This post discusses how you can use WarpPLS to test a mediating effect using what is often referred to as the classic Baron and Kenny approach (for a recent discussion, see: Kock, 2014). You can also test mediating effects directly with WarpPLS, using indirect and total effect outputs:

http://warppls.blogspot.com/2013/04/testing-mediating-effects-directly-with.html

Using WarpPLS, one can test the significance of a mediating effect of a variable M, which is hypothesized to mediate the relationship between two other variables X and Y, by using Baron & Kenny’s (1986) criteria. The procedure is outlined below. It can be easily adapted to test multiple mediating effects, and more complex mediating effects (e.g., with multiple mediators). Please note that we are not referring to moderating effects here; these can be tested directly with WarpPLS, by adding moderating links to a model.

First two models must be built. The first model should have X pointing at Y, without M being included in the model. (You can have the variable in the WarpPLS model, but there should be no links from or to it.) The second model should have X pointing at Y, X pointing at M, and M pointing at Y. This is a “triangle”-looking model. A WarpPLS analysis must be conducted with both models, which may be saved in two different project files; this analysis may use linear or nonlinear analysis algorithms. The mediating effect will be significant if the three following criteria are met:

- In the first model, the path between X and Y is significant (e.g., P < 0.05, if this is the significance level used).

- In the second model, the path between X and M is significant.

- In the second model, the path between M and Y is significant.

Note that, in the second model, the path between M and Y controls for the effect of X. That is the way it should be. Also note that the effect of X on Y in the second model is irrelevant for this mediation significance test. Nevertheless, if the effect of X on Y in the second model is insignificant (i.e., indistinguishable from zero, statistically speaking), one can say that the case is one of “perfect” mediation. On the other hand, if the effect of X on Y in the second model is significant, one can say that the case is one of “partial” mediation. This of course assumes that the three criteria are met.

Generally, the lower the direct effect of X on Y in the second model, the more “perfect” the mediation is, if the three criteria for mediating effect significance are met.

**References**

Baron, R. M., & Kenny, D. A. (1986). The moderator–mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations.

*Journal of Personality & Social Psychology*, 51(6), 1173-1182.

Kock, N. (2014). Advanced mediating effects tests, multi-group analyses, and measurement model assessments in PLS-based SEM.

*International Journal of e-Collaboration*, 10(1), 1-13.

## 27 comments:

Dear Prof. Dr. Ned Kock:

My doubt is on model specification for moderating effect. In Warppls when introducing the moderating variable, only the dotted line on the direct link is shown. However, a direct link from the moderating variable to the dependent variable is not automatically added. Should I add this? Because the results of the path coefficient doesn't report the direct effect of moderating variable on the dependent variable, which is a necessity in specifying this model (Cohen et al 2003; Aiken West 1991). Please correct me if I am wrong.

If you need to test a moderating effect AND and direct effect, then you should add a direct link as well. The direct link is not necessary if all you want to do is to test a moderating effect.

Dear Prof. Kock,

I am working on a model predicting export intention. In the model I include a moderator called "collaboration" the construct involves 14 items. the model has two independent variables and on dependent (and one moderator). The sample size is 103 Algerian potential exporters. When I run the analysis, the software informs that the sample size is not big enough and the results might be unreliable. The problem is that I can't increase the sample size as in the whole Algeria there are only 300 potential exporters (SMEs), so having a 100 is already very representative.

The measurement model is good and th structural model is giving me an R2 of 50%. How unreliable would be the results? can I stillcarry on and use the software?

Many thanks for your help Prof. Kock

Yacine

Hi Yacine. What is the exact message that the software gives you?

Dear Prof. Kock,

Thank you very much for your reply. The message given by the software is

The data may be rank deficient, which may lead to misleading results.

(This is not related to the data being ranked, being “rank-deficient” is usually associated with small samples)

The number of data columns if 167

The number of data rows (usually called sample size) is 103

Yet, the maximum number of independent data rows or columns is only 77.

This problem may be caused too narrow a range having been chosen for a range restriction variable.

Would you like to proceed with the analysis anyway?

If you choose to proceed, the analysis may proceed very slowly and/or the results may be very unreliable.

End of message

Many thanks for your help Prof. Kock

Regards

Yacine

I'd suggest that your minimum sample size meet the requirement in the blog linked below:

http://warppls.blogspot.com/search/label/minimum%20sample%20size

If no additional data collection is possible, this can be met by simplifying the model.

