When we perform an usual multiple linear regression analysis, we must check some assumptions like residuals are normally distributed, no multicollinearity of predictors and homoscedasticity. For each assumption, we usually perform a hypothesis test while trying to validate our model.

My question is the following one: If we perform a partial least squares regression analysis (PLSR model), do we need to check any assumptions? If so, which are these assumptions and how do we check them (are there any hypothesis tests that must be performed)? If there are no assumptions, why there are none?

  • $\begingroup$ Also take note of accepted answer to the above question, that it is incorrect to say "we must check some assumptions". Assumptions are only needed under certain conditions relating to what you are going to use the model for. Also it is wrong to say that "For each assumption, we usually perform a hypothesis test" $\endgroup$ – Robert Long Feb 15 '20 at 9:19