how to interpret the effect of mediators in smartPLS?

[staythirsty]

Dear all,

My research model has to mediators. How to interpret or validate the effects of mediations is my question. I mean, I want to know whether relationships between two independent variables and one dependent variable in my model are fully or partially mediated by the mediators. Is it enough to notify the significance of each path (i.e., IVs -> M, M -> DV, IVs -> DV)? Is there any of more rigorious approach to validate the mediating effects?

I have read some postings about direct, indirect, total effect. Is this approach also one of the things I have to follow to get mediating effect analysis done? Also, regarding Baron and Kenny approach for mediation test, is it just enough to notify my research model fits with the conditions in each step? Lastly, would you please give me more knowledge about peudeo F statistic for mediating effect testing?

Sorry for this stupid question..

Thanks you very much in advance

[kuperbeigo]

I think an easy way to look at this is to compare the path weights of model 1 (assumed full mediation) with those of model 2 (no-mediation, i.e. only direct paths from IVs) and with those of model 3 (partial mediation with both direct paths and indirect path through mediator M), as recently illustrated by Guenzi et al. (2009):

Guenzi, P., Georges, L. & Pardo, C. (2009) The impact of strategic account managers' behaviors on relational outcomes: An empirical study. Industrial Marketing Management, 38 , pp 300-11.

As I understand (please correct me if I am wrong):
1. If the original significant direct path from IV to DV in model 2 becomes insignificant in model 3, while the path from M to DV still significant, then it is full mediation.
2. If the original significant path from the same IV to DV in model 2 remains significant but the path from M to DV becomes insignificant, then there is no mediation.
3. If the original significant path from an IV to DV remains significant but lower, and the path from M to DV remains significant (most likely lower), then there is partial mediation.

Of course in your model, there might be support for partial mediation for IV1 and possibly a support for full mediation fro IV2, or any other combination.

As for total effect, according to my understanding also:

1. we consider the indirect effect when we have a full mediation model, i.e. we try to assess which of the two IVs has more influence on DV via the mediator M. (of course in model 1, there are only indirect paths from IVs to DV)
2. we consider the total effect when we have a partial mediation, again to compare which IVs has more influence considering both direct and indirect effects on DV. (of course in model 3, we have both direct and indirect paths from IVs to DV)

again, if I am wrong, please correct me.

[elianacarraca]

I think an easy way to look at this is to compare the path weights of model 1 (assumed full mediation) with those of model 2 (no-mediation, i.e. only direct paths from IVs) and with those of model 3 (partial mediation with both direct paths and indirect path through mediator M), as recently illustrated by Guenzi et al. (2009):

Guenzi, P., Georges, L. & Pardo, C. (2009) The impact of strategic account managers' behaviors on relational outcomes: An empirical study. Industrial Marketing Management, 38 , pp 300-11.

As I understand (please correct me if I am wrong):
1. If the original significant direct path from IV to DV in model 2 becomes insignificant in model 3, while the path from M to DV still significant, then it is full mediation.
2. If the original significant path from the same IV to DV in model 2 remains significant but the path from M to DV becomes insignificant, then there is no mediation.
3. If the original significant path from an IV to DV remains significant but lower, and the path from M to DV remains significant (most likely lower), then there is partial mediation.

Of course in your model, there might be support for partial mediation for IV1 and possibly a support for full mediation fro IV2, or any other combination.

As for total effect, according to my understanding also:

1. we consider the indirect effect when we have a full mediation model, i.e. we try to assess which of the two IVs has more influence on DV via the mediator M. (of course in model 1, there are only indirect paths from IVs to DV)
2. we consider the total effect when we have a partial mediation, again to compare which IVs has more influence considering both direct and indirect effects on DV. (of course in model 3, we have both direct and indirect paths from IVs to DV)

again, if I am wrong, please correct me.

I usually test mediation, using only two models... I also don't know if that is correct! One model including Iv -> DV, and a second model including direct and indirect effects between Iv and DV, via M. From this second output, I get IV - M, M - DV, and also IV - DV (controlling for the presence of M). I believe is similar to the way you described.

I have a question regarding one of your comments...
"2. If the original significant path from the same IV to DV in model 2 remains significant but the path from M to DV becomes insignificant, then there is no mediation. "

In the model I am testing, I obtained something like this... when I added was testing model 2 (both direct and indirect effects), the path between M and DV was no longer significant.... How should I interpret this result? Does it mean that IV has an independent effect on DV, so strong that it conceals M effect on DV, that was also previously significant?

Please help me here!!!

