# How to interpret null or nearly null coefficients with VIP > 1 in PLSR?

I try to interpret a PLSr model that I used to predict a response variable using full range spectroscopy (500 - 2400 nm). I followed the method from Serbin et al. 2014 (https://doi.org/10.1890/13-2110.1) to build the PLSr model, ie to chose the number of components and to validate the model.

To interpret the model I use two different indicators, (i) the Variable importance of projection (VIP) and (ii) the coefficients of the PLSr model. I chose a threshold of 1 for the VIP so the spectral regions under 1 should be not important. In the mean-time, the coefficients which are null or close to null should have no effect in the prediction whereas coefficients which strongly departs from 0 should have an importance.

But there are some apparent contradictions that I would like to understand. I obtain spectral regions with VIP >1 with regression coefficients null or nearly null. How to interpret that?

I have the intuition that the region with VIP >1 might be regions where the X variables have a strong variability, but that doesn't really help for the prediction of the Y variables. Do I understand well?

## 1 Answer

In PLSR the coefficients are the direction and magnitude of the contribution of each x variable to modelling y. VIP weighs this contribution, but also takes into account how important each x variable is to modelling the entire block of x variables. So if your variable is not important to the model (zero coefficient), but high VIP (>1), then it means the given x variable is important in modelling X.

Have you centered and scaled your X data before inputing into PLSR? e.g. standardize by subtracting mean and dividing by standard deviation of each variable? Also, are these noisy regions of the spectra,..e.g. near the limits of the range of your spectrometer? If so, one interpretation could be that you are fitting your model to noise, and should remove.

• Hello, thanks a lot, your explanation is very clear. Yes I centered the X but didn't standardize them. I am curious about your answer. Does it imply that we can model X knowing y? i.e model the reflectance spectra (X) if we know Y? This way inverting the PLSR model? I tried to somehow do that but didnt succeed. Maybe it should be a different question though. Thanks again! – user297736 Dec 5 '20 at 21:18
• Yes, with PLSR you can predict multiple response variables. Standardizing (aka autoscaling) will weigh the variables more equally, making VIP and coefficients more similar, and also potentially giving you a better model of X, but can drastically amplify noise, to the point where signals become lost in the noise. Pareto scaling can be a compromise. Check out the important article, "PLS-regression: a basic tool of chemometrics", by Svante Wold et al, 2001. Also youtube QualityAndTechnology has very clear and informative videos. – woodfoot Dec 6 '20 at 16:23