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# st: Re: Re: Re: FW: Mediation with endogenous mediator and endogenous independent variables

 From "A.M. Aranda Gutierrez" To "statalist@hsphsun2.harvard.edu" Subject st: Re: Re: Re: FW: Mediation with endogenous mediator and endogenous independent variables Date Thu, 20 Jun 2013 09:46:26 +0000

```Dear John,

Thank you for your help. I'm indeed taking into account the fact that the mediator is endogenous by using a 2sls instrumental variable estimator. The specific problem in the mediation model that I'm estimating is that there's simultaneity between the mediator and the dependent variable, and potentially between the independent variables and the mediator. Therefore, I'd like to use instruments not only for the mediator but also for the independent variables. I also estimated the models using reg3 but I'm not sure how robust the reg3 estimates are in small samples. In respect to SEM, does Stata offer an instrumental variable estimation as an alternative to the ML estimation?

I find the article you suggested to be quite useful, thanks!

Best,

Ana

>Hi:
>
>
>ivregress y c (x1 x2 m = z1 z2 z3), first r
>
>To establish mediation, if m is endogenous (you can see if m is endogenous by running "estat endog" postestimation) then you can only use z1, z2, z3, and c as instruments for m (with z1-z3 being the >excluded instruments). What you ask below makes no sense (to me). If you want to see the indirect effect precisely via a Sobel test, then move this into sem (or you could use reg3 if you wish to have >2sls estimates, though you can't combine -robust- with reg3 but you can bootstrap):
>
>sem (y<- c x1 x2 m) (x1 x2 m <- z1 z2 z3), covstructure(e._OEn, unstructured) vce(robust)
>
>To see what the coefficients are named, postestimation do:
>
>sem, coeflegent
>
>Then test what non-linear effects you want:
>
>nlcom _b[y:m]*_b[m:z1]
>nlcom _b[y:m]*_b[m:z1] + _b[y:m]*_b[m:z2] + _b[y:m]*_b[m:z3]
>etc.
>
>Hope this helps.
>
>J.
>
>P.S. if you wish take a look at:
>
>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
>
>We discuss the traditional Baron-Kenny method for testing mediation (or related procedures like Preacher-Hayes), who methods only work is the mediator is exogenous. I all other cases you must use an >instrumental variable estimator (via 2SLS or ML estimation).
>
>
>
>__________________________________________
>
>John Antonakis
>Professor of Organizational Behavior
>Director, Ph.D. Program in Management
>
>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 19.06.2013 12:47, A.M. Aranda Gutierrez wrote:
> Dear John,
>
> Thanks again for your help. I'm sorry my message is still unclear.
> I think you already gave an answer to my question, but  just to clarify,
> Are you suggesting me to interpret the impact of the independent variables on the mediator by looking at the impact of the instruments on the mediator? > In other words, if the instruments are strong, can I make a conclusion about the impact of the endogenous independent variables on the mediator by looking at the impact of the instruments on the mediator? > So, is it not possible for Stata to produce an output of m = c (x1 x2 x3 = z1 z2 z3) when using the ivregress 2sls command?
>
> Best,
>
> Ana
>
>
>
> *
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>Dear J,
>
>
>ivregress dep.var exogenous_variables (endogenous_indep._var1 endogenous_indep_var2 mediator = instruments), first r so, ivregress y c (x1 x2 m = z1 z2 z3), first r
>
>Thus, the first stage output shows three regressions:
>
>x1 = z1 z2 z3 c (the endogenous_indep._var1 on the instruments and controls)
>x2 = z1 z2 z3 c (the endogenous_indep._var2 on the instruments and controls) m = z1 z2 z3 c (the mediator on the instruments and controls)
>
>Now, I need to know the impact of the independent variables on the mediator in order to be able to test the second condition for mediation. However, with the current specification this is not possible. >Therefore, I'd like to know if there is a way in which I can instrument both the independent variables and the mediators and still be able to calculate the impact of the former on the latter. I hope it >is clear now, please let me know if you have any other questions. I really appreciate your help!
>
>Best,
>
>Ana
>
*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
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*   http://www.ats.ucla.edu/stat/stata/Dear J,

>Hi Ana:
>
>Can you show your equations and/or how you set up your model in ivregress? Then maybe your question will become clearer (it is unclear to me at this time).
>
>Best,
>J.
>
>__________________________________________
>
>John Antonakis
>Professor of Organizational Behavior
>Director, Ph.D. Program in Management
>
>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 18.06.2013 17:27, A.M. Aranda Gutierrez wrote:
>Dear Statalisters,
>
>I have a question regarding the interpretation of mediation models when using Stata's ivregress command. I am estimating a mediation model with 2 independent variables, 1 mediator, and 1 dependent >variable. Both the mediator and the independent variables are endogenous. Following  the paper titled "Testing for Mediating Variables in Management Research: Concerns, Implications, and Alternative >Strategies" [Shaver (2005), Journal of Management] I'm using the 2sls estimator. Now, the problem is that I need to know the impact of the independent variables on the mediator in order to check the 2nd >condition for mediation which states that the independent variables have to have an impact on the mediator. However, when using the ivregress command Stata reports the first stage results with the >endogenous variables regressed on the exogenous variables. In other words, the first stage reports three regressions: 2 for the independent variables and 1 for the mediator, but from the o!
utp!
>ut!
>   it is not possible to assess the impact of the independent variables (which are endogenous) on the mediator. Hence, my question is, how can I estimate a mediation model when both the independent >variables and the mediator are endogenous?
>
>
>Best regards,
>
>Ana
>
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```