Number of latents The same number of factors will be extracted for PLS responses as for PLS factors. The researcher must specify how many latents to extract (in SPSS the default is 5). There is no one criterion for deciding how many latents to employ. Common alternatives are: 1. Cross-validating the model with increasing numbers of factors, then choosing the number with minimum prediction error...

Partial least squares (PLS) was not originally designed as a tool for statistical discrimination. In spite of this, applied scientists routinely use PLS for classification and there is substantial empirical evidence to suggest that it performs well in that role. The interesting question is: why can a procedure that is principally designed for overdetermined regression problems locate and emphas...

Pls regression is a recent technique that generalizes and combines features from principal component analysis and multiple regression. It is particularly useful when we need to predict a set of dependent variables from a (very) large set of independent variables (i.e., predictors). It originated in the social sciences (specifically economy, Herman Wold 1966) but became popular first in chemomet...

In this paper I review covariance-based Partial Least Squares (PLS) methods, focusing on common features of their respective algorithms and optimization criteria. I then show how these algorithms can be adjusted for use as optimal scaling tools. Three new PLS-type algorithms are proposed for the analysis of one, two or several blocks of variables: the NonMetric NIPALS, the Non-Metric PLS Regres...

Orthonormalized partial least squares (OPLS) is often used to find a low-rank mapping between inputs X and outputs Y by estimating loading matrices A and B. In this paper, we introduce sparse orthonormalized PLS as an extension of conventional PLS that finds sparse estimates of A through the use of the elastic net algorithm. We apply sparse OPLS to the reconstruction of presented images from BO...