Description Usage Arguments Details Value Author(s) References See Also Examples
Function for fitting generalized additive models for location, scale and shape (GAMLSS) with functional data using componentwise gradient boosting, for details see Brockhaus et al. (2018).
1 2 3 
formula 
a symbolic description of the model to be fit.
If 
timeformula 
onesided formula for the expansion over the index of the response.
For a functional response Y_i(t) typically 
data 
a data frame or list containing the variables in the model. 
families 
an object of class 
control 
a list of parameters controlling the algorithm.
For more details see 
weights 
does not work! 
method 
fitting method, currently two methods are supported:

... 
additional arguments passed to 
For details on the theory of GAMLSS, see Rigby and Stasinopoulos (2005).
FDboostLSS
calls FDboost
to fit the distribution parameters of a GAMLSS 
a functional boosting model is fitted for each parameter of the response distribution.
In mboostLSS
, details on boosting of GAMLSS based on
Mayr et al. (2012) and Thomas et al. (2018) are given.
In FDboost
, details on boosting regression models with functional variables
are given (Brockhaus et al., 2015, Brockhaus et al., 2017).
An object of class FDboostLSS
that inherits from mboostLSS
.
The FDboostLSS
object is a named list containing one list entry per distribution parameter
and some attributes. The list is named like the parameters, e.g. mu and sigma,
if the parameters mu and sigma are modeled. Each listelement is an object of class FDboost
.
Sarah Brockhaus
Brockhaus, S., Scheipl, F., Hothorn, T. and Greven, S. (2015). The functional linear array model. Statistical Modelling, 15(3), 279300.
Brockhaus, S., Melcher, M., Leisch, F. and Greven, S. (2017): Boosting flexible functional regression models with a high number of functional historical effects, Statistics and Computing, 27(4), 913926.
Brockhaus, S., Fuest, A., Mayr, A. and Greven, S. (2018): Signal regression models for location, scale and shape with an application to stock returns. Journal of the Royal Statistical Society: Series C (Applied Statistics), 67, 665686.
Mayr, A., Fenske, N., Hofner, B., