Dear All (I am using SEM, and SmartPLS the latest Version 3.xxxx)
Is it correct to sum the R^2 for several indigenous latent variables?.
The aim is to compare the contribution for certain path with other paths by summing the related R^2s?.
In other words: I have the following model: Path A consists of latent variables say (A1, A2), and Path B consists of (B1, B2) both of A's and B's latent variables lead to the final latent Variable C. as an example:
A1, A2 have R^2. B1, B2 have R^2. And finally C of course, have another R^2. in order to report the contribution percentage for the Branch A and Branch B towards C,
Can I use the comparison of the summation of R^2 for A's and B's to report how much each branch contribute towards the final one C and which branch has the highest contribution?
Or can I use the summation of Path Coefficients instead for each branch in this comparison?
The aim is to find the latent variables (or factors) level of contribution.
(any related References will be appreciated)
R^2 OR Path Coefficient are used for LV contribution percentage ?

 SmartPLS Developer
 Posts: 971
 Joined: Tue Mar 28, 2006 11:09 am
 Real name and title: Dr. JanMichael Becker
Re: R^2 OR Path Coefficient are used for LV contribution percentage ?
I don't quite understand your problem.
The R² of A1 and A2 are determined by the predictors of A1 and A2. They don't tell you anything about how much A1 and A2 contribute to C.
The R² contribution is calculated as difference between R²_included and R²_excluded, where R²_included contains all predictors and R²_excluded contains the reduced set of predictors. Thereby you can calculate the R² contribution of single predictors or sets of predictors.
For single predictors, we report the f² effect size which is a variant of the R² contribution deviding the R² contribution by (1R²_included; i.e., the unexplained variance). For sets of multiple predictors you have to calculate such numbers on your own.
You may also get significance estimates if you use the bootstrapping results for all samples and calculate you measure for each of the samples. The new bootstrapping distribution provides you with the ability to construct confidence intervals or standard deviations and pvalues.
The R² of A1 and A2 are determined by the predictors of A1 and A2. They don't tell you anything about how much A1 and A2 contribute to C.
The R² contribution is calculated as difference between R²_included and R²_excluded, where R²_included contains all predictors and R²_excluded contains the reduced set of predictors. Thereby you can calculate the R² contribution of single predictors or sets of predictors.
For single predictors, we report the f² effect size which is a variant of the R² contribution deviding the R² contribution by (1R²_included; i.e., the unexplained variance). For sets of multiple predictors you have to calculate such numbers on your own.
You may also get significance estimates if you use the bootstrapping results for all samples and calculate you measure for each of the samples. The new bootstrapping distribution provides you with the ability to construct confidence intervals or standard deviations and pvalues.
Dr. JanMichael 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
Researchgate: https://www.researchgate.net/profile/Ja ... v=hdr_xprf
GoogleScholar: http://scholar.google.de/citations?user ... AAAJ&hl=de