Dear Prof Kock,

I understand indirect and total effects are directly available in the latest WarpPLS version. Are the p values corresponding to these effects calculated via Bootstrapping (Preacher & Hayes, 2004)approach.

Hi Aparna. The method used is the one you select for resampling under: Settings > View or change general settings.

Dear Prof Kock,

How would we go about testing and interpreting serial mediation in PLS SEM?

The indirect and total effects outputs provided by WarpPLS are very extensive, and are particularly well suited for testing serial, or cascading, mediation. I hope that the following links to video clips will be useful:

View Indirect and Total Effects in WarpPLS

http://youtu.be/D9m4K_fv2vI

Isolate Mediating Effects in WarpPLS

http://youtu.be/1wk5eedKupI

Dear Prof Kock,

Is it possible that the effect of an antecedent on a mediator and the mediator on the consequence are both significant and still the indirect effect estimated in WarpPLS is insignificant? If so how can we explain these results. Are the indirect effects estimated considering Baron & Kenny's 4 causal steps or it only estimated by the set resampling method? In either case how do we explain an insignificant indirect effect when the effect of antecedent on mediator, mediator on consequence and total effects are all significant?

That is certainly possible. Products of path coefficients tend to be lower than the individual path coefficients that make up the products. See the following, particularly pages 3-4:

Kock, N. (2014). Advanced mediating effects tests, multi-group analyses, and measurement model assessments in PLS-based SEM. International Journal of e-Collaboration, 10(3), 1-13.

http://www.scriptwarp.com/warppls/pubs/Kock_2014_UseSEsESsLoadsWeightsSEM.pdf

Dear Prof Kock,

As per the videos, the indirect effect estimates in WarpPLS output do not control for the direct effect of the variables, but should not the indirect effects be estimated after controlling for the direct effects?

Dear Prof Kock,

Can you please suggest some papers by other authors in A* marketing or strategic management journals which have reported direct and indirect effects from warppls?

The indirect effects are calculated controlling for competing direct effects. This is why the “isolation” procedure discussed in the video clip linked below is needed.

Isolate Mediating Effects in WarpPLS

http://youtu.be/1wk5eedKupI

The link below takes you to Google Scholar, with a search that returns a list of links to academic publications using or discussing WarpPLS, some of which are available in full text.

https://scholar.google.com/scholar?start=0&q=warppls

If you change the search (for example, by adding the term “marketing”) I think you will get what you are looking for after some tries.

Respected Sir, Kindly guide if if there are two mediating variables in the model then we have to run it separately or they can be incorporated in the same model.

My Model contains one independent one dependent variable and two mediators.

Kindly explain the process and how we can control the effect of some variables which are known as control variables ( Some of the demographics are control variables so what is the procedure of it while running SEM.

Regards,

Hi Asbah. I hope that the materials linked below can be of use in connection with this.

User Manual (link to specific page):

http://www.scriptwarp.com/warppls/UserManual_v_5_0.pdf#page=80

Video: View Indirect and Total Effects in WarpPLS

http://youtu.be/D9m4K_fv2vI

Video: Isolate Mediating Effects in WarpPLS

http://youtu.be/1wk5eedKupI

The links above, as well as other links that may be relevant in this context, are available from:

http://warppls.com/

hello prof

the model which I am using is a multivariate independent variables with two mediating variables and a dependent variable

for looking p value of indirect effect in warppls, one way is to delete one direct link with one mediating effect(as you mention in your video(https://www.youtube.com/watch?v=1wk5eedKupI)). I n this way I can get the indirect effect of both mediation.

but I am not getting significance P value although every thing is checked twice. I may not be following the rule which is applied in warppls. need help!!

the model which I am using is a multivariate independent variables with two mediating variables and a dependent variable

for looking p value of indirect effect in warppls, one way is to delete one direct link with one mediating effect(as you mention in your video(https://www.youtube.com/watch?v=1wk5eedKupI)). I n this way I can get the indirect effect of both mediation.

but I am not getting significance P value although every thing is checked twice. I may not be following the rule which is applied in warppls. need help!!

Hi Wasim.

What are the path coefficients and P values that you are currently getting for the various indirect effect tests?

Dear Prof Kock,

My problem is the same as Yacine Haddoud. I have simplified the model, also reduces the indicator of the variables. But still appear the same message "rank deficient". while the sample is very limited. How to solve this problem

Many thanks

Regards,

Keumala

Hi Keumala. Rank deficiency can lead to model-wide collinearity; but that is not always the case. How do your full collinearity VIFs look like, after you analyze your model?

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