# Analysis of model and data relationship in PLSR

Validated!

This is a quite broad subject topic but I will try to boil it down into a few specific questions.

I've been working with a clients data on a PLS (partial least squares/project to latent squares) regression type model for a while now having known little to nothing about PCA/PLS or multivariate analysis in general and learning as I go. I've succesfully fitted a model that I like, chosen number of components to work with and comparing different statistics between models to find a suitable candidate. Now my next problem is to actually analyze the results of the data and I've been struggling to find literature that deals with this particular instance.

Firstly, I've been looking at VIP-scores as it is detailed in Chong and Jun (2004) and implementing these into my code as a step to say something about the importance of variables in my model. This seems like an accepted method of quantifying importance and seems to be used in some software as a way to do variable selection (although I'm skeptical to these types of computerized variable removal schemes).

Secondly, I've been wanting to look at the loadings obtained via the model algorithm but this is where I've ran into a halt. I understand some basics regarding the loadings such as sums of squares over variable loadings gives us an eigenvalue for that variable and how to obtain the variance explained through these eigenvalues. Still what I've been unable to find is some thorough literature on these and what we can do, analytically, with them. I've tried to consult literature on PCA and PLS but google mostly leads me to brief threads on here, researchgate or similar dealing with specific questions.

I guess my questions are twofold:

$$\cdot$$ Is there any suggestion of literature (behind paywall or not) that I could consult to better understand loadings and how we may use them for interpretations?

$$\cdot$$ Are these two tools apropriate to understand my PLS-model or should I look at different statistics entirely?

Hopefully my text and questions were understandable. Thanks!