Compute R2 for moderation models in excel for statistical significance

Frequently asked questions about PLS path modeling.
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Alexg
PLS Junior User
Posts: 9
Joined: Fri May 18, 2018 11:34 am
Real name and title: Mr. Alessandro Grillo

Compute R2 for moderation models in excel for statistical significance

Post by Alexg » Sat Jun 22, 2019 7:00 pm

Hello,

I am trying to compute Bias corrected bootstrapping intervals in excel to test for statistical significance of R2.

However, before to do that I computed the R2 of the endogenous variable in excel.
I am following the procedure suggested by Streukens & Leroi-Werelds (2016) and the formula provided in their paper coming from
Tenenhaus, Vinzi, Chatelin, and Lauro's (2005). The formula to compute the endogenous construct's coefficient of determination is:

R2= ∑i |βi *cor(Xi,Yi)|

where,βi is the structural model parameter describing the relationship between Xi and Yi, whereas cor(Xi,Yi) is the (latent variables)
correlation between the two constructs.

When applying this formula to simple models I get in excel the same R2 that I get in SmartPls.

However, when trying to compute the formula for moderated models the results are slightly different (i.e. R2 in SmartPls 0.316 and R2 in Excel 0.330).

What I did in the moderation model with M as moderator of X-->Y was to multiply the path coefficient of the interaction term for the correlation of the interaction term with the endogenous variable (as suggested by the formula so). Then, I added the result to the other parameters obtained in the model through βx-->y * cor (X,Y) and βm-->y * cor (M,Y).

Is the above procedure the correct one to get R2 for moderation models?
If no, could you please advise on the right procedure?


Thank you!
Alex

Reference
Streukens, S. & Leroi-Werelds, S., (2016). "Bootstarpping and PLS-SEM: a step by step guide to get more out of your bootstrap results". European Management Journal, 1-15.

jmbecker
SmartPLS Developer
Posts: 1010
Joined: Tue Mar 28, 2006 11:09 am
Real name and title: Dr. Jan-Michael Becker

Re: Compute R2 for moderation models in excel for statistical significance

Post by jmbecker » Wed Jul 03, 2019 7:46 am

Why don't you use the confidence intervals caluclated by SmartPLS? When you choose complete boostrapping you will also get the correct confidence intervals for R² etc.

The formula actually only works when all variables are standardized and have the same sign.
The value of multiple R2, in the case of standardized variables, may be decomposed in terms of the multiple regression coefficients and correlations between the dependent variable and the explanatory ones as follows: ... This decomposition allows understanding the contribution of each explanatory variable to the prediction of the dependent one and it makes sense only when the regression coefficients and the related correlations have the same sign (Tenenhaus et al. 2005, p. 178-179).
In a moderation model the interaction term is not standardized and thus you would need to take the covaiance and not the correlation.
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

Alexg
PLS Junior User
Posts: 9
Joined: Fri May 18, 2018 11:34 am
Real name and title: Mr. Alessandro Grillo

Re: Compute R2 for moderation models in excel for statistical significance

Post by Alexg » Fri Jul 05, 2019 10:33 am

Dear Dr. Becker

thank you for your reply and your suggestion!

I will try to work on that!

Kind regrads

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