I am working on a spatial linear regression and I can tell there is collinearity between covariates. Can I use PCA (Principal Component Analysis) images instead of original covariates to estimate the dependent variable? I am assuming PC1=Variable 1, PC2=Variable 2, etc. Or are there any other methods to solve the collinearity problem?
There is a method called partial least square that is something very close to what you are trying to do.
The choice to use the PCA transformation of the data can lead to a better estimation of the output $y$ but to understand the role of the original variables will be more difficult.
I suggest you to start with the lasso estimator https://en.wikipedia.org/wiki/Lasso_%28statistics%29#Lasso_method