Principal Component Regression

Fits a PCR model using the singular value decomposition.

svdpc.fit(X, Y, ncomp, center = TRUE, stripped = FALSE, ...)

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.
...	other arguments. Currently ignored.

Details

This function should not be called directly, but through the generic functions pcr or mvr with the argument method="svdpc". The singular value decomposition is used to calculate the principal components.

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.

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.

References

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

See also

mvr plsr pcr cppls