Model selection for Partial Least Squares based on cross-validation

This function computes the optimal model parameter using cross-validation.

pls.cv(
  X,
  y,
  k = 10,
  groups = NULL,
  m = ncol(X),
  use.kernel = FALSE,
  compute.covariance = FALSE,
  method.cor = "pearson"
)

Arguments

X	matrix of predictor observations.
y	vector of response observations. The length of `y` is the same as the number of rows of `X`.
k	number of cross-validation splits. Default is 10.
groups	an optional vector with the same length as `y`. It encodes a partitioning of the data into distinct subgroups. If `groups` is provided, `k=10` is ignored and instead, cross-validation is performed based on the partioning. Default is `NULL`.
m	maximal number of Partial Least Squares components. Default is `m=ncol(X)`.
use.kernel	Use kernel representation? Default is `use.kernel=FALSE`.
compute.covariance	If `TRUE`, the function computes the covariance for the cv-optimal regression coefficients.
method.cor	How should the correlation to the response be computed? Default is ''pearson''.

Value

cv.error.matrix

matrix of cross-validated errors based on mean squared error. A row corresponds to one cross-validation split.

cv.error

vector of cross-validated errors based on mean squared error

m.opt

optimal number of components based on mean squared error

intercept

intercept of the optimal model, based on mean squared error

coefficients

vector of regression coefficients of the optimal model, based on mean squared error

cor.error.matrix

matrix of cross-validated errors based on correlation. A row corresponds to one cross-validation split.

cor.error

vector of cross-validated errors based on correlation

m.opt.cor

optimal number of components based on correlation

intercept.cor

intercept of the optimal model, based on correlation

coefficients.cor

vector of regression coefficients of the optimal model, based on mean squared error

covariance

If TRUE and use.kernel=FALSE, the covariance of the cv-optimal regression coefficients (based on mean squared error) is returned.

Details

The data are centered and scaled to unit variance prior to the PLS algorithm. It is possible to estimate the covariance matrix of the cv-optimal regression coefficients (compute.covariance=TRUE). Currently, this is only implemented if use.kernel=FALSE.

References

Kraemer, N., Sugiyama M. (2011). "The Degrees of Freedom of Partial Least Squares Regression". Journal of the American Statistical Association 106 (494) https://www.tandfonline.com/doi/abs/10.1198/jasa.2011.tm10107

Kraemer, N., Braun, M.L. (2007) "Kernelizing PLS, Degrees of Freedom, and Efficient Model Selection", Proceedings of the 24th International Conference on Machine Learning, Omni Press, 441 - 448

Author

Nicole Kraemer, Mikio L. Braun

Examples


n<-50 # number of observations
p<-5 # number of variables
X<-matrix(rnorm(n*p),ncol=p)
y<-rnorm(n)

# compute linear PLS
pls.object<-pls.cv(X,y,m=ncol(X))

# define random partioning
groups<-sample(c("a","b","c"),n,replace=TRUE)
pls.object1<-pls.cv(X,y,groups=groups)