Index of moderated mediation - application & interpretation

Questions about the implementation and application of the PLS-SEM method, that are not related to the usage of the SmartPLS software.
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Leho
PLS Junior User
Posts: 5
Joined: Mon Nov 27, 2017 11:38 am
Real name and title: Holger Leuveld

Index of moderated mediation - application & interpretation

Post by Leho »

Dear all,

also this forum has already discussed moderated mediation (e.g. Topic: „Hayes index of moderated mediation“), I am still wondering about the application and interpretation of modelling moderated mediation in SmartPLS.

As you can see in the model below, there are two mediation effects but only the moderated mediation (A->D->E) is of further interest here. In this case, the direct effect (A -> E) is statistically significant at p<0.001 with a direct path coefficient of 0.404. The indirect effect is not significant at p<0.1 with a specific indirect effect of 0.031; the total effect is about 0.434.

The calculation of a moderated mediation can be done by the index of moderated mediation, developed by Hayes (2015) in Multivariate Behavioral Research. The index of Hayes is calculated by

w=p1 x p2 + p2 x p5 x M

(see Hayes, 2015, p 4; also Hair et al., A primer… (2017), p 260).

The used moderator is continuous. It was argued in this forum, if the moderating effect is significant (in the case below Mod. HxA -> D-> E), a moderated mediation is supported for the case, that the moderation occurs between the independent variable and the mediator variable (see e.g. Topic: „Index of moderated mediation“), even if p2 x p5 is only the quantification of the effect of the modertor (as part of the second term of the index). The specific indirect moderating effect Mod. HxA -> D -> E is about 0.033 and significant at p<0.05, calculated via a two stage approach.

Am I right if I argue that under the described condition, the first term of the moderated mediation index of Hayes is not relevant because we know, there is a significant moderating effect? Therefore the (insignificant) path coefficients for the mediation (A->D->E) represent those at an average moderator level!? Also, I argue that it is a mediation because of the significance of the moderator; with respect to Zhao et al. (2010), even the indirect is not significant, because of the indirect effect of Mod. HxA -> D-> E, there is a mediation effect!?

Is it also plausible if I argue, that the moderation effect about 0.146 with a f2 of 0.027 is quite strong, means an increase by one standard deviation of Mod. HxA leads to an increase by + 0.146 for the relation A->D. However, the indirect path (A->D->E) is only marginally (even significantly) effected by an increase about 0.033, at an increase of one standard deviation at Mod. HxA?

I would be very lucky for your comments!

Best regards!
LeHo
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