GBlockBoost: Computation of the GBlockBoost Algorithm or Componentwise Boosting

Description

This function fits a GLM based on penalized likelihood inference by the GBlockBoost algorithm. However, it is primarily intended for internal use. You can access it via the argument setting method = "GBlockBoost" in lqa, cv.lqa or plot.lqa. If you use componentwise = TRUE then componentwise boosting will be applied.

Usage

GBlockBoost (x, y, family = NULL, penalty = NULL, intercept = 
       TRUE, weights = rep (1, nobs), control = lqa.control (), 
       componentwise, ...)

Arguments

matrix of standardized regressors. This matrix does not need to include a first column of ones when a GLM with intercept is to be fitted.

vector of observed response values.

family

a description of the error distribution and link function to be used in the model. This can be a character string naming a family function, a family function or the result of a call to a family function. See family() for further details.

penalty

a description of the penalty to be used in the fitting procedure, e.g. penalty = lasso (lambda = 1.7).

intercept

a logical object indicating whether the model should include an intercept (this is recommended) or not. The default value is intercept = TRUE.

weights

some additional weights for the observations.

control

a list of parameters for controlling the fitting process. See lqa.control.

componentwise

if TRUE then componentwise boosting will be applied, e.g. there is just a single regressors updated during each iteration. Otherwise GBlockBoost will be applied. If this argument is missing and your penalty is

...

further arguments.

Value

GBlockBoost returns a list containing the following elements:
coefficientsthe vector of standardized estimated coefficients.
beta.matmatrix containing the estimated coefficients from all iterations (rowwise).
m.stopthe number of iterations until AIC reaches its minimum.
stop.atthe number of iterations until convergence.
aic.vecvector of AIC criterion through all iterations.
bic.vecvector of BIC criterion through all iterations.
convergeda logical variable. This will be TRUE if the algorithm has indeed converged.
min.aicminimum value of AIC criterion.
min.bicminimum value of BIC criterion.
tr.Hthe trace of the hat matrix.
tr.Hatmatvector of hat matrix traces through all iterations.
dev.mvector of deviances through all iterations.

Details

The GBlockBoost algorithm has been introduced in Ulbricht & Tutz (2008). For a more detailed technical description, also for componentwise boosting, see Ulbricht (2010).

References

Ulbricht, Jan (2010) Variable Selection in Generalized Linear Models. Ph.D. Thesis. LMU Munich.