Model selection for Princinpal Components regression based on cross-validation

This function computes the optimal model parameter using cross-validation. Mdel selection is based on mean squared error and correlation to the response, respectively.

pcr.cv(
  X,
  y,
  k = 10,
  m = min(ncol(X), nrow(X) - 1),
  groups = NULL,
  scale = TRUE,
  eps = 1e-06,
  plot.it = FALSE,
  compute.jackknife = TRUE,
  method.cor = "pearson",
  supervised = FALSE
)

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.
m	maximal number of principal components. Default is m=min(ncol(X),nrow(X)-1).
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.
scale	Should the predictor variables be scaled to unit variance? Default is TRUE.
eps	precision. Eigenvalues of the correlation matrix of X that are smaller than eps are set to 0. The default value is eps=10^{-6}.
plot.it	Logical. If TRUE, the function plots the cross-validation-error as a function of the number of components. Default is FALSE.
compute.jackknife	Logical. If TRUE, the regression coefficients on each of the cross-validation splits is stored. Default is TRUE.
method.cor	How should the correlation to the response be computed? Default is ''pearson''.
supervised	Should the principal components be sorted by decreasing squared correlation to the response? Default is FALSE.

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 correlation

coefficients.jackknife

Array of the regression coefficients on each of the cross-validation splits, if compute.jackknife=TRUE. In this case, the dimension is ncol(X) x (m+1) x k.

Details

The function computes the principal components on the scaled predictors. Based on the regression coefficients coefficients.jackknife computed on the cross-validation splits, we can estimate their mean and their variance using the jackknife. We remark that under a fixed design and the assumption of normally distributed y-values, we can also derive the true distribution of the regression coefficients.

See also

pls.model, pls.ic

Author

Nicole Kraemer, Mikio L. Braun

Examples

n<-500 # number of observations
p<-5 # number of variables
X<-matrix(rnorm(n*p),ncol=p)
y<-rnorm(n)

# compute PCR 
pcr.object<-pcr.cv(X,y,scale=FALSE,m=3)
pcr.object1<-pcr.cv(X,y,groups=sample(c(1,2,3),n,replace=TRUE),m=3)