Package 'rbridge' reference manual

Title:	Restricted Bridge Estimation
Description:	Bridge Regression estimation with linear restrictions defined in Yuzbasi et al. (2019) <arXiv:1910.03660>. Special cases of this approach fit the restricted LASSO, restricted RIDGE and restricted Elastic Net estimators.
Authors:	Bahadir Yuzbasi, Mohammad Arashi and Fikri Akdeniz
Maintainer:	Bahadir Yuzbasi <[email protected]>
License:	GPL-3
Version:	1.0.2
Built:	2024-11-06 04:11:19 UTC
Source:	https://github.com/cran/rbridge

Fit a Bridge Estimation

Description

Fit a 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

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

Computes bridge estimation

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 [email protected]

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)

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

model1 <- bridge(X, y, q = 1)
print(model1)

model2 <- bridge(X, y, q = 2)
print(model2)

set.seed(2019) 
beta <- c(3, 1.5, 0, 0, 2, 0, 0, 0)
p <- length(beta)
beta <- matrix(beta, nrow = p, ncol = 1)

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

model1 <- bridge(X, y, q = 1)
print(model1)

model2 <- bridge(X, y, q = 2)
print(model2)

Extract coefficients from a 'bridge' object

Description

Extract coefficients from a 'bridge' object.

Usage

## S3 method for class 'bridge'
coef(object, s = c("lambda.1se", "lambda.min"), ...)
## S3 method for class 'bridge'
coef(object, s = c("lambda.1se", "lambda.min"), ...)

Arguments

`object`	A 'bridge' object.
`s`	Value(s) of the penalty parameter lambda at which predictions are required.
`...`	Additional arguments for compatibility.

Value

A vector of coefficients

Author(s)

Bahadir Yuzbasi, Mohammad Arashi and Fikri Akdeniz
Maintainer: Bahadir Yuzbasi [email protected]

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)

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

model1 <- bridge(X, y, q = 1)
coef(model1,s='lambda.min')
set.seed(2019) 
beta <- c(3, 1.5, 0, 0, 2, 0, 0, 0)
p <- length(beta)
beta <- matrix(beta, nrow = p, ncol = 1)

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

model1 <- bridge(X, y, q = 1)
coef(model1,s='lambda.min')

Extract coefficients from a 'cv.bridge' object

Description

Extract coefficients from a 'cv.bridge' object.

Usage

## S3 method for class 'cv.bridge'
coef(object, s = c("lambda.1se", "lambda.min"), ...)
## S3 method for class 'cv.bridge'
coef(object, s = c("lambda.1se", "lambda.min"), ...)

Arguments

`object`	A 'cv.bridge' object.
`s`	Value(s) of the penalty parameter lambda at which predictions are required.
`...`	Additional arguments for compatibility.

Value

A vector of coefficients

Author(s)

Bahadir Yuzbasi, Mohammad Arashi and Fikri Akdeniz
Maintainer: Bahadir Yuzbasi [email protected]

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)

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

model1 <- cv.bridge(X, y, q = 1)
coef(model1,s='lambda.min')
set.seed(2019) 
beta <- c(3, 1.5, 0, 0, 2, 0, 0, 0)
p <- length(beta)
beta <- matrix(beta, nrow = p, ncol = 1)

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

model1 <- cv.bridge(X, y, q = 1)
coef(model1,s='lambda.min')

Extract coefficients from a 'cv.rbridge' object

Description

Extract coefficients from a 'cv.rbridge' object.

Usage

## S3 method for class 'cv.rbridge'
coef(object, s = c("lambda.1se", "lambda.min"), ...)
## S3 method for class 'cv.rbridge'
coef(object, s = c("lambda.1se", "lambda.min"), ...)

Arguments

`object`	A 'cv.rbridge' object.
`s`	Value(s) of the penalty parameter lambda at which predictions are required.
`...`	Additional arguments for compatibility.

