dglars (version 1.0.2)

gdf: Compute the generalized degrees-of-freedom.

Description

gdf is used to compute the first order estimator of the generalized degrees-of-freedom for logistic regression model.

Usage

gdf(object)

Arguments

object

fitted dglars object.

Value

• gdf returns a vector of length np with the generalized degrees-of-freedom.

Details

For a general nonlinear modelling procedure, a more rigorous definition of degrees-of-freedom is obtained using the covariance penalty theory (Efron, 2004). When we work with a logistic regression model defined in a low dimensional setting, the gdf function can be used to compute the first order estimator proposed in Augugliaro et al. (2013). How to define an estimator of the generalized degrees-of-freedom in a high-dimensional setting is still an open question. Simulation studies seem to show that for a Poisson regression model the number of nonzero coefficients can be considered a satisfying approximation to the generalized degrees-of-freedom, for this reason the first order estimator is not implemented for this model.

References

Augugliaro L., Mineo A.M. and Wit E.C. (2013) dgLARS: a differential geometric approach to sparse generalized linear models, Journal of the Royal Statistical Society. Series B., Vol 75(3), 471-498.

Efron B. (2004) The estimation of prediction error: covariance penalties and cross-validation, Journal of the American Statistical Association, Vol. 99(467), 619-632.

See Also

dglars function.

Examples

set.seed(123)

n <- 100
p <- 10
X <- matrix(rnorm(n*p), n, p)
b <- 1:2
eta <- b[1] + X[,1] * b[2]
mu <- binomial()$linkinv(eta)
y <- rbinom(n, 1, mu)
fit <- dglars.fit(X, y, family = "binomial")
gdf(fit)