# TIBCO Statistica® General Partial Least Squares Models

The General Partial Least Squares Models (PLS) module's purpose is to build a linear model. Partial least squares regression has been used in various disciplines such as chemistry, economics, medicine, psychology, and pharmaceutical science where predictive linear modeling, especially with a large number of predictors, is necessary. Especially in chemometrics, partial least squares regression has become a standard tool for modeling linear relations between multivariate measurements (de Jong, 1993).

PLS implements partial least squares regression using the NIPALS (Rannar, Lindgren, Geladi, and Wold, 1994) and the SIMPLS (de Jong, 1993) algorithms for extracting partial least squares regression components. It is an extension of the multiple linear regression model that does not impose the restrictions employed by discriminant analysis, principal components regression, and canonical correlation. In partial least squares regression, prediction functions are represented by factors extracted from the Y'XX'Y matrix. The number of such prediction functions that can be extracted typically will exceed the maximum of the number of Y and X variables.

Therefore, partial least squares regression is probably the least restrictive of the various multivariate extensions of the multiple linear regression model. This flexibility allows it to be used in situations where the use of traditional multivariate methods is severely limited, such as when there are fewer observations than predictor variables. Furthermore, partial least squares regression can be used as an exploratory analysis tool to select suitable predictor variables and to identify outliers before classical linear regression.

Types of analyses available are Analysis of Covariance, Factorial ANOVA, Factorial Regression, General MANOVA/MANCOVA, omogeneity-of-Slopes Model, Huge Balanced ANOVA, Main Effects ANOVA, Mixture Surface Regression, Multiple Regression, Nested Design ANOVA, One-Way ANOVA, Polynomial Regression, Repeated Measures ANOVA, Response Surface Regression, Separate Slopes Model, and Simple Regression.