Value

A vector of coefficients

Author(s)

Bahadir Yuzbasi, Mohammad Arashi and Fikri Akdeniz
Maintainer: Bahadir Yuzbasi [email protected]

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)

### Restricted Matrix and vector
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)

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)
coef(model1,s='lambda.min')
set.seed(2019) 
beta <- c(3, 1.5, 0, 0, 2, 0, 0, 0)
p <- length(beta)
beta <- matrix(beta, nrow = p, ncol = 1)

### Restricted Matrix and vector
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)

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)
coef(model1,s='lambda.min')

Extract coefficients from a 'rbridge' object

Description

Makes predictions from a cross-validated 'rbridge' model

Usage

## S3 method for class 'rbridge'
coef(object, s = c("lambda.1se", "lambda.min"), ...)
## S3 method for class 'rbridge'
coef(object, s = c("lambda.1se", "lambda.min"), ...)

Arguments

`object`	A 'rbridge' object.
`s`	Value(s) of the penalty parameter lambda at which predictions are required.
`...`	Additional arguments for compatibility.

Value

Among a matrix with predictions, a vector non-zero indexing or a vector of coefficients

Author(s)

Bahadir Yuzbasi, Mohammad Arashi and Fikri Akdeniz
Maintainer: Bahadir Yuzbasi [email protected]

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)

### Restricted Matrix and vector
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)

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)
coef(model1,s='lambda.min')

set.seed(2019) 
beta <- c(3, 1.5, 0, 0, 2, 0, 0, 0)
p <- length(beta)
beta <- matrix(beta, nrow = p, ncol = 1)

### Restricted Matrix and vector
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)

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)
coef(model1,s='lambda.min')

Cross-validation for bridge

Description

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

Usage

cv.bridge(X, y, q, lambda, nfolds = 10, lambda.min = ifelse(n > p,
  0.001, 0.05), nlambda = 100, eta = 1e-07, converge = 10^10,
  num_threads = 10)
cv.bridge(X, y, q, 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`	`X` matrix as in bridge.
`y`	response `y` as in bridge.
`q`	is the degree of norm which includes ridge regression with `q=2` and lasso estimates with `q=1` as special cases
`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,

Details

Computes bridge

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
`nz`	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

Author(s)

Bahadir Yuzbasi, Mohammad Arashi and Fikri Akdeniz
Maintainer: Bahadir Yuzbasi [email protected]

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)

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

######## Model 1 
model1 <- cv.bridge(X, y, q = 1)
print(model1)
coef(model1,s='lambda.min')
predict(model1,newx=X[1:5,], s="lambda.min", type="response")
predict(model1, s="lambda.min",type="coefficient")

######## Model 2 
model2 <- cv.bridge(X, y, q = 2)
print(model2)
coef(model2,s='lambda.min')
predict(model2,newx=X[1:5,], s="lambda.min", type="response")
predict(model2, s="lambda.min",type="coefficient")

set.seed(2019) 
beta <- c(3, 1.5, 0, 0, 2, 0, 0, 0)
p <- length(beta)
beta <- matrix(beta, nrow = p, ncol = 1)

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

######## Model 1 
model1 <- cv.bridge(X, y, q = 1)
print(model1)
coef(model1,s='lambda.min')
predict(model1,newx=X[1:5,], s="lambda.min", type="response")
predict(model1, s="lambda.min",type="coefficient")

######## Model 2 
model2 <- cv.bridge(X, y, q = 2)
print(model2)
coef(model2,s='lambda.min')
predict(model2,newx=X[1:5,], s="lambda.min", type="response")
predict(model2, s="lambda.min",type="coefficient")

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)
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`	`X` matrix as in rbridge.
`y`	response `y` as in rbridge.
`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`	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,

Details

Computes cv.rbridge

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
`nz`	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

Author(s)

Bahadir Yuzbasi, Mohammad Arashi and Fikri Akdeniz
Maintainer: Bahadir Yuzbasi [email protected]

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 <- 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")


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")

Plot a 'cv.bridge' object function

Description

Plots the cross-validation curve, and upper and lower standard deviation curves, as a function of the lambda values used.

Usage

## S3 method for class 'cv.bridge'
plot(x, sign.lambda = 1, ...)
## S3 method for class 'cv.bridge'
plot(x, sign.lambda = 1, ...)

Arguments

`x`	Design matrix.
`sign.lambda`	Either plot against `log(lambda)` (default) or its negative if sign.`lambda=-1`.
`...`	Other graphical parameters to plot

Author(s)

Bahadir Yuzbasi, Mohammad Arashi and Fikri Akdeniz
Maintainer: Bahadir Yuzbasi [email protected]

Plot a 'cv.rbridge' object function

Description

Plots the cross-validation curve, and upper and lower standard deviation curves, as a function of the lambda values used.

