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

 From John Antonakis To statalist@hsphsun2.harvard.edu Subject Re: reL Re: st: Interpreting mediation model sobel goodman test Date Sat, 12 Nov 2011 17:24:13 +0100

```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
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
__________________________________________

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
>
> From: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of John
> Antonakis
> Sent: Tuesday, October 18, 2011 12:11 PM
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: Interpreting mediation model sobel goodman test
>
> 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)
>
> 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)
>
>
> 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
> __________________________________________
>
>
> 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
>
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```