Orthogonal scores PLSR

Fits a PLSR model with the orthogonal scores algorithm (aka the NIPALS algorithm).

Usage

oscorespls.fit(
  X,
  Y,
  ncomp,
  center = TRUE,
  stripped = FALSE,
  tol = .Machine$double.eps^0.5,
  maxit = 100,
  ...
)

Arguments

X: a matrix of observations. NAs and Infs are not allowed.
Y: a vector or matrix of responses. NAs and Infs are not allowed.
ncomp: the number of components to be used in the modelling.
center: logical, determines if the \(X\) and \(Y\) matrices are mean centered or not. Default is to perform mean centering.
stripped: logical. If TRUE the calculations are stripped as much as possible for speed; this is meant for use with cross-validation or simulations when only the coefficients are needed. Defaults to FALSE.
tol: numeric. The tolerance used for determining convergence in multi-response models.
maxit: positive integer. The maximal number of iterations used in the internal Eigenvector calculation.
...: other arguments. Currently ignored.

Value

A list containing the following components is returned:

coefficients: an array of regression coefficients for 1, ..., ncomp components. The dimensions of coefficients are c(nvar, npred, ncomp) with nvar the number of X variables and npred the number of variables to be predicted in Y.
scores: a matrix of scores.
loadings: a matrix of loadings.
loading.weights: a matrix of loading weights.
Yscores: a matrix of Y-scores.
Yloadings: a matrix of Y-loadings.
projection: the projection matrix used to convert X to scores.
Xmeans: a vector of means of the X variables.
Ymeans: a vector of means of the Y variables.
fitted.values: an array of fitted values. The dimensions of fitted.values are c(nobj, npred, ncomp) with nobj the number samples and npred the number of Y variables.
residuals: an array of regression residuals. It has the same dimensions as fitted.values.
Xvar: a vector with the amount of X-variance explained by each component.
Xtotvar: Total variance in X.

If stripped is TRUE, only the components coefficients, Xmeans and Ymeans are returned.

Details

This function should not be called directly, but through the generic functions plsr or mvr with the argument method="oscorespls". It implements the orthogonal scores algorithm, as described in Martens and Næs (1989). This is one of the two “classical” PLSR algorithms, the other being the orthogonal loadings algorithm.

References

Martens, H., Næs, T. (1989) Multivariate calibration. Chichester: Wiley.

Author

Ron Wehrens and Bjørn-Helge Mevik