Eliana

[nuttmeg]

I have a question regarding mediation and indirect effects. It seems to be a relevant thread to post it. Let me first emphasize that I have no formal education in statistics, all I know about PLS and path modeling in general is something I taught myself (probably many other people here are like that).

The thing I am puzzled about is that all that the (covariance-based) SEM books say about direct and indirect effects is how to calculate them and the total effect. So they present the simple classic model with an IV, DV, and a mediating variable. They identify which path is the direct effect and which is the indirect one. Usually the example that is present involves only significant paths (a, b, c), and conclude that IV has an indirect effect on DV equivalent to a*b and explain that if IV increases M also increases and part of it is passed on to DV. Nothing is said about testing for mediation (like the analytical process you guys have been discussing here).

Their treatment of the issue seems to suggest that all you have to do is read off the path coefficients and do the maths to get to indirect and total effects.

I have a model with a single DV (knowledge for sustainability) and four other variables. One is directly connected to DV as a predictor (diversity of social network), and two other variables (organizational centralization and organizational trust) are mediated by the forth variable (learning culture).
All paths are significant.

If I followed CB-SEM books, I would say--based on significant paths--that organizational centralization and organizational trust has an indirect effect on my DV. I would calculate indirect effects A*D and B*D.

However, following the lead in the PLS literature (e.g. articles cited here), I would want to test if learning culture is really a mediating variable. As it turns out organizational centralization is not a significant predictor of my DV if I test the direct effects model (omitting learning culture from the model). I should conclude then--as the path between centralization and knowledge for sustainability is not significant--that there is not any kind of mediation (neither full nor partial). But then what is it that I have it in my picture above? How should I interpret it? I mean path A is fairly large, so is D. Should I just say that organizational centralization has a substantial impact on learning culture and at the same time learning culture has a substantial impact on knowledge for sustainability, but the impact of organizational centralization is not passed on to knowledge for sustainability? I guess, then, that calculating A*D would not make sense, right? But then why do SEM books make the reader believe that the calculation of indirect effects is ok in every case?

By the way, organizational centralization has a significant zero-order correlation with knowledge for sustainability. Does this make any difference? I am uncertain about this.

Thanks for any hints in advance.

Csaba-

---UPDATE-----
I went on reading and in the "Advanced SEM Topics and PLS" chapter of Hair et al's "Multivariate Data Analysis" book, the example to illustrate testing for mediation starts out with Step 1 'Establish Significant Relationships Between the Constructs' and notes that the correlation was demonstrated in the CFA model. So they establish (zero-order) correlation between constructs outside their structural model rather than re-specifying it to have direct effects only. It is actually a covariance-based SEM model, though.
I was thinking, and this is a layman's understanding, that the lack of presenting mediation testing in SEM books may have to do something with the fact that model fit for CB-SEM models can be assessed with "hard wired" measures: e.g. chi-square, so if you "incorrectly" specify a model say with a mediating variable (construct), while no such relationship exists, the mis-specification is reflected in the detoriating goodness-of-fit measures. Similarly, if full mediation is specified in the model (A->B->C), while there is partial mediation (direct path A->C), it will be hinted by the modification indices (and residual covariances). I wonder if at least some of my thinking is correct.. :)

[elianacarraca]

Csaba,

There is some controversy related to the necessary criteria for having a mediating effect. Some authors have recently suggested that the direct effect between IV - DV is not necessary to be significant; only the indirect effect should be significant. Classic criteria to test mediation such as those proposed by Baron and Kenny have been criticized. Please check MacKinnon et al., 2002 and later work to further understand this issue. I think this might help you.

Reference: Mackinnon, D.; Lockwood, C.; Hoffman, J.; West, S.; Sheets, V. (2002). A comparison of methods to test mediation and other intervening variable effects. Psychological Methods, 7:83-104.

Eliana

[ruchi]

Hi

From reading all the post, what i understood is like below
Here I will represent two models-MODEL 1( without mediating variable) and MODEL 2(with Mediating Variable)

Model 1

X---> Y this path was insignificant.

Even in model 1 if the path is insignificant between X and Y , I can have indirect effect . So i build Model 2 with mediating effect

Model 2
X----> Y
X--->M --->Y

When i did bootstrapping on MODEL 2 to get significance , i got
X----> Y This was again-insignificant
X--->M Significant
M--->Y Significant

Now here I can say that there is FULL mediation.

Please give me ur suggestions or let me know if i m wrong.

Thanks
Ruchi

[jiwatr]

Yes that is correct.

Regards

Jiwat