Usage

## S3 method for class 'cv.rbridge'
plot(x, sign.lambda = 1, ...)
## S3 method for class 'cv.rbridge'
plot(x, sign.lambda = 1, ...)

Arguments

`x`	Design matrix.
`sign.lambda`	Either plot against `log(lambda)` (default) or its negative if sign.`lambda=-1`.
`...`	Other graphical parameters to plot

Author(s)

Bahadir Yuzbasi, Mohammad Arashi and Fikri Akdeniz
Maintainer: Bahadir Yuzbasi [email protected]

Make predictions from a 'bridge' object

Description

Makes predictions from a cross-validated 'bridge' model

Usage

## S3 method for class 'bridge'
predict(object, newx, s = c("lambda.min", "lambda.1se"),
  type = c("response", "nonzero", "coefficients"), ...)
## S3 method for class 'bridge'
predict(object, newx, s = c("lambda.min", "lambda.1se"),
  type = c("response", "nonzero", "coefficients"), ...)

Arguments

`object`	A 'bridge' object.
`newx`	Matrix of new values for x at which predictions are to be made.
`s`	Value(s) of the penalty parameter lambda at which predictions are required.
`type`	It should one of "response", "nonzero" or "coefficients". The "response" is for predicted values, the "nonzero" is for exacting non-zero coefficients and the "coefficients" is for the estimated coefficients.
`...`	Additional arguments for compatibility.

Value

Among a matrix with predictions, a vector non-zero indexing or a vector of coefficients

Author(s)

Bahadir Yuzbasi, Mohammad Arashi and Fikri Akdeniz
Maintainer: Bahadir Yuzbasi [email protected]

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)

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

model1 <- bridge(X, y, q = 1)
predict(model1,newx=X[1:5,], s="lambda.min", type="response")
predict(model1, s="lambda.min",type="coefficient")
set.seed(2019) 
beta <- c(3, 1.5, 0, 0, 2, 0, 0, 0)
p <- length(beta)
beta <- matrix(beta, nrow = p, ncol = 1)

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

model1 <- bridge(X, y, q = 1)
predict(model1,newx=X[1:5,], s="lambda.min", type="response")
predict(model1, s="lambda.min",type="coefficient")

Make predictions from a 'cv.bridge' object

Description

Makes predictions from a cross-validated 'cv.bridge' model

Usage

## S3 method for class 'cv.bridge'
predict(object, newx, s = c("lambda.min",
  "lambda.1se"), type = c("response", "nonzero", "coefficients"), ...)
## S3 method for class 'cv.bridge'
predict(object, newx, s = c("lambda.min",
  "lambda.1se"), type = c("response", "nonzero", "coefficients"), ...)

Arguments

`object`	A 'cv.bridge' object.
`newx`	Matrix of new values for x at which predictions are to be made.
`s`	Value(s) of the penalty parameter lambda at which predictions are required.
`type`	It should one of "response", "nonzero" or "coefficients". The "response" is for predicted values, the "nonzero" is for exacting non-zero coefficients and the "coefficients" is for the estimated coefficients.
`...`	Additional arguments for compatibility.

Value

Among a matrix with predictions, a vector non-zero indexing or a vector of coefficients

Author(s)

Bahadir Yuzbasi, Mohammad Arashi and Fikri Akdeniz
Maintainer: Bahadir Yuzbasi [email protected]

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)

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

model1 <- cv.bridge(X, y, q = 1)
coef(model1,s='lambda.min')
predict(model1,newx=X[1:5,], s="lambda.min", type="response")
predict(model1, s="lambda.min",type="coefficient")
set.seed(2019) 
beta <- c(3, 1.5, 0, 0, 2, 0, 0, 0)
p <- length(beta)
beta <- matrix(beta, nrow = p, ncol = 1)

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

model1 <- cv.bridge(X, y, q = 1)
coef(model1,s='lambda.min')
predict(model1,newx=X[1:5,], s="lambda.min", type="response")
predict(model1, s="lambda.min",type="coefficient")

Make predictions from a 'cv.rbridge' object

Description

Makes predictions from a cross-validated 'cv.rbridge' model

Usage

## S3 method for class 'cv.rbridge'
predict(object, newx, s = c("lambda.min",
  "lambda.1se"), type = c("response", "nonzero", "coefficients"), ...)
## S3 method for class 'cv.rbridge'
predict(object, newx, s = c("lambda.min",
  "lambda.1se"), type = c("response", "nonzero", "coefficients"), ...)

