Description Usage Arguments Details Warning Note References See Also Examples
Methods for models fitted by boosting algorithms.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84  ## S3 method for class 'glmboost'
print(x, ...)
## S3 method for class 'mboost'
print(x, ...)
## S3 method for class 'mboost'
summary(object, ...)
## S3 method for class 'mboost'
coef(object, which = NULL,
aggregate = c("sum", "cumsum", "none"), ...)
## S3 method for class 'glmboost'
coef(object, which = NULL,
aggregate = c("sum", "cumsum", "none"), off2int = FALSE, ...)
## S3 method for class 'mboost'
x[i, return = TRUE, ...]
mstop(x) < value
## S3 method for class 'mboost'
AIC(object, method = c("corrected", "classical", "gMDL"),
df = c("trace", "actset"), ..., k = 2)
## S3 method for class 'mboost'
mstop(object, ...)
## S3 method for class 'gbAIC'
mstop(object, ...)
## S3 method for class 'cvrisk'
mstop(object, ...)
## S3 method for class 'mboost'
predict(object, newdata = NULL,
type = c("link", "response", "class"), which = NULL,
aggregate = c("sum", "cumsum", "none"), ...)
## S3 method for class 'glmboost'
predict(object, newdata = NULL,
type = c("link", "response", "class"), which = NULL,
aggregate = c("sum", "cumsum", "none"), ...)
## S3 method for class 'mboost'
fitted(object, ...)
## S3 method for class 'mboost'
residuals(object, ...)
## S3 method for class 'mboost'
resid(object, ...)
## S3 method for class 'glmboost'
variable.names(object, which = NULL, usedonly = FALSE, ...)
## S3 method for class 'mboost'
variable.names(object, which = NULL, usedonly = FALSE, ...)
## S3 method for class 'mboost'
extract(object, what = c("design", "penalty", "lambda", "df",
"coefficients", "residuals",
"variable.names", "bnames", "offset",
"nuisance", "weights", "index", "control"),
which = NULL, ...)
## S3 method for class 'glmboost'
extract(object, what = c("design", "coefficients", "residuals",
"variable.names", "offset",
"nuisance", "weights", "control"),
which = NULL, asmatrix = FALSE, ...)
## S3 method for class 'blg'
extract(object, what = c("design", "penalty", "index"),
asmatrix = FALSE, expand = FALSE, ...)
## S3 method for class 'mboost'
logLik(object, ...)
## S3 method for class 'gamboost'
hatvalues(model, ...)
## S3 method for class 'glmboost'
hatvalues(model, ...)
## S3 method for class 'mboost'
selected(object, ...)
## S3 method for class 'mboost'
risk(object, ...)
## S3 method for class 'mboost'
nuisance(object)
downstream.test(object, ...)

object 
objects of class 
x 
objects of class 
model 
objects of class mboost 
newdata 
optionally, a data frame in which to look for variables with
which to predict. In case the model was fitted using the 
which 
a subset of baselearners to take into account for computing
predictions or coefficients. If 
usedonly 
logical. Indicating whether all variable names should be returned or only those selected in the boosting algorithm. 
type 
the type of prediction required. The default is on the scale
of the predictors; the alternative 
aggregate 
a character specifying how to aggregate predictions
or coefficients of single baselearners. The default
returns the prediction or coefficient for the final number of
boosting iterations. 
off2int 
logical. Indicating whether the offset should be added to the intercept (if there is any) or if the offset is returned as attribute of the coefficient (default). 
i 
integer. Index specifying the model to extract. If 
value 
integer. See 
return 
a logical indicating whether the changed object is returned. 
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:

k 
numeric, the penalty per parameter to be used; the default

what 
a character specifying the quantities to 
asmatrix 
a logical indicating whether the the returned
matrix should be coerced to a matrix (default) or if the
returned object stays as it is (i.e., potentially a
sparse matrix). This option is only applicable if

