Non-normal distr data vs residuals and PLS

[Tobjoh]

Dear SmartPLS-users and designers,

I have a very basic, and probably stupid, question regarding when to use PLS rather than other regression and SEM methods.
One central notion is that if data follows a non-normal distribution PLS is advisable (several review articles about PLS state that), but isn’t the case with the distribution that it is the residual(s) that should follow a normal distribution, in e.g. OLS-regression and CB_SEM, and not the data per se?

Is it possible to get information about the residuals and their distribution in SmartPLS and/or is it of little interest because the bootstrap method does not require residuals to be “normal”?

Best regards
Tobias

[jmbecker]

It is a common misunderstanding that PLS does not require normal data. Highly skewed or kurtotic data can also harm the PLS estimates as they are basically based on correlations and regressions. It is the bootstrap procedure that does not directly impose assumptions about the distribution of the parameter estimates to makes statistical inferences. Nevertheless, analyzing the distribution of the bootstrap estimates (histogram plots) and the residuals might be very useful to detect strange results.
In SmartPLS 3 there is a result section in the PLS algorithm that is called “Residuals”. It has the inner and outer model residuals.

[Tobjoh]

Hi,
Thank you very much for the answer!
Then it is as I assumed. Many articles that have non-normal data choose PLS and thinks that everything is fine, but PLS is not the silver bullet in that respect. They might still have problems and it should probably be assessed by analyzing additional output from the smarPLS software.

[Katy2]

This generally means, I have to normalize my data set before I use SmartPLS?

[cringle]

You may use the data as is and run bias-corrected and accelerated bootstrapping (BCa), which does a bias correction and accounts for skewed data.

Best
Christian