grpnet (version 0.5)

family.grpnet: Prepare 'family' Argument for grpnet

Description

Takes in the family argument from grpnet and returns a list containing the information needed for fitting and/or tuning the model.

Usage

family.grpnet(object, theta = 1)

Value

List with components:

family

same as input object, i.e., character specifying the family

linkinv

function for computing inverse of link function

dev.resids

function for computing deviance residuals

Arguments

object

one of the following characters specifying the exponential family: "gaussian", "binomial", "multinomial", "poisson", "negative.binomial", "Gamma", "inverse.gaussian"

theta

Additional ("size") parameter for negative binomial responses, where the variance function is defined as \(V(\mu) = \mu + \mu^2/ \theta\)

Author

Nathaniel E. Helwig <[e-mail]>

Details

There is only one available link function for each family:
* gaussian (identity): \(\mu = \mathbf{X}^\top \boldsymbol\beta\)
* binomial (logit): \(\log(\frac{\pi}{1 - \pi}) = \mathbf{X}^\top \boldsymbol\beta\)
* multinomial (symmetric): \(\pi_\ell = \frac{\exp(\mathbf{X}^\top \boldsymbol\beta_\ell)}{\sum_{l = 1}^m \exp(\mathbf{X}^\top \boldsymbol\beta_l)}\)
* poisson (log): \(\log(\mu) = \mathbf{X}^\top \boldsymbol\beta\)
* negative.binomial (log): \(\log(\mu) = \mathbf{X}^\top \boldsymbol\beta\)
* Gamma (log): \(\log(\mu) = \mathbf{X}^\top \boldsymbol\beta\)
* inverse.gaussian (log): \(\log(\mu) = \mathbf{X}^\top \boldsymbol\beta\)

References

Helwig, N. E. (2024). Versatile descent algorithms for group regularization and variable selection in generalized linear models. Journal of Computational and Graphical Statistics. tools:::Rd_expr_doi("10.1080/10618600.2024.2362232")

See Also

grpnet for fitting group elastic net regularization paths

cv.grpnet for k-fold cross-validation of lambda

Examples

family.grpnet("gaussian")

family.grpnet("binomial")

family.grpnet("multinomial")

family.grpnet("poisson")

family.grpnet("negbin", theta = 10)

family.grpnet("Gamma")

family.grpnet("inverse.gaussian")