# kernelpls.fit

##### Kernel PLS (Dayal and MacGregor)

Fits a PLSR model with the kernel algorithm.

- Keywords
- multivariate, regression

##### Usage

`kernelpls.fit(X, Y, ncomp, stripped = FALSE, ...)`

##### Arguments

- X
- a matrix of observations.
`NA`

s and`Inf`

s are not allowed. - Y
- a vector or matrix of responses.
`NA`

s and`Inf`

s are not allowed. - ncomp
- the number of components to be used in the modelling.
- 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 `plsr`

or `mvr`

with the argument
`method="kernelpls"`

(default). Kernel PLS is particularly efficient
when the number of objects is (much) larger than the number of
variables. The results are equal to the NIPALS algorithm. Several
different forms of kernel PLS have been described in literature, e.g.
by De Jong and Ter Braak, and two algorithms by Dayal and
MacGregor. This function implements the
fastest of the latter, not calculating the crossproduct matrix of
X. In the Dyal & MacGregor paper, this is “algorithm 1”.

##### Value

- 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 number of components.
- Xtotvar
- Total variance in
`X`

. If

`stripped`

is `TRUE`

, only the components
`coefficients`

, `Xmeans`

and `Ymeans`

are returned.
##### References

de Jong, S. and ter Braak, C. J. F. (1994) Comments on the PLS kernel
algorithm. *Journal of Chemometrics*, **8**, 169--174.

Dayal, B. S. and MacGregor, J. F. (1997) Improved PLS algorithms.
*Journal of Chemometrics*, **11**, 73--85.

##### See Also

`mvr`

`plsr`

`cppls`

`pcr`

`widekernelpls.fit`

`simpls.fit`

`oscorespls.fit`

*Documentation reproduced from package pls, version 2.5-0, License: GPL-2*