Principal Component Regression (PCR)

The goal of PCR is to extract intrinsic effects in the data matrix X and to use these effects to predict the values of Y.
PCR is a combination of PCA and MLR. First, a principal component analysis is carried out which yields a loading matrix P and a scores matrix T as described in the section above covering PCA. For the ensuing MLR only PCA scores are used for modeling Y. The PCA scores are inherently uncorrelated, thus they can directly be employed for MLR.
The selection of relevant effects for the MLR in PCR can be quite a complex task. A straightforward approach is to take those PCA scores which have a variance above a certain threshold. By varying the number of used PCA components the regression model can be optimized. However, if the relevant effects are rather small compared to the irrelevant effects they will not be included in the first few principal components. A solution to this problem is the application of PLS.



Ulrike Burkard, Dec. 12, 2002