# Combining principal component analysis and partial least squares

I know PCA and PLS are considered as alternative method to each other. But I am thinking about a kind of combination of the two in case of lots of predictors with little variability.

In that case, when I run 1-component PLS with original predictors, it does not produce a meaningful model in terms of prediction. But if I first compute 10-20 PCA components and run 1-component PLS with those PC scores as predictors, practically, the model is quite good in terms of prediction power. But I would like to know why.

Can anybody explain why this is better than 1-component PLS with original predictors?

• @rolando2 "run 1-component PLS" means building a regression model with the first component of PLS analysis. An example of such data would be Redness as dependent and reflectance intensities over 380nm-780nm as predictors. Apr 5, 2012 at 13:04
• Are you trying to reinvent principal component regression by any chance? (en.wikipedia.org/wiki/Principal_component_regression ; function pcr in R package pls) Apr 5, 2012 at 13:58

In any case, from predictive power perspective, it does not really make sense to limit the number of components in PLS (or PCR) to one - instead the number of components in PLS/PCR should be treated as a "meta" parameter which should be tuned using resampling (e.g. using package caret which provides a really nice harness for that)