Modified version of Sijmen de Jong's SIMPLS
Description
Fits a PLSR model with the SIMPLS algorithm, modified to allow a weighted analysis.
Usage
1 
Arguments
X 
a matrix of observations. 
Y 
a vector or matrix of responses. 
ncomp 
the number of components to be used in the modelling. 
stripped 
logical. If 
... 
other arguments. Currently ignored. 
Details
This function is a modified version of
simpls.fit
from package pls
. Four
modification have been made:
The input matrices
X
andY
are not centered,The scores (
tt
in the code) are not centered,Added code to calculate the total variance in the
Y
matrix,Ytotvar
, and the variance inY
accounted for by each PLS axis,Yvar
(See Value below), andAdditional components are returned if argument
stripped
isTRUE
.
This function should not be called directly, but through
the generic function coca
.
SIMPLS is much faster than the NIPALS algorithm, especially when the number of X variables increases, but gives slightly different results in the case of multivariate Y. SIMPLS truly maximises the covariance criterion. According to de Jong, the standard PLS2 algorithms lie closer to ordinary leastsquares regression where a precise fit is sought; SIMPLS lies closer to PCR with stable predictions.
Value
A list containing the following components is returned:
coefficients 
an array of regression coefficients for 1, ...,

scores 
a matrix of scores. 
loadings 
a matrix of loadings. 
Yscores 
a matrix of Yscores. 
Yloadings 
a matrix of Yloadings. 
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

residuals 
an array of regression residuals. It has the same
dimensions as 
Xvar 
a vector with the amount of Xvariance explained by each number of components. 
Yvar 
a vector with the amount of Yvariance explained by each number of components. 
Xtotvar 
Total variance in 
Ytotvar 
Total variance in 
If stripped
is TRUE
, only the components
coefficients
, Xmeans
and Ymeans
, Xvar
and
Yvar
, and Xtotvar
and Ytotvar
are returned.
Author(s)
Based on simpls.fit
by Ron Wehrens and
BjornHelge Mevik, with simple modifications by Gavin L. Simpson.
References
de Jong, S. (1993) SIMPLS: an alternative approach to partial least squares regression. Chemometrics and Intelligent Laboratory Systems, 18, 251–263.
See Also
coca