Ridge Regression.

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

Usage

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.

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)