rbridge {rbridge}

Fit a Restricted Bridge Estimation

Description

Fit a restricted linear model via bridge penalized maximum likelihood. It is computed the regularization path which is consisted of lasso or ridge penalty at the a grid values for lambda

Usage

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

Arguments

X

Design matrix.

y

Response vector.

q

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

R

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

r

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.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

lambda

A user supplied lambda sequence. By default, the program compute a squence of values the length of nlambda.

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.

Details

In order to couple the bridge estimator with the restriction R beta = r, we solve the following optimization problem

\min RSS w.r.t ||\beta||_q and R\beta = r.

Value

An object of class rbridge, a list with entries

betas

Coefficients computed over the path of lambda

lambda

The lambda values which is given at the function

Author(s)

Bahadir Yuzbasi, Mohammad Arashi and Fikri Akdeniz
Maintainer: Bahadir Yuzbasi [e-mail]

See Also

cv.rbridge

Examples

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 <- rbridge(X, y, q = 1, R1.mat, r1.vec)
print(model1)

######## Model 2 based on second restrictions
model2 <- rbridge(X, y, q = 1, R2.mat, r2.vec)
print(model2)

######## Model 3 based on third restrictions
model3 <- rbridge(X, y, q = 1, R3.mat, r3.vec)
print(model3)

######## Model 4 based on fourth restrictions
model4 <- rbridge(X, y, q = 1, R4.mat, r4.vec)
print(model4)