123
set obs 1000
gen x = rnormal()
gen e = rnormal()
gen m = .5*x + rnormal()
gen y = .5*m + rnormal()
reg3 (y = m) (m = x), 2sls
nlcom [m]x*[y]m
reg3 (y = m) (m = x), ols
nlcom [m]x*[y]m
sgmediation y, mv(m) iv(x)

Notice that the 2SLS model is still consistent (but less efficient). The OLS estimator and sgmediation pretty much give the same estimates and standard errors.

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 18.10.2011 19:41, Meredith T. Niles wrote:
> Hello all,
>   I am working on running multiple and single mediation models to assess
> farmer climate change perceptions and potential adoption of climate
> change practices.  I am getting an odd result when running a Sobel
> goodman test in Stata with regards to the portion of total effect that
> is mediated (5.139).  Does anyone have any perspective on why this
> number is so large?  Running the same test with another set of climate
> change practices yields a proportion of total effect that is mediated at
> 0.79 which seems much more in line with other results I've seen.
>
>
> Sobel-Goodman Mediation Tests
>
>              Coef         Std Err     Z           P>|Z|
> Sobel       -.09959383    .05075882  -1.962      .04975096
> Goodman-1   -.09959383    .05217108  -1.909      .05626401
> Goodman-2   -.09959383    .04930612   -2.02      .04339293
>
> Indirect effect = -.09959383
>   Direct effect = .08021537
>    Total effect = -.01937846
>
> Proportion of total effect that is mediated:  5.1394091
> Ratio of indirect to direct effect:      -1.2415804
>
>
> Thanks for your thoughts.
>
> Best,
> Meredith Niles
>
>
> PhD Candidate, Graduate Group in Ecology
> NSF REACH IGERT Trainee
> Deputy External Chair, Graduate Student Association
> University of California, Davis
> 2126 Wickson
> http://environmentalpolicy.ucdavis.edu
>
>
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