select: Select an value of lambda along a grpreg path

Description

Selects a point along the regularization path of a fitted grpreg object according to the AIC, BIC, or GCV criteria.

Usage

select(obj, ...)
# S3 method for grpreg
select(
  obj,
  criterion = c("BIC", "AIC", "GCV", "AICc", "EBIC"),
  df.method = c("default", "active"),
  smooth = FALSE,
  ...
)

Value

A list containing:

lambda: The selected value of the regularization parameter, lambda.
beta: The vector of coefficients at the chosen value of lambda.
df: The effective number of model parameters at the chosen value of lambda.
IC: A vector of the calculated model selection criteria for each point on the regularization path.

Arguments

obj: A fitted grpreg object.
...: For S3 method compatibility.
criterion: The criterion by which to select the regularization parameter. One of "AIC", "BIC", "GCV", "AICc", or "EBIC"; default is "BIC".
df.method: How should effective model parameters be calculated? One of: "active", which counts the number of nonzero coefficients; or "default", which uses the calculated df returned by grpreg. Default is "default".
smooth: Applies a smoother to the information criteria before selecting the optimal value.

Details

The criteria are defined as follows, where $L$ is the deviance (i.e, -2 times the log-likelihood), $\nu$ is the degrees of freedom, and $n$ is the sample size:

$$AIC = L + 2\nu$$ $$BIC = L + \log(n)\nu$$ $$GCV = \frac{L}{(1-\nu/n)^2}$$ $$AICc = AIC + 2\frac{\nu(\nu+1)}{n-\nu-1}$$ $$EBIC = BIC + 2 \log{p \choose \nu}$$

Examples

Run this code

data(Birthwt)
X <- Birthwt$X
y <- Birthwt$bwt
group <- Birthwt$group
fit <- grpreg(X, y, group, penalty="grLasso")
select(fit)
select(fit,crit="AIC",df="active")
plot(fit)
abline(v=select(fit)$lambda)
par(mfrow=c(1,3))
l <- fit$lambda
xlim <- rev(range(l))
plot(l, select(fit)$IC, xlim=xlim, pch=19, type="o", ylab="BIC")
plot(l, select(fit,"AIC")$IC, xlim=xlim, pch=19, type="o",ylab="AIC")
plot(l, select(fit,"GCV")$IC, xlim=xlim, pch=19, type="o",ylab="GCV")