Hello,
I have one question about testing moderated mediation analysis using Hayes (2015) index. The 2nd edition of Hair et al. PLS book recommended this method when testing moderated mediation relationships. However, they did not provide clear guidelines on how to do this in PLS.
I was wondering what is the best approach that I should follow when testing this type of relationship. Should I test the mediation and moderation together in the same model?, but again I have no clue about how to examine the whole moderated mediation relationship.
Or, should I use the PROCESS in SPSS to test such a relationship using Hayes index?
Best regards,
Abdulrahman
Hayes index of moderated mediation
 cringle
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Re: Hayes index of moderated mediation
Thanks. But in the book we explain how to compute the Hayes index using PLS results. The tricky part is to use the bootstrap results to compute the bootstrap outcomes of that index. Here, you need to use the SmartPLS Excel report and to manually compute things. But that's not super diffcult. A more important question is if you really want to run a moderated mediation and if you can corretly intpret the outcomes. These things are oftentimes extremely tricky. I never touched such complicated things in my own applications... Usually, the simpler the analysis, the better the results and their interpretation.
Best
Christian
Best
Christian
Prof. Dr. Christian M. Ringle, Hamburg University of Technology (TUHH), SmartPLS
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Re: Hayes index of moderated mediation
Dear Prof. Ringle,
Many thanks for your clarification.
Best regards,
Abdulrahman
Many thanks for your clarification.
Best regards,
Abdulrahman

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Re: Hayes index of moderated mediation
Hello, Abdulrahman. I'm as well study the issue of moderated mediation at the moment. However, I only have the 1st ed. of A Primer on Partial Least Squares, and thus have not idea how to manually compute the index. Could you please send me a ecopy of this section? I think the path coefficients can be retrieved from unstandardized path coefficient table, but CI computation still an unsolved problem.

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Re: Hayes index of moderated mediation
Actually, you don't need to compute the results manually, if you have a moderated mediation as depicted in the book in exhibit 7.19 (i.e., where the first part of the indirect effect is moderated). In this case, the index of moderated mediation by Hayes is simply the indirect effect of the interaction term (M*Y1) on the final dependent variable (Y3), because Haye’s index of moderated mediation is only the p2*p5 from the equation in the book (based on Exhibit 7.20) and not the p1*p2 part.
p2*p5 is the indirect effect of M*Y1 on Y3. You will get this result from the SmartPLS output and also it significance from the bootstrapping without any additional calculations.
It is more complicated if the moderation happens in the second part of the indirect effect because then you have to manually calculate the index using the first part of the indirect effect p1 times the interaction effect p5 (i.e., p1*p5), which will not be provided by standard PLS outputs.
p2*p5 is the indirect effect of M*Y1 on Y3. You will get this result from the SmartPLS output and also it significance from the bootstrapping without any additional calculations.
It is more complicated if the moderation happens in the second part of the indirect effect because then you have to manually calculate the index using the first part of the indirect effect p1 times the interaction effect p5 (i.e., p1*p5), which will not be provided by standard PLS outputs.
Dr. JanMichael Becker, University of Cologne, SmartPLS Developer
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Re: Hayes index of moderated mediation
Hi All
I want to know, how can I calculate moderated mediation in SmartPls3 for my thesis.
I have one IV (X) , two mediators (M1 and M2), one DV (Y) and one Moderator (W) in my model. My moderation hypotheses are second part (i.e., "the relationship between M and Y are moderated by W).
Need your support.
Regards
Muhammad Adnan Khurshid
PhD Student
I want to know, how can I calculate moderated mediation in SmartPls3 for my thesis.
I have one IV (X) , two mediators (M1 and M2), one DV (Y) and one Moderator (W) in my model. My moderation hypotheses are second part (i.e., "the relationship between M and Y are moderated by W).
Need your support.
Regards
Muhammad Adnan Khurshid
PhD Student

 SmartPLS Developer
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Re: Hayes index of moderated mediation
Lets only consider a single mediation. You can easily transfer the principle to multiple mediators using the specific indirect effects.
If your model is X > p1 > M > p2 > Y and X > p3 > Y and you have a moderator W which is moderating the relationship between M and Y. Therefoe you also have W*M > p4 > Y (i.e., p4 is the coefficient of the interaction effect)
The conditional indirect effect is in this case p1*(p2+p4*W) because p2+p4*W is the effect of M on Y accounting for a moderating effect of W.
This is equal to p1*p2+p1*p4*W. Therefore, similar to a normal moderation your moderated mediation effect is p1*p4. Hayes (2015) calls this the index of moderated mediation.
This is the one that you want to test for moderated mediation. The problem is that you need to calculate this effect on your own and then assess its significance using the Samples data form the path coefficient in the bootstrapping output to calculate pvalues or confidence intervals.
In general, the principal for this is similar as in Nitzl, C., Nitzl, C., Roldan, J. L., Roldan, J. L., Cepeda, G., & Cepeda, G. (2016). Mediation analysis in partial least squares path modeling: Helping researchers discuss more sophisticated models. Industrial management & data systems, 116(9), 18491864.
Hayes, A. F. (2015). An index and test of linear moderated mediation. Multivariate Behavioral Research, 50(1), 122.
If your model is X > p1 > M > p2 > Y and X > p3 > Y and you have a moderator W which is moderating the relationship between M and Y. Therefoe you also have W*M > p4 > Y (i.e., p4 is the coefficient of the interaction effect)
The conditional indirect effect is in this case p1*(p2+p4*W) because p2+p4*W is the effect of M on Y accounting for a moderating effect of W.
This is equal to p1*p2+p1*p4*W. Therefore, similar to a normal moderation your moderated mediation effect is p1*p4. Hayes (2015) calls this the index of moderated mediation.
This is the one that you want to test for moderated mediation. The problem is that you need to calculate this effect on your own and then assess its significance using the Samples data form the path coefficient in the bootstrapping output to calculate pvalues or confidence intervals.
In general, the principal for this is similar as in Nitzl, C., Nitzl, C., Roldan, J. L., Roldan, J. L., Cepeda, G., & Cepeda, G. (2016). Mediation analysis in partial least squares path modeling: Helping researchers discuss more sophisticated models. Industrial management & data systems, 116(9), 18491864.
Hayes, A. F. (2015). An index and test of linear moderated mediation. Multivariate Behavioral Research, 50(1), 122.
Dr. JanMichael Becker, University of Cologne, SmartPLS Developer
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Re: Hayes index of moderated mediation
Dear Prof. Becker
Thank you so much for the clarification.
Adnan
Thank you so much for the clarification.
Adnan