select.grpreg: 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, …)

Arguments

obj

A fitted grpreg object.

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.

…

For S3 method compatibility.

Value

A list containing:

lambda

The selected value of the regularization parameter, lambda.

beta

The vector of coefficients at the chosen value of lambda.

The effective number of model parameters at the chosen value of lambda.

A vector of the calculated model selection criteria for each point on the regularization path.

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

# NOT RUN {
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")
# }