Partial Least Squares Regression (PLS)

PLS comprise a wide range of methods for relating between sets of observed variables by means of latent variables.

Traditionally, multiple linear regression is used to predict some response properties from a set of independent variables, but the multiple linear regression methodology yields imprecise (at best) predictions when the independent variables are correlated. The PLS method overcomes some of these numeric problems since it first extracts uncorrelated factors, and works from there. This makes the PLS method less restrictive (and less powerful) than other regression methods, and makes the method particularly useful when there are fewer observations than predictor variables. This is probably the main reason for the popularity of PLS in subjects where instruments generate large quantities of correlated data per case/analysis.

The PLS method implemented in Aabel (i) uses principal component analysis (PCA) to derive the prediction functions from factors calculated from cross-product matrices involving both Y and X variables, and (ii) allows predicting one or more dependent variables from a set of independent (predictor variables).

• PLS regression can be performed on a single data set (as for multiple regression), or using a training data set for predicting unknowns, new events, etc.
• To use a calibration (training) data set, you can run a PLS regression on a representative data set and check the performance of the model before using it for predictive purposes.
• The predictor coefficients and the predictions will be stored in two auto-generated worksheets.