Two models : Comparison based on path coefficient and R²

Frequently asked questions about PLS path modeling.
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etudiant
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Two models : Comparison based on path coefficient and R²

Post by etudiant » Thu Jul 05, 2018 2:22 pm

My question is related to the PLS approach ,and I can rephrase it as follows:

If I have 2 PLS models (developed with the same data set):
-The first model contains two latent variables: A1 and B.
-The 2nd model contains two latent variables: A2 and B (the same B of the model 1).
- Both models show that A1 and A2 have a positive and significant effect on B ( Path coefficient> 0.1 and t> 1, 645, One-tailed (Using Bootstrap).

I now want to show that the effect of A1 on B is greater than the effect of A2 on B
-By comparing the 2 models we find that:
- [Path coefficient of A1 => B (model1)=0,573 ] > [Path coefficient A2 => B (model2)= 0,398]
- [R² of B (model1)=0,328] > [R² of B (model2)=0,158]

With this comparison (based on the path coefficient and R²) can we conclude that: "the effect of A1 on B is greater than the effect of A2 on B" ?
If no, how can I demonstrate it?

jmbecker
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Re: Two models : Comparison based on path coefficient and R²

Post by jmbecker » Fri Jul 06, 2018 7:27 am

Without having both variables in the same model it is very hard to make claims about one effect being significantly larger than the other. Especially in PLS where we do not have distributional assumptions.
You could investigate the confidence intervals, If they do not overlap that could be an indication for the one effect being larger than the other.
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

etudiant
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Real name and title: M Abdo

Re: Two models : Comparison based on path coefficient and R²

Post by etudiant » Mon Jul 09, 2018 3:22 am

Below my confidence intervals Histogram charts ,how can I investigate them ?

A1==> B
Image

A2==>B
Image

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

Re: Two models : Comparison based on path coefficient and R²

Post by jmbecker » Mon Jul 09, 2018 7:42 am

Based on the histograms it seems that they overlap. But you also get the confidence intervals in SmartPLS. If they overlap you cannot conclude that one effect is larger than the other.
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

Alexandra
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Real name and title: Dr. Alexandra S. Kang

Re: Two models : Comparison based on path coefficient and R²

Post by Alexandra » Tue Jul 31, 2018 4:12 am

what it means when the confidence intervals overlap?

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