Partial least squares regression and projection on latent structure regression (PLS Regression)

Partial least squares (pls) regression (a.k.a projection on latent structures) is a recent technique that combines features from and generalizes principal component analysis (pca) and multiple linear regression. Its goal is to predict a set of dependent variables from a set of independent variables or predictors. This prediction is achieved by extracting from the predictors a set of orthogonal factors called latent variables which have the best predictive power. These latent variables can be used to create displays akin to pca displays. The quality of the prediction obtained from a pls regression model is evaluated with cross-validation techniques such as the bootstrap and jackknife. There are two main variants of pls regression: The most common one separates the rôles of independent and independent variables; the second one—used mostly to analyze brain imaging data—gives the same rôles to dependent and independent variables.