I've read a lot of sources about Partial Least Squares (PLS) Regression and, based on my readings, it seems that it has some advantages over a Principal Component Regression (PCR). Different sources indicate that a PLS regression takes into account the variability of the dependent variables (while PCR doesn't). Why is this aspect so important and why it is considered to be an advantage over PCR?
Also, are there any other concrete advantages of conducting a PLS regression instead of a PCR?
I conducted both types of analyses on different datasets and I computed the corresponding MSEs. I remarked two things:
1) The MSE of a PLSR was lower than the MSE of a PCR;
2) PLSR extracts more components than the PCA (a PCA is done as a part of the PCR).
I think that the MSE of a PLSR is lower because the optimal number of extracted components is higher. However, I don't consider that extracting a higher number of components is an advantage of PLSR over PCR. Am I right to say that this would be a disadvantage of PLSR over PCR? Mainly, for both methods, we are interested in extracting a small number of components...
Lastly, I remarked that when I perform a PLSR and I work with a small number of predictors, the optimal number of extracted components is approximately equal to the no. of predictors. How this may be explained?