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, returnX=FALSE, ...)

Arguments

X

The design matrix, as in grpreg.

y

The response vector (or matrix), as in grpreg.

group

The grouping vector, as in grpreg.

family

Either "gaussian" or "binomial", depending on the response.

nlambda

The number of lambda values, as in grpreg.

lambda

A user supplied sequence of lambda values, as in grpreg.

lambda.min

The smallest value for lambda, as in grpreg.

lambda.max

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 to guess lambda.max, but this is not particularly accurate.

alpha

Tuning parameter for the balance between the group penalty and the L2 penalty, as in grpreg.

eps

Convergence threshhold, as in grpreg.

delta

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.

max.iter

Maximum number of iterations, as in grpreg.

gamma

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.

group.multiplier

The multiplicative factor by which each group's penalty is to be multiplied, as in grpreg.

warn

Should the function give a warning if it fails to converge? As in grpreg.

returnX

Return the standardized design matrix (and associated group structure information)? Default is FALSE.

...

Not used.

Details

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.min 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.

Value

An object with S3 class "grpreg", as in grpreg.

References

  • Huang J, Ma S, Xie H, and Zhang C. (2009) A group bridge approach for variable selection. Biometrika, 96: 339-355. doi: 10.1093/biomet/asp020

  • Breheny P and Huang J. (2009) Penalized methods for bi-level variable selection. Statistics and its interface, 2: 369-380. doi: 10.4310/sii.2009.v2.n3.a10

Author

Patrick Breheny

See also

Examples

data(Birthwt) X <- Birthwt$X group <- Birthwt$group ## Linear regression y <- Birthwt$bwt fit <- gBridge(X, y, group) plot(fit)
select(fit)$beta
#> (Intercept) age1 age2 age3 lwt1 lwt2 #> 2.99879014 0.00000000 0.89255360 0.28150939 1.01892522 0.00000000 #> lwt3 white black smoke ptl1 ptl2m #> 0.73433117 0.26506631 -0.04017367 -0.22057110 -0.17179296 0.00000000 #> ht ui ftv1 ftv2 ftv3m #> -0.28667606 -0.38431366 0.00000000 0.00000000 0.00000000
## Logistic regression y <- Birthwt$low fit <- gBridge(X, y, group, family="binomial") plot(fit)
select(fit)$beta
#> (Intercept) age1 age2 age3 lwt1 lwt2 #> -1.0653116 0.0000000 0.0000000 0.0000000 -4.2881399 0.0000000 #> lwt3 white black smoke ptl1 ptl2m #> -2.1227947 0.0000000 0.0000000 0.0000000 1.3568294 0.0000000 #> ht ui ftv1 ftv2 ftv3m #> 0.8476535 0.0000000 0.0000000 0.0000000 0.0000000