There are two main advantages of using WarpPLS to conduct a multiple regression analysis. The advantages are over a traditional multiple regression analysis, where the independent and dependent variables are measured through single indicators. With WarpPLS, this would be implemented through the creation of "latent" variables that would each be associated with a single indicator; which means that they would not be true latent variables in the sense normally assumed in structural equation modeling.

The first advantage is that the calculation of P values with WarpPLS is based on nonparametric algorithms, resampling or "stable" algorithms, and thus does not require that the variables be normally distributed. A traditional multiple regression analysis, on the other hand, requires that the variables be normally distributed.

**In this sense, WarpPLS can be seen as conducting a robust, or nonparametric, multiple regression analysis**. This first advantage assumes that all one is doing is a plain linear analysis with WarpPLS, for which one would typically use the algorithm Robust Path Analysis. See the software's User Manual for more details.

The second advantage is that WarpPLS allows for nonlinear relationships between the independent and dependent variables to be explicitly modeled. This provides a much richer view of the associations between variables, and sometimes leads to path coefficients that are different from (often higher than) those obtained through a linear analysis (as in a traditional multiple regression analysis). The nonlinear analysis algorithms available are Warp3 and variants, which yield S curves; and Warp2 and variants, which yield U curves. Again, see the software's User Manual for more details.

## 4 comments:

I have a question concerning the comparison of two countries. Before calculating the p-values for the path coefficients I would like to check whether the weights do not have a significant p-value (as indicated in you paper 'Advanced mediating effects tests, multi-group analyses, and

measurement model assessments in PLS-based SEM'). However, my standard errors slightly differ for the different paths. Which of the standard erros should I use to calculate the p-value for the weights? Thank you very much for your help.

Kind regards

Hanne

Different standard errors are used for different groups, whether you are using the pooled standard error or Satterthwaite method. See also the sheet linked below:

http://www.scriptwarp.com/warppls/rscs/Kock_2013_MultiGroup.xls

Thanks for the useful post. Are you aware of any articles that used WrapPLS for multiple regression. Also, could you elaborate on the procedure? What did you mean by this statement?

"With WarpPLS, this would be implemented through the creation of "latent" variables that would each be associated with a single indicator; which means that they would not be true latent variables in the sense normally assumed in structural equation modeling".

Does this imply that drawing the model for PLS-SEM is different from drawing the model for multiple regression in WarpPLS?

Thanks a lot

The following article (PDF linked on https://warppls.com/) may be useful in this respect. It conducts a path analysis, which is a more general method of which multiple regression is conceptually a sub-type. Here the variables are not "latent", technically speaking, since they are measured via single indicators.

Kock, N., & Gaskins, L. (2014). The mediating role of voice and accountability in the relationship between Internet diffusion and government corruption in Latin America and Sub-Saharan Africa. Information Technology for Development, 20(1), 23-43.

The article linked below may also be useful. It conducts a stepwise SEM with WarpPLS, in a way similar to what is done in a stepwise multiple regression analysis.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5063655/

Best regards!

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