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Re: st: Mediating variables


From   Alan Acock <acock@mac.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Mediating variables
Date   Sun, 05 Oct 2008 15:47:23 -0700

Jaime Gómez,
If you have access to an SEM program such as Mplus, it is very easy to
estimate this model correctly, i.e., allowing the residual for the mediators
to be correlated. Mplus also provides a test of the indirect effect for each
linkage. When people estimated these models without correlating the errors
between the mediating variables, they were effectively assuming that the
exogenous variable explained all of the correlation between them. In other
words they were assuming that the partial correlation between r and s, r and
t, and s and t are all zero when controlling for x. This is an unreasonable
assumption/miss specification in most models.

Alan Acock


On 10/5/08 1:33 PM, "Jaime Gómez" <jaime.gomez@unizar.es> wrote:Jaime Gómez

> Thanks for your quick answer.
> Yes, x predicts three mediators. They, in turn, predict y. Following Baron
> and Kenny (1986) I want to see whether the introduction of one of the
> mediators ("r") in the equation that expresses the relationship between "x"
> and "y" changes the value or the significance of the coefficient
> accompanying "x". This is the reason why the predictor ("x") is introduced
> in all the equations of the system.
> Ideally, I would need to introduce the three mediators in my main equation,
> but I am only focusing on one of them ("r"). In a paper by Shaver (2005) it
> is suggested that 2SLS should be used to account for the correlation among
> the errors. My doubts are:
> 1. I do not know whether omitting the other two mediators ("s" and "t") can
> cause a problem and, in that case, I am looking for an econometric solution
> 2. I have data panel data: on different firms and for different years for
> "x", "y" and "r"; I know that Stata gives you the possibility of estimating
> an instrumental variables estimation with fixed effects, for example, but I
> do not know whether this (or other alternatives) makes sense in this
> context. In other words, even if 2SLS were the right procedure for
> cross-section data, I do not know whether it would be the best alternative
> in the presence of panel data
> Thanks
> Jaime Gómez
> Universidad de Zaragoza
> 
> Baron, R.M. and 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, 1173-1182
> 
> Shaver, J.M. (2005) "Testing for Mediating Variables in Management Research:
> Concerns, Implications, and Alternative Strategies", Journal of Management,
> 31 (3), 330-353
> 
> 
> 
> -----Mensaje original-----
> De: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu] En nombre de John Antonakis
> Enviado el: domingo, 05 de octubre de 2008 21:06
> Para: statalist@hsphsun2.harvard.edu
> Asunto: Re: st: Mediating variables
> 
> If I understand your question correctly (from your first sentence), x
> predicts three mediators, which in term predict y.
> 
> This system is not identified for 2sls or 3sls analysis (you need at
> least as many IVs as you have mediators).
> 
> You could estimate it using mvreg or sureg (and then request whether
> errors are correlated like this):
> 
> sureg (y = r s t ) (r s t = x), corr
> 
> note: corr will give you a Breusch-Pagan test of independence (for the
> residuals)--a Hausman test will not help you here.
> 
> However, the above is not a strong test.
> 
> I am not following what you state regarding the panel structure.
> 
> HTH,
> John.
> 
> ____________________________________________________
> 
> Prof. John Antonakis
> Associate Dean 
> Faculty of Business and Economics
> 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&cl=en
> ____________________________________________________
> 
> 
> 
> Jaime Gómez wrote:
>> Dear Stata users
>> I have a model in which the relationship between a predictor ³x² and an
>> outcome ³y² is mediated by three factors (³r², ³s² and ³t²). I am only
> able
>> to test whether one of the predictors (³r²) mediates the relationship
>> between ³x² and ³y² (I only have data on this mediating variable and I
>> cannot get data on the other two). I would like to implement Baron and
> Kenny
>> (1986)¹s test for mediation. At least, this involves estimating the
>> following system:
>> Y=a1+b*r+c*x+epsilon1
>> r=a2+d*x+epsilon2
>> Given that the errors of the two equations are potentially correlated, it
>> has been suggested that a 2SLS approach should be used. I have seen  that
>> this could be done with ivregress, provided that I can find data on at
> least
>> one variable that affects ³r² and does not affect ³y². My doubts are the
>> following:
>> 1) Given that I have a triangular system, do I have to use the
>> traditional approach implemented by ivregress or the ³modified² proposed
> in
>> http://www.stata.com/support/faqs/stat/ivr_faq.html ? Are both valid?
>> 2) How do I test for the hypothesis that the errors are correlated? I
>> have seen that the use of a Hausman test is suggested in the literature,
> but
>> I do not know how to implement this in Stata (specially in the case I use
>> the ³modified² approach)
>> 3) Given that I have panel data, could I take advantage of the panel
>> structure of my data to correct for the fact that I do not have
> information
>> on two of the mediating variables (³s² and ³t²)? Is there a procedure in
>> Stata for that?
>> Thanks a lot 
>> Jaime Gómez
>> Universidad de Zaragoza
>> 
>> 
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