# 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

1 | ```
gdf(object)
``` |

### Arguments

`object` |
fitted |

### 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.

### Value

`gdf`

returns a vector of length `np`

with the generalized degrees-of-freedom.

### Author(s)

Luigi Augugliaro

Maintainer: Luigi Augugliaro luigi.augugliaro@unipa.it

### References

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

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

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