Fit regularization paths for linear and logistic group bridge-penalized regression models over a grid of values for the regularization parameter lambda.
gBridge(X, y, group=1:ncol(X), family=c("gaussian", "binomial",
"poisson"), nlambda=100, lambda, lambda.min={if (nrow(X) > ncol(X)) .001
else .05}, lambda.max, alpha=1, eps=.001, delta=1e-7, max.iter=10000,
gamma=0.5, group.multiplier, warn=TRUE)
The design matrix, as in grpreg
.
The response vector (or matrix), as in grpreg
.
The grouping vector, as in grpreg
.
Either "gaussian" or "binomial", depending on the response.
The number of lambda
values, as in
grpreg
.
A user supplied sequence of lambda
values, as in
grpreg
.
The smallest value for lambda
, as in
grpreg
.
The maximum value for lambda
. Unlike the
penalties in grpreg
, it is not possible to solve for
lambda.max
directly with group bridge models. Thus, it must
be specified by the user. If it is not specified, gBridge
will attempt a guess at lambda.max
, but this is not
particularly accurate.
Tuning parameter for the balance between the group
penalty and the L2 penalty, as in grpreg
.
Convergence threshhold, as in grpreg
.
The group bridge penalty is not differentiable at zero,
and requires a small number delta
to bound it away from
zero. There is typically no need to change this value.
Maximum number of iterations, as in
grpreg
.
Tuning parameter of the group bridge penalty (the exponent to which the L1 norm of the coefficients in the group are raised). Default is 0.5, the square root.
The multiplicative factor by which each
group's penalty is to be multiplied, as in grpreg
.
Should the function give a warning if it fails to
converge? As in grpreg
.
An object with S3 class "grpreg"
, as in
grpreg
.
This method fits the group bridge method of Huang et al. (2009).
Unlike the penalties in grpreg
, the group bridge is not
differentiable at zero; because of this, a number of changes must be
made to the algorithm, which is why it has its own function. Most
notably, the method is unable to start at lambda.max
; it must
start at lambda.max
and proceed in the opposite direction.
In other respects, the usage and behavior of the function is similar
to the rest of the grpreg
package.
Huang, J., Ma, S., Xie, H., and Zhang, C. (2009) A group bridge approach for variable selection. Biometrika, 96: 339-355.
Breheny, P. and Huang, J. (2009) Penalized methods for bi-level variable selection. Statistics and its interface, 2: 369-380.
# NOT RUN {
data(Birthwt)
X <- Birthwt$X
group <- Birthwt$group
## Linear regression
y <- Birthwt$bwt
fit <- gBridge(X, y, group)
plot(fit)
select(fit)
## Logistic regression
y <- Birthwt$low
fit <- gBridge(X, y, group, family="binomial")
plot(fit)
select(fit)
# }
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