expand 
a logical indicating whether the design matrix should
be expanded (default: 
... 
additional arguments passed to callies. 
These functions can be used to extract details from fitted models.
print
shows a dense representation of the model fit and
summary
gives a more detailed representation.
The function coef
extracts the regression coefficients of a
linear model fitted using the glmboost
function or an
additive model fitted using the gamboost
. Per default,
only coefficients of selected baselearners are returned. However, any
desired coefficient can be extracted using the which
argument
(see examples for details). Per default, the coefficient of the final
iteration is returned (aggregate = "sum"
) but it is also
possible to return the coefficients from all iterations simultaniously
(aggregate = "cumsum"
). If aggregate = "none"
is
specified, the coefficients of the selected baselearners are
returned (see examples below).
For models fitted via glmboost
with option center
= TRUE
the intercept is rarely selected. However, it is implicitly
estimated through the centering of the design matrix. In this case the
intercept is always returned except which
is specified such
that the intercept is not selected. See examples below.
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. For
predict
newdata
can be specified, otherwise the fitted
values are returned. If which
is specified, marginal effects of
the corresponding baselearner(s) are returned. The argument
type
can be used to make predictions on the scale of the
link
(i.e., the linear predictor X * beta),
the response
(i.e. h(X * beta), where h is the
response function) or the class
(in case of
classification). Furthermore, the predictions can be aggregated
analogously to coef
by setting aggregate
to either
sum
(default; predictions of the final iteration are given),
cumsum
(predictions of all iterations are returned
simultaniously) or none
(change of prediction in each
iteration). If applicable the offset
is added to the predictions.
If marginal predictions are requested the offset
is attached
to the object via attr(..., "offset")
as adding the offset to
one of the marginal predictions doesn't make much sense.
The [.mboost
function can be used to enhance or restrict a given
boosting model to the specified boosting iteration i
. Note that
in both cases the original x
will be changed to reduce the
memory footprint. If the boosting model is enhanced by specifying an
index that is larger than the initial mstop
, only the missing
i  mstop
steps are fitted. If the model is restricted, the
spare steps are not dropped, i.e., if we increase i
again,
these boosting steps are immediately available. Alternatively, the
same operation can be done by mstop(x) < i
.
The residuals
function can be used to extract the residuals
(i.e., the negative gradient of the current iteration). resid
is is an alias for residuals
.
Variable names (including those of interaction effects specified via
by
in a baselearner) can be extracted using the generic
function variable.names
, which has special methods for boosting
objects.
The generic extract
function can be used to extract various
characteristics of a fitted model or a baselearner. Note that the
sometimes a penalty function is returned (e.g. by
extract(bols(x), what = "penalty")
) even if the estimation is
unpenalized. However, in this case the penalty paramter lambda
is set to zero. If a matrix is returned by extract
one can to
set asmatrix = TRUE
if the returned matrix should be coerced to
class matrix
. If asmatrix = FALSE
one might get a sparse
matrix as implemented in package Matrix
. If one requests the
design matrix (what = "design"
) expand = TRUE
expands
the resulting matrix by taking the duplicates handeled via
index
into account.
The ids of baselearners selected during the fitting process can be
extracted using selected()
. The nuisance()
method
extracts nuisance parameters from the fit that are handled internally
by the corresponding family object, see
"boost_family"
. The risk()
function can be
used to extract the computed risk (either the "inbag"
risk or
the "oobag"
risk, depending on the control argument; see
boost_control
).
For (generalized) linear and additive models, the AIC
function
can be used to compute both the classical AIC (only available for
familiy = Binomial()
and familiy = Poisson()
) and
corrected AIC (Hurvich et al., 1998, only available when family
= Gaussian()
was used). Details on the used approximations for the
hat matrix can be found in Buehlmann and Hothorn (2007). The AIC 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 (nonzero coefficients) that entered
the model so far (faster but only meaningful for linear models fitted
via gamboost
(see Hastie, 2007)). For a discussion of
the use of AIC based stopping see also Mayr, Hofner and Schmid (2012).
In addition, the general Minimum Description Length criterion
(Buehlmann 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.
downstream.test
computes tests for linear models fitted via glmboost
with a likelihood based loss function and only suitable without early stopping, i.e.,
if likelihood based model converged. In order to work, the Fisher matrix must