Arguments

`object`	A 'cv.rbridge' object.
`newx`	Matrix of new values for x at which predictions are to be made.
`s`	Value(s) of the penalty parameter lambda at which predictions are required.
`type`	It should one of "response", "nonzero" or "coefficients". The "response" is for predicted values, the "nonzero" is for exacting non-zero coefficients and the "coefficients" is for the estimated coefficients.
`...`	Additional arguments for compatibility.

Value

Among a matrix with predictions, a vector non-zero indexing or a vector of coefficients

Author(s)

Bahadir Yuzbasi, Mohammad Arashi and Fikri Akdeniz
Maintainer: Bahadir Yuzbasi [email protected]

Bahadir Yuzbasi maintainer Baha

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)

### Restricted Matrix and vector
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)

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)
coef(model1,s='lambda.min')
predict(model1,newx=X[1:5,], s="lambda.min", type="response")
predict(model1, s="lambda.min",type="coefficient")
set.seed(2019) 
beta <- c(3, 1.5, 0, 0, 2, 0, 0, 0)
p <- length(beta)
beta <- matrix(beta, nrow = p, ncol = 1)

### Restricted Matrix and vector
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)

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)
coef(model1,s='lambda.min')
predict(model1,newx=X[1:5,], s="lambda.min", type="response")
predict(model1, s="lambda.min",type="coefficient")

Make predictions from a 'rbridge' object

Description

Makes predictions from a cross-validated 'rbridge' model

Usage

## S3 method for class 'rbridge'
predict(object, newx, s = c("lambda.min",
  "lambda.1se"), type = c("response", "nonzero", "coefficients"), ...)
## S3 method for class 'rbridge'
predict(object, newx, s = c("lambda.min",
  "lambda.1se"), type = c("response", "nonzero", "coefficients"), ...)

Arguments

`object`	A 'rbridge' object.
`newx`	Matrix of new values for x at which predictions are to be made.
`s`	Value(s) of the penalty parameter lambda at which predictions are required.
`type`	It should one of "response", "nonzero" or "coefficients". The "response" is for predicted values, the "nonzero" is for exacting non-zero coefficients and the "coefficients" is for the estimated coefficients.
`...`	Additional arguments for compatibility.

Value

Among a matrix with predictions, a vector non-zero indexing or a vector of coefficients

Author(s)

Bahadir Yuzbasi, Mohammad Arashi and Fikri Akdeniz
Maintainer: Bahadir Yuzbasi [email protected]

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)

### Restricted Matrix and vector
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)

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)
predict(model1,newx=X[1:5,], s="lambda.min", type="response")
predict(model1, s="lambda.min",type="coefficient")
set.seed(2019) 
beta <- c(3, 1.5, 0, 0, 2, 0, 0, 0)
p <- length(beta)
beta <- matrix(beta, nrow = p, ncol = 1)

### Restricted Matrix and vector
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)

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)
predict(model1,newx=X[1:5,], s="lambda.min", type="response")
predict(model1, s="lambda.min",type="coefficient")

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)
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 [email protected]

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)

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)

Package 'rbridge'

Help Index

Fit a Bridge Estimation

Description

Usage

Arguments

Details

Value

Author(s)

See Also

Examples

Extract coefficients from a 'bridge' object

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Extract coefficients from a 'cv.bridge' object

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Extract coefficients from a 'cv.rbridge' object

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Extract coefficients from a 'rbridge' object

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Cross-validation for bridge

Description

Usage

Arguments

Details

Value

Author(s)

See Also

Examples

Cross-validation for rbridge

Description

Usage

Arguments

Details

Value

Author(s)

See Also

Examples

Plot a 'cv.bridge' object function

Description

Usage

Arguments

Author(s)

Plot a 'cv.rbridge' object function

Description

Usage

Arguments

Author(s)

Make predictions from a 'bridge' object

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Make predictions from a 'cv.bridge' object