cv.rbridge: Cross-validation for rbridge

Description

Does k-fold cross-validation for rbridge, produces a plot, and returns a value for lambda

Usage

cv.rbridge(X, y, q, R, r, lambda, nfolds = 10, lambda.min = ifelse(n >
  p, 0.001, 0.05), nlambda = 100, eta = 1e-07, converge = 10^10,
  num_threads = 10)

Arguments

X matrix as in rbridge.

response y as in rbridge.

is the degree of norm which includes ridge regression with q=2 and lasso estimates with q=1 as special cases

is m by p (m<p) matrix of constants.

is a m-vector of known prespecified constants. If it is given true restriction, then $$r - R\beta = 0.$$ Values for r should be given as a matrix. See "Examples".

lambda

lambda sequence; default is NULL. It is given by user or cv.rbridge chooses its own sequence.

nfolds

number of folds - default is 10.

lambda.min

The smallest value for lambda if n>p is 0.001 and 0.05 otherwise.

nlambda

The number of lambda values - default is 100

eta

is a preselected small positive threshold value. It is deleted jth variable to make the algorithm stable and also is excluded jth variable from the final model. Default is 1e-07.

converge

is the value of converge. Defaults is 10^10. In each iteration, it is calculated by sum of square the change in linear predictor for each coefficient. The algorithm iterates until converge > eta.

num_threads

Number of threads used for parallel computation over the folds,

Value

An object of class rbridge, a list with entries

cve

the mean cross-validated error.

cvse

estimate of standard error of cvm.

cvup

upper curve = cvm+cvsd.

cvlo

lower curve = cvm-cvsd.

lambda

the values of lambda used in the fits

number of non-zero coefficients at each lambda.

betas

estimated coefficient at each lambda.

lambda.min

value of lambda that gives minimum cve

lambda.1se

largest value of lambda such that error is within 1 standard error of the minimum

Details

Computes cv.rbridge

Examples

Run this code

# NOT RUN {
set.seed(2019) 
beta <- c(3, 1.5, 0, 0, 2, 0, 0, 0)
p <- length(beta)
beta <- matrix(beta, nrow = p, ncol = 1)
p.active <- which(beta != 0)

### Restricted Matrix and vector
### Res 1
c1 <- c(1,1,0,0,1,0,0,0)
R1.mat <- matrix(c1,nrow = 1, ncol = p)
r1.vec <- as.matrix(c(6.5),1,1)
### Res 2
c2 <- c(-1,1,0,0,1,0,0,0)
R2.mat <- matrix(c2,nrow = 1, ncol = p)
r2.vec <- matrix(c(0.5),nrow = 1, ncol = 1)
### Res 3
R3.mat <- t(matrix(c(c1,c2),nrow = p, ncol = 2))
r3.vec <- matrix(c(6.5,0.5),nrow = 2, ncol = 1)
### Res 4
R4.mat = diag(1,p,p)[-p.active,]
r4.vec <- matrix(rep(0,p-length(p.active)),nrow = p-length(p.active), ncol = 1)

n = 100
X = matrix(rnorm(n*p),n,p)
y = X%*%beta + rnorm(n) 

######## Model 1 based on first restrictions
model1 <- cv.rbridge(X, y, q = 1, R1.mat, r1.vec)
print(model1)
coef(model1,s='lambda.min')
coef(model1,s='lambda.1se')
predict(model1,newx=X[1:5,], s="lambda.min", type="response")
predict(model1, s="lambda.min",type="coefficient")
predict(model1, s="lambda.1se",type="coefficient")

######## Model 2 based on second restrictions
model2 <- cv.rbridge(X, y, q = 1, R2.mat, r2.vec)
print(model2)
coef(model2,s='lambda.min')
coef(model2,s='lambda.1se')
predict(model2,newx=X[1:5,], s="lambda.min", type="response")
predict(model2, s="lambda.min",type="coefficient")
predict(model2, s="lambda.1se",type="coefficient")

######## Model 3 based on third restrictions
model3 <- cv.rbridge(X, y, q = 1, R3.mat, r3.vec)
print(model3)
coef(model3,s='lambda.min')
coef(model3,s='lambda.1se')
predict(model3,newx=X[1:5,], s="lambda.min", type="response")
predict(model3, s="lambda.min",type="coefficient")
predict(model3, s="lambda.1se",type="coefficient")

######## Model 4 based on fourth restrictions
model4 <- cv.rbridge(X, y, q = 1, R4.mat, r4.vec)
print(model4)
coef(model4,s='lambda.min')
coef(model4,s='lambda.1se')
predict(model4,newx=X[1:5,], s="lambda.min", type="response")
predict(model4, s="lambda.min",type="coefficient")
predict(model4, s="lambda.1se",type="coefficient")


# }