be implemented in the Family
; currently this is only the case for
family RCG
.
The coefficients resulting from boosting with family
Binomial(link = "logit")
are 1/2 of the coefficients of a logit model obtained via glm
(see Binomial
).
The [.mboost
function changes the original object, i.e.
gbmodel[10]
changes gbmodel
directly!
Benjamin Hofner, Andreas Mayr, Nikolay Robinzonov and Matthias Schmid
(2014). Modelbased Boosting in R: A Handson Tutorial Using the R
Package mboost. Computational Statistics, 29, 3–35.
doi: 10.1007/s0018001203825
Clifford M. Hurvich, Jeffrey S. Simonoff and ChihLing 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 Buehlmann and Torsten Hothorn (2007), Boosting algorithms: regularization, prediction and model fitting. Statistical Science, 22(4), 477–505.
Trevor Hastie (2007), Discussion of “Boosting algorithms: Regularization, prediction and model fitting” by Peter Buehlmann and Torsten Hothorn. Statistical Science, 22(4), 505.
Peter Buehlmann and Bin Yu (2006), Sparse boosting. Journal of Machine Learning Research, 7, 1001–1024.
Andreas Mayr, Benjamin Hofner, and Matthias Schmid (2012). The
importance of knowing when to stop  a sequential stopping rule for
componentwise gradient boosting. Methods of Information in
Medicine, 51, 178–186.
DOI: doi: 10.3414/ME11020030
gamboost
, glmboost
and
blackboost
for model fitting.
plot.mboost
for plotting methods.
cvrisk
for crossvalidated stopping iteration.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108  ### a simple twodimensional example: cars data
cars.gb < glmboost(dist ~ speed, data = cars,
control = boost_control(mstop = 2000),
center = FALSE)
cars.gb
### initial number of boosting iterations
mstop(cars.gb)
### AIC criterion
aic < AIC(cars.gb, method = "corrected")
aic
### extract coefficients for glmboost
coef(cars.gb)
coef(cars.gb, off2int = TRUE) # offset added to intercept
coef(lm(dist ~ speed, data = cars)) # directly comparable
cars.gb_centered < glmboost(dist ~ speed, data = cars,
center = TRUE)
selected(cars.gb_centered) # intercept never selected
coef(cars.gb_centered) # intercept implicitly estimated
# and thus returned
## intercept is internally corrected for meancentering
 mean(cars$speed) * coef(cars.gb_centered, which="speed") # = intercept
# not asked for intercept thus not returned
coef(cars.gb_centered, which="speed")
# explicitly asked for intercept
coef(cars.gb_centered, which=c("Intercept", "speed"))
### enhance or restrict model
cars.gb < gamboost(dist ~ speed, data = cars,
control = boost_control(mstop = 100, trace = TRUE))
cars.gb[10]
cars.gb[100, return = FALSE] # no refitting required
cars.gb[150, return = FALSE] # only iterations 101 to 150
# are newly fitted
### coefficients for optimal number of boosting iterations
coef(cars.gb[mstop(aic)])
plot(cars$dist, predict(cars.gb[mstop(aic)]),
ylim = range(cars$dist))
abline(a = 0, b = 1)
### example for extraction of coefficients
set.seed(1907)
n < 100
x1 < rnorm(n)
x2 < rnorm(n)
x3 < rnorm(n)
x4 < rnorm(n)
int < rep(1, n)
y < 3 * x1^2  0.5 * x2 + rnorm(n, sd = 0.1)
data < data.frame(y = y, int = int, x1 = x1, x2 = x2, x3 = x3, x4 = x4)
model < gamboost(y ~ bols(int, intercept = FALSE) +
bbs(x1, center = TRUE, df = 1) +
bols(x1, intercept = FALSE) +
bols(x2, intercept = FALSE) +
bols(x3, intercept = FALSE) +
bols(x4, intercept = FALSE),
data = data, control = boost_control(mstop = 500))
coef(model) # standard output (only selected baselearners)
coef(model,
which = 1:length(variable.names(model))) # all baselearners
coef(model, which = "x1") # shows all baselearners for x1
cf1 < coef(model, which = c(1,3,4), aggregate = "cumsum")
tmp < sapply(cf1, function(x) x)
matplot(tmp, type = "l", main = "Coefficient Paths")
cf1_all < coef(model, aggregate = "cumsum")
cf1_all < lapply(cf1_all, function(x) x[, ncol(x)]) # last element
## same as coef(model)
cf2 < coef(model, aggregate = "none")
cf2 < lapply(cf2, rowSums) # same as coef(model)
### example continued for extraction of predictions
yhat < predict(model) # standard prediction; here same as fitted(model)
p1 < predict(model, which = "x1") # marginal effects of x1
orderX < order(data$x1)
## rowSums needed as p1 is a matrix
plot(data$x1[orderX], rowSums(p1)[orderX], type = "b")
## better: predictions on a equidistant grid
new_data < data.frame(x1 = seq(min(data$x1), max(data$x1), length = 100))
p2 < predict(model, newdata = new_data, which = "x1")
lines(new_data$x1, rowSums(p2), col = "red")
### extraction of model characteristics
extract(model, which = "x1") # design matrices for x1
extract(model, what = "penalty", which = "x1") # penalty matrices for x1
extract(model, what = "lambda", which = "x1") # df and corresponding lambda for x1
## note that bols(x1, intercept = FALSE) is unpenalized
extract(model, what = "bnames") ## name of complete baselearner
extract(model, what = "variable.names") ## only variable names
variable.names(model) ## the same
### extract from baselearners
extract(bbs(x1), what = "design")
extract(bbs(x1), what = "penalty")
## weights and lambda can only be extracted after using dpp
weights < rep(1, length(x1))
extract(bbs(x1)$dpp(weights), what = "lambda")

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