dglars (version 2.1.7)

gdf: Estimate the Generalized Degrees-of-Freedom

Description

gdf returns to estimate of the generalized degrees-of-freedom.

Usage

gdf(object)

Value

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

Arguments

object

fitted dglars object.

Author

Luigi Augugliaro and Hassan Pazira
Maintainer: Luigi Augugliaro

Details

For a general nonlinear modelling procedure, a rigorous definition of degrees-of-freedom is obtained using the covariance penalty theory (Efron, 2004). This theory was used in Augugliaro et al. (2013) to define a measure of model complexity for the dgLARS method, called “generalized degrees-of-freedom”. The gdf function implements the estimator proposed in Augugliaro et al. (2013).

References

Augugliaro L., Mineo A.M. and Wit E.C. (2014) <doi:10.18637/jss.v059.i08> dglars: An R Package to Estimate Sparse Generalized Linear Models, Journal of Statistical Software, Vol 59(8), 1-40. https://www.jstatsoft.org/v59/i08/.

Augugliaro L., Mineo A.M. and Wit E.C. (2013) <doi:10.1111/rssb.12000> 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) <doi:10.1198/016214504000000692> The estimation of prediction error: covariance penalties and cross-validation, Journal of the American Statistical Association, Vol. 99(467), 619-632.

See Also

dglars, AIC.dglars, BIC.dglars and summary.dglars.

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(y ~ X, binomial)
gdf(fit)