| mboostLSS {gamboostLSS} | R Documentation |
Fitting GAMLSS by Boosting
Description
Functions for fitting GAMLSS (generalized additive models for location, scale and shape) using boosting techniques. Two algorithms are implemented: (a) The cyclic algorithm iteratively rotates between the distribution parameters, updating one while using the current fits of the others as offsets (for details see Mayr et al., 2012). (b) The noncyclic algorithm selects in each step the update of a base-learner for the distribution parameter that best fits the negative gradient (algorithm with inner loss of Thomas et al., 2018).
Usage
mboostLSS(formula, data = list(), families = GaussianLSS(),
control = boost_control(), weights = NULL,
method = c("cyclic", "noncyclic"), ...)
glmboostLSS(formula, data = list(), families = GaussianLSS(),
control = boost_control(), weights = NULL,
method = c("cyclic", "noncyclic"), ...)
gamboostLSS(formula, data = list(), families = GaussianLSS(),
control = boost_control(), weights = NULL,
method = c("cyclic", "noncyclic"), ...)
blackboostLSS(formula, data = list(), families = GaussianLSS(),
control = boost_control(), weights = NULL,
method = c("cyclic", "noncyclic"), ...)
## fit function:
mboostLSS_fit(formula, data = list(), families = GaussianLSS(),
control = boost_control(), weights = NULL,
fun = mboost, funchar = "mboost", call = NULL, method, ...)
Arguments
formula |
a symbolic description of the model to be fit. See
|
data |
a data frame containing the variables in the model. |
families |
an object of class |
control |
a list of parameters controlling the algorithm. For
more details see |
weights |
a numeric vector of weights (optional). |
method |
fitting method, currently two methods are supported:
|
fun |
fit function. Either |
funchar |
character representation of fit function. Either |
call |
used to forward the call from |
... |
Further arguments to be passed to |
Details
For information on GAMLSS theory see Rigby and Stasinopoulos (2005) or
the information provided at https://www.gamlss.com/. For a tutorial on
gamboostLSS see Hofner et al. (2016). Thomas et al. (2018)
developed a novel non-cyclic approach to fit gamboostLSS models. This approach
is suitable for the combination with stabsel and speeds up
model tuning via cvrisk (see also below).
glmboostLSS uses glmboost to fit the
distribution parameters of a GAMLSS – a linear boosting model is
fitted for each parameter.
gamboostLSS uses gamboost to fit the
distribution parameters of a GAMLSS – an additive boosting model (by
default with smooth effects) is fitted for each parameter. With the
formula argument, a wide range of different base-learners can
be specified (see baselearners). The
base-learners imply the type of effect each covariate has on the
corresponding distribution parameter.
mboostLSS uses mboost to fit the
distribution parameters of a GAMLSS. The type of model (linear,
tree-based or smooth) is specified by fun.
blackboostLSS uses blackboost to fit the
distribution parameters of a GAMLSS – a tree-based boosting model is
fitted for each parameter.
mboostLSS, glmboostLSS, gamboostLSS and
blackboostLSS all call mboostLSS_fit while fun is
the corresponding mboost function, i.e., the same
function without LSS. For further possible arguments see
these functions as well as mboost_fit.
Note that mboostLSS_fit is usually not called directly by the user.
For method = "cyclic" it is possible to specify one or
multiple mstop and nu values via
boost_control. In the case of one single value, this
value is used for all distribution parameters of the GAMLSS model.
Alternatively, a (named) vector or a (named) list with separate values
for each component can be used to specify a separate value for each
parameter of the GAMLSS model. The names of the list must correspond
to the names of the distribution parameters of the GAMLSS family. If
no names are given, the order of the mstop or nu values
is assumed to be the same as the order of the components in the
families. For one-dimensional stopping, the user therefore can
specify, e.g., mstop = 100 via boost_control. For
more-dimensional stopping, one can specify, e.g., mstop =
list(mu = 100, sigma = 200) (see examples).
If method is set to "noncyclic", mstop has
to be a one dimensional integer. Instead of cycling through all distribution
parameters, in each iteration only the best base-learner is used. One base-learner of every
parameter is selected via RSS, the distribution parameter is then chosen via the loss
(in Thomas et. al., 2018, called inner loss).
For details on the noncyclic fitting method see Thomas et. al. (2018).
To (potentially) stabilize the model estimation by standardizing the
negative gradients one can use the argument stabilization of
the families. See Families for details.
Value
An object of class mboostLSS or nc_mboostLSS (inheriting from
class mboostLSS) for models fitted with method = "cyclic"
and method = "non-cyclic", respectively, with corresponding methods to
extract information. A mboostLSS model object is a named list
with one list entry for each modelled distribution parameter.
