Partial least squares (PLS) refers to a set of iterative algorithms based on least squares that implement a broad spectrum of both explanatory and exploratory multivariate techniques, from regression to path modeling, and from principal component to multi‐block data analysis. This article focuses on PLS regression and PLS path modeling, which are PLS approaches to regularized regression and to predictive path modeling. The computational flows and the optimization criteria of these methods are reviewed in detail, as well as the tools for the assessment and interpretation of PLS models. The most recent developments and some of the most promising on going researches are enhanced. WIREs Comput Stat 2013, 5:1–19. doi: 10.1002/wics.1239 This article is categorized under: Statistical Learning and Exploratory Methods of the Data Sciences > Exploratory Data Analysis Statistical and Graphical Methods of Data Analysis > Multivariate Analysis Statistical Models > Linear Models Algorithms and Computational Methods > Least Squares

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We introduce a new regression method-called Correlated Component Regression (CCR)-which provides reliable predictions even with near multicollinear data. Near multicollinearity occurs when a large number of correlated predictors and relatively small sample size exists as well as situations involving a relatively small number of correlated predictors. Different variants of CCR are tailored to different types of regression (e.g. linear, logistic, Cox regression). We also present a step-down variable selection algorithm for eliminating irrelevant predictors. Unlike PLS-R and penalized regression approaches, CCR is scale invariant. CCR is illustrated in several examples involving real data and its performance is compared with other approaches using simulated data. 1 1

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