Chapter 6.3 application

Today, I read Chapter 6 (6.3) and find something which could be useful for my research.

Summary

Partial Least Squares

The removal of highly correlated pairwise predictors may not guarantee a stable least squares solution. Alternatively, using PCA for pre-processing guarantees that the resulting predictors, or combinations thereof, will be uncorrelated.

Pre-processing predictors via PCA prior to performing regression in known as principal component regression (PCR).

If the variability in the predictor space is not related to the variability of the response, then PCR can have difficulty identifying a predictive relationship when one might actually exist. Because of this, it is recommended to use PLS when there are correlated predictors and a linear regression-type solution is desired.

While the PCA linear combinations are chosen to maximally summarize predictor space variability, the PLS linear combinations of predictors are chosen to maximally summarize covariance with the response. This means that PLS finds components that maximally summarize the variation of the predictors while simultaneously requiring these components to have maximum correlation with the response. (predictors-components-response)

PLS has one tuning parameter: the number of components to retain.

Tomorrow, I will continue to read the book.