Partial Least Squares

Partial least squares (PLS) is a method for constructing predictive models when the factors are many and highly collinear. Note that the emphasis is on predicting the responses and not necessarily on trying to understand the underlying relationship between the variables. For example, PLS is not usually appropriate for screening out factors that have a negligible effect on the response. However, when prediction is the goal and there is no practical need to limit the number of measured factors, PLS can be a useful tool.

In short, 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.

It is an alternative technique of principal component regression when you have independent variables highly correlated. It is also useful when there are a large number of independent variables.

Difference between PLS and PCR

Both techniques create new independent variables called components which are linear combinations of the original predictor variables but PCR creates components to explain the observed variability in the predictor variables, without considering the response variable at all. While PLS takes the dependent variable into account, and therefore often leads to models that are able to fit the dependent variable with fewer components.

PLS Regression in R

library(plsdepot)
data(vehicles)
pls.model = plsreg1(vehicles[, c(1:12,14:16)], vehicles[, 13], comps = 3)
# R-Square
pls.model$R2