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RE: st: Mediating variables


From   Jaime Gómez <jaime.gomez@unizar.es>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: Mediating variables
Date   Mon, 6 Oct 2008 15:02:17 +0200

Thanks John
In fact, looking at my data I have information on one more variable, "q",
that could be used to estimate "r". This variable "q" is directly linked to
"r" in the literature (it is a predictor of "r"), but does not have a direct
relationship with "y". If I understand you correctly, this should allow me
to obtain an estimation for r that could be introduced in my main equation,
perhaps using "ivreg". In any case, I still do not know whether this solves
the problem of not having data on the other two mediators (intuitively, I
imagine that if "s" and "t" are not introduced as mediators, this could
create correlation between the error term of my main equation and the
predictor "x", given that "x" is also a predictor of "s" and "t"). From your
answer, I assume that the panel structure of the data is of no use in this
context. Is that ok?
Thank you very much.
Jaime Gómez
Universidad de Zaragoza

-----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 22:58
Para: statalist@hsphsun2.harvard.edu
Asunto: Re: st: Mediating variables

OK...then just estimate

sureg (y = r s t x) (r s t = x), corr

est store mediators

sureg (y = x) (r s t = x), corr

hausman mediators, equations(1:1)

If the Hausman test is undefined, do it by hand (Wooldridge has the
formulas).

Note: you want tosee if x drops when introducing r s t.

I am just showing you the mechanics of how to run the tests. Again, I would
feel better running a 2sls or reg3 model; but you need to have more
instruments (not just x) to estimate this.

Best,
J.

____________________________________________________

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:
> 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 “x” and an
>> outcome “y” is mediated by three factors (“r”, “s” and “t”). I am only
>>     
> able
>   
>> to test whether one of the predictors (“r”) mediates the relationship
>> between “x” and “y” (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)’s 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 “r” and does not affect “y”. 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 “modified” 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 “modified” 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 (“s” and “t”)? Is there a procedure in
>> Stata for that?
>> Thanks a lot 
>> Jaime Gómez
>> Universidad de Zaragoza
>>
>>
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