EMA (version 1.4.4)

PLS: Partial Least Squares

Description

Partial Least Squares

Usage

PLS(E, F, n = 1, scale = TRUE)

Arguments

E

Matrix which correspond to the predictor variables.

F

Matrix which corresponds to the outcome variables.

n

Number of components to compute.

scale

If TRUE, each variable is sacled to have a unit variance.

Value

• A list whith the following elements:
• T
  PLS components. T = EW(P'W)^(-1)
• E0
  The input E matrix. If scale=TRUE, then E is scaled.
• F0
  The input F matrix. If scale=TRUE, then F is scaled.
• C
  Covariance between the PLS componants and the outcome variables F.
• Wstar
  EW(P'W)^(-1)
• P
  Regression vectors.
• param.center
  Means of E columns.
• param.scaled
  Standard-deviation of E colums.

Details

The function implements the PLS1 algorithm (Wold, 1966; Wold et al., 1982) (details about this algorithm and other implementations can be found in Tenenhaus (1998)).

References

Tenenhaus, M. (1998). La regression PLS - Theorie et pratique. Editions TECHNIP.

Wold, H. (1966). Estimation of principal component and related models by iterative least squares. In Krishnaiah, P. R., editor, Multivariate Analysis, pages 391-420. New-York: Academic Press.

Wold, S., Martens, H., and Wold, H. (1982). The multivariate calibration problem in chemistry solved by the PLS method. In Ruhe, A. and Kastrom, B., editors, Matrix Pencils, Lecture Notes in Mathematics, pages 286-293. Springer Berlin / Heidelberg.

Examples

X <- matrix(rnorm(100), 20, 5)
Y <- matrix(c(rep(0,10), rep(1,10)))
res <- PLS(X,Y)