Ridge Regression.

This function computes the optimal ridge regression model based on cross-validation.

ridge.cv(
  X,
  y,
  lambda = NULL,
  scale = TRUE,
  k = 10,
  plot.it = FALSE,
  groups = NULL,
  method.cor = "pearson",
  compute.jackknife = TRUE
)

Arguments

X	matrix of input observations. The rows of X contain the samples, the columns of X contain the observed variables
y	vector of responses. The length of y must equal the number of rows of X
lambda	Vector of penalty terms.
scale	Scale the columns of X? Default is scale=TRUE.
k	Number of splits in k-fold cross-validation. Default value is k=10.
plot.it	Plot the cross-validation error as a function of lambda? Default is FALSE.
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.
method.cor	How should the correlation to the response be computed? Default is ''pearson''.
compute.jackknife	Logical. If TRUE, the regression coefficients on each of the cross-validation splits is stored. Default is TRUE.

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

lambda.opt

optimal value of lambda, 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

lambda.opt.cor

optimal value of lambda, 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

coefficients.jackknife

Array of the regression coefficients on each of the cross-validation splits. The dimension is ncol(X) x length(lambda) x k.

Details

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.cv, pcr.cv, benchmark.regression

Author

Nicole Kraemer

Examples

n<-100 # number of observations
p<-60 # number of variables
X<-matrix(rnorm(n*p),ncol=p) 
y<-rnorm(n)
ridge.object<-ridge.cv(X,y)