mboost (version 1.1-4)

methods: Methods for Gradient Boosting Objects

Description

Methods for models fitted by boosting algorithms.

Usage

## S3 method for class 'glmboost':
print(x, ...)
## S3 method for class 'gamboost':
print(x, ...)
## S3 method for class 'glmboost':
coef(object, ...)
## S3 method for class 'gamboost':
coef(object, ...)
## S3 method for class 'gamboost':
AIC(object, method = c("corrected", "classical", "gMDL"), ..., k = 2)
## S3 method for class 'glmboost':
AIC(object, method = c("corrected", "classical", "gMDL"),
    df = c("trace", "actset"), ..., k = 2)
## S3 method for class 'gbAIC':
mstop(object, ...)
## S3 method for class 'gb':
mstop(object, ...)
## S3 method for class 'cvrisk':
mstop(object, ...)
## S3 method for class 'blackboost':
mstop(object, ...)
## S3 method for class 'gb':
predict(object, newdata = NULL, type = c("lp", "response"),
       allIterations = FALSE, ...)
## S3 method for class 'blackboost':
predict(object, newdata = NULL, type = c("lp", "response"),
       allIterations = FALSE, ...)
## S3 method for class 'gb':
fitted(object, type = c("lp", "response"), ...)
## S3 method for class 'gb':
logLik(object, ...)

Arguments

object

objects of class glmboost, gamboost, blackboost or gbAIC.

x

objects of class glmboost or gamboost.

newdata

optionally, a data frame in which to look for variables with which to predict.

type

a character indicating whether the fit or the response (classes) should be predicted in case of classification problems.

allIterations

computes the (linear) predictor for all boosting iterations simultaneously and returns a matrix.

method

a character specifying if the corrected AIC criterion or a classical (-2 logLik + k * df) should be computed.

df

a character specifying how degrees of freedom should be computed: trace defines degrees of freedom by the trace of the boosting hat matrix and actset uses the number of non-zero coefficients

k

numeric, the penalty per parameter to be used; the default k = 2 is the classical AIC. Only used when method = "classical".

...

additional arguments passed to callies.

Details

These functions can be used to extract details from fitted models. print shows a dense representation of the model fit and coef extracts the regression coefficients of a linear model fitted using the glmboost function or the gamboost function.

The predict function can be used to predict the status of the response variable for new observations whereas fitted extracts the regression fit for the observations in the learning sample. When allIterations = TRUE, the matrix of all (linear) predictors for boosting iterations 1 to mstop is returned.

For (generalized) linear and additive models, the AIC function can be used to compute both the classical and corrected AIC (Hurvich et al., 1998, only available when family = GaussReg() was used), which is useful for the determination of the optimal number of boosting iterations to be applied (which can be extracted via mstop). The degrees of freedom are either computed via the trace of the boosting hat matrix (which is rather slow even for moderate sample sizes) or the number of variables (non-zero coefficients) that entered the model so far (faster but only meaningful for linear models fitted via gamboost (see Hastie, 2007).

In addition, the general Minimum Description Length criterion (Buhlmann and Yu, 2006) can be computed using function AIC.

Note that logLik and AIC only make sense when the corresponding Family implements the appropriate loss function.

References

Clifford M. Hurvich, Jeffrey S. Simonoff and Chih-Ling Tsai (1998), Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion. Journal of the Royal Statistical Society, Series B, 20(2), 271--293.

Peter Buhlmann and Torsten Hothorn (2007), Boosting algorithms: regularization, prediction and model fitting. Statistical Science, 22(4), 477--505.

Travor Hastie (2007), Discussion of ``Boosting Algorithms: Regularization, Prediction and Model Fitting'' by Peter Buhlmann and Torsten Hothorn. Statistical Science, 22(4), 505.

Peter Buhlmann and Bin Yu (2006), Sparse Boosting. Journal of Machine Learning Research, 7, 1001--1024.

See Also

gamboost, glmboost and blackboost for model fitting. See cvrisk for cross-validated stoping iteration.

Examples

### a simple two-dimensional example: cars data
    cars.gb <- glmboost(dist ~ speed, data = cars,
                        control = boost_control(mstop = 2000))
    cars.gb

    ### initial number of boosting iterations
    mstop(cars.gb)

    ### AIC criterion
    aic <- AIC(cars.gb, method = "corrected")
    aic

    ### coefficients for optimal number of boosting iterations
    coef(cars.gb[mstop(aic)])
    plot(cars$dist, predict(cars.gb[mstop(aic)]),
         ylim = range(cars$dist))
    abline(a = 0, b = 1)