Total Effects Vs Path Coefficient Values

Frequently asked questions about PLS path modeling.
sbax123
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Real name and title: Sam B.- PhD Candidate

Total Effects Vs Path Coefficient Values

Hi:
I am a PhD candidate and have just started testing my structural model with SmartPLS3.

I understand that Total Effects is equivalent to the direct + indirect effects of constructs through mediation. But whilst on most occasions the value of the Total Effect from one construct to another it is directly linked to is the same as the value of the Path Coefficient, on other occasions it may not be.

Take for example the Corporate Reputation Extended example in the Primer on Partial Least Squares book (2014). Running the PLS Algorithm returns the values displayed in the model diagram on page 187. Selecting the Total Effects link from the PLS Algorithm Run Report displays the Total Effects calculated:
Total Effects for Corporate Reputation Extended
Capture.PNG (15.05 KiB) Viewed 4554 times
Now whilst many of the Total Effects values match the Coefficients for the direct paths between the constructs (e.g. Attractiveness -> Competence = 0.086 and Corporate Social Responsibility -> Competence = 0.059), some of the figures do not match at all (e.g. Competence -> Customer Loyalty = 0.079 Path Coefficient = 0.06, and Likeability -> Customer Loyalty = 0.564 Path Coefficient = 0.344). The same thing is occurring for the Total Effects within my research model.

Could you please inform me if I am missing something here? I have read the relevant sections in the PLS Primer book and tried to do some research on my own but have not been able to find any answers to this question.

Please help me out with this. Your help is much appreciated :),

Sam

jmbecker
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Real name and title: Dr. Jan-Michael Becker

Re: Total Effects Vs Path Coefficient Values

You are correct the total effect is the direct effect + the indirect effect. If you have a relation that has no indirect effect then the total effect equal the direct effect. It is as easy as it seems.
Dr. Jan-Michael Becker, University of Cologne, SmartPLS Developer
Researchgate: https://www.researchgate.net/profile/Ja ... v=hdr_xprf
GoogleScholar: http://scholar.google.de/citations?user ... AAAJ&hl=de

sbax123
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Posts: 11
Joined: Wed Sep 16, 2015 4:49 am
Real name and title: Sam B.- PhD Candidate

Re: Total Effects Vs Path Coefficient Values

Thank you for your reply Dr Becker.

But how does that explain the discrepancies between the Path Coefficient and the Total Effect of constructs directly linked in my model and the example in the PLS book?

Thank you for your help explaining this.

Sam

jmbecker
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Joined: Tue Mar 28, 2006 11:09 am
Real name and title: Dr. Jan-Michael Becker

Re: Total Effects Vs Path Coefficient Values

Maybe I don't understand your problem. If you only have the direct effect the total effect equals the direct effect. If you also have an indirect effect the total effect is different from the direct effect, because it is total effect = direct effect + indirect effect.
Dr. Jan-Michael Becker, University of Cologne, SmartPLS Developer
Researchgate: https://www.researchgate.net/profile/Ja ... v=hdr_xprf
GoogleScholar: http://scholar.google.de/citations?user ... AAAJ&hl=de

sbax123
PLS User
Posts: 11
Joined: Wed Sep 16, 2015 4:49 am
Real name and title: Sam B.- PhD Candidate

Re: Total Effects Vs Path Coefficient Values

Thank you for your input Dr Becker.

As an example from the PLS Primer book model on pg 187:

The Path Coefficient for Competence -> Customer Loyalty (a direct path) is 0.06
The Total Effect for the same relationship is 0.079

The Path Coefficient for Likeability -> Customer Loyalty (a direct path) is 0.344
The Total Effect for the same relationship is 0.564

My question is why are they different?
-Could it be that there is actually some kind of indirect effect influencing the dependant constructs? and how would I find this out?
-Or have I just made a horrible mistake?

Thank you for your time.

Sam

jmbecker
SmartPLS Developer
Posts: 932
Joined: Tue Mar 28, 2006 11:09 am
Real name and title: Dr. Jan-Michael Becker

Re: Total Effects Vs Path Coefficient Values

Yes, there is an indirect effect (through Customer Satisfaction) in the model. You will find that indirect effect in the indirect effect table and you will see it in your model.

Competence -> Customer Loyalty (direct path) is 0.0057
Competence -> Customer Loyalty (indirect effect) is 0.0735
Competence -> Customer Loyalty (total effect) is 0.0792 (=0.0057+0.0735; direct effect + indirect effect)

Likeability -> Customer Loyalty (direct path) is 0.3440
Likeability -> Customer Loyalty (indirect effect) is 0.2200
Likeability -> Customer Loyalty (total effect) is 0.5640 (=0.3440+0.2200; direct effect + indirect effect)
Dr. Jan-Michael Becker, University of Cologne, SmartPLS Developer
Researchgate: https://www.researchgate.net/profile/Ja ... v=hdr_xprf
GoogleScholar: http://scholar.google.de/citations?user ... AAAJ&hl=de

sbax123
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Posts: 11
Joined: Wed Sep 16, 2015 4:49 am
Real name and title: Sam B.- PhD Candidate

Re: Total Effects Vs Path Coefficient Values

Last one Dr Becker - I promise

I understand what you mean by your explanation of Total Effects (Direct + Indirect). But why do these values NOT match the Path Coefficients? Or are they not supposed to?

Thank you so much,
Sam

sbax123
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Posts: 11
Joined: Wed Sep 16, 2015 4:49 am
Real name and title: Sam B.- PhD Candidate

Re: Total Effects Vs Path Coefficient Values

Sorry. I can see what you are getting at now :(

Thank you so much for clearing that up Dr Becker!

arunavaiimidr93
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Real name and title: Arunava Ghosh

Re: Total Effects Vs Path Coefficient Values

SmartPLS3 automatically creates an indirect path (if possible). Then it finds out that had this indirect path existed, would it be significant or not (that is, whether mediation would have existed or not).

Let us consider my below model.
My Model
1.png (13.08 KiB) Viewed 62 times
You will find that I haven't connected Trust and Satisfaction. Yet when I run the bootstrapping, and check for the indirect effects, I get the following table:
Indirect Effect
Untitled.png (21.28 KiB) Viewed 62 times
You will see that PLS gives the indirect effect of Trust and Satisfaction by a pseudo-connection (that is, connection not made by you). This is the very reason, why even if you didn't want to see an indirect effect of between Competence -> Customer Loyalty or Likeability -> Customer Loyalty, PLS calculates anyhow and finds out that an Indirect Effect exists, hence affecting the Total Effect.

jmbecker
SmartPLS Developer
Posts: 932
Joined: Tue Mar 28, 2006 11:09 am
Real name and title: Dr. Jan-Michael Becker

Re: Total Effects Vs Path Coefficient Values

I would not call this a "pseudo-connection (that is, connection not made by you).
In fact, it is a model implied connection. You implicitly make a connection between A and C by linking A-->B and B-->C.
Dr. Jan-Michael Becker, University of Cologne, SmartPLS Developer
Researchgate: https://www.researchgate.net/profile/Ja ... v=hdr_xprf
GoogleScholar: http://scholar.google.de/citations?user ... AAAJ&hl=de