Special "subclasses" inheriting from mboostLSS exist for each of the
model-types (with the same name as the function, e.g., gamboostLSS).
References
B. Hofner, A. Mayr, M. Schmid (2016). gamboostLSS: An R Package for Model Building and Variable Selection in the GAMLSS Framework. Journal of Statistical Software, 74(1), 1-31.
Available as vignette("gamboostLSS_Tutorial").
Mayr, A., Fenske, N., Hofner, B., Kneib, T. and Schmid, M. (2012): Generalized additive models for location, scale and shape for high-dimensional data - a flexible approach based on boosting. Journal of the Royal Statistical Society, Series C (Applied Statistics) 61(3): 403-427.
M. Schmid, S. Potapov, A. Pfahlberg, and T. Hothorn. Estimation and regularization techniques for regression models with multidimensional prediction functions. Statistics and Computing, 20(2):139-150, 2010.
Rigby, R. A. and D. M. Stasinopoulos (2005). Generalized additive models for location, scale and shape (with discussion). Journal of the Royal Statistical Society, Series C (Applied Statistics), 54, 507-554.
Buehlmann, P. and Hothorn, T. (2007), Boosting algorithms: Regularization, prediction and model fitting. Statistical Science, 22(4), 477–505.
Thomas, J., Mayr, A., Bischl, B., Schmid, M., Smith, A., and Hofner, B. (2018),
Gradient boosting for distributional regression - faster tuning and improved
variable selection via noncyclical updates.
Statistics and Computing. 28: 673-687.
doi:10.1007/s11222-017-9754-6
(Preliminary version: https://arxiv.org/abs/1611.10171).
See Also
Families for a documentation of available GAMLSS distributions.
The underlying boosting functions mboost, gamboost, glmboost,
blackboost are contained in the mboost package.
See for example risk or coef for methods
that can be used to extract information from mboostLSS objects.
Examples
### Data generating process:
set.seed(1907)
x1 <- rnorm(1000)
x2 <- rnorm(1000)
x3 <- rnorm(1000)
x4 <- rnorm(1000)
x5 <- rnorm(1000)
x6 <- rnorm(1000)
mu <- exp(1.5 +1 * x1 +0.5 * x2 -0.5 * x3 -1 * x4)
sigma <- exp(-0.4 * x3 -0.2 * x4 +0.2 * x5 +0.4 * x6)
y <- numeric(1000)
for( i in 1:1000)
y[i] <- rnbinom(1, size = sigma[i], mu = mu[i])
dat <- data.frame(x1, x2, x3, x4, x5, x6, y)
### linear model with y ~ . for both components: 400 boosting iterations
model <- glmboostLSS(y ~ ., families = NBinomialLSS(), data = dat,
control = boost_control(mstop = 400),
center = TRUE)
coef(model, off2int = TRUE)
### estimate model with different formulas for mu and sigma:
names(NBinomialLSS()) # names of the family
### Do not test the following code per default on CRAN as it takes some time to run:
# Note: Multiple formulas must be specified via a _named list_
# where the names correspond to the names of the distribution parameters
# in the family (see above)
model2 <- glmboostLSS(formula = list(mu = y ~ x1 + x2 + x3 + x4,
sigma = y ~ x3 + x4 + x5 + x6),
families = NBinomialLSS(), data = dat,
control = boost_control(mstop = 400, trace = TRUE),
center = TRUE)
coef(model2, off2int = TRUE)
### END (don't test automatically)
### Offset needs to be specified via the arguments of families object:
model <- glmboostLSS(y ~ ., data = dat,
families = NBinomialLSS(mu = mean(mu),
sigma = mean(sigma)),
control = boost_control(mstop = 10),
center = TRUE)
# Note: mu-offset = log(mean(mu)) and sigma-offset = log(mean(sigma))
# as we use a log-link in both families
coef(model)
log(mean(mu))
log(mean(sigma))
### Do not test the following code per default on CRAN as it takes some time to run:
### use different mstop values for the two distribution parameters
### (two-dimensional early stopping)
### the number of iterations is passed to boost_control via a named list
model3 <- glmboostLSS(formula = list(mu = y ~ x1 + x2 + x3 + x4,
sigma = y ~ x3 + x4 + x5 + x6),
families = NBinomialLSS(), data = dat,
control = boost_control(mstop = list(mu = 400,
sigma = 300),
trace = TRUE),
center = TRUE)
coef(model3, off2int = TRUE)
### Alternatively we can change mstop of model2:
# here it is assumed that the first element in the vector corresponds to
# the first distribution parameter of model2 etc.
mstop(model2) <- c(400, 300)
par(mfrow = c(1,2))
plot(model2, xlim = c(0, max(mstop(model2))))
## all.equal(coef(model2), coef(model3)) # same!
### END (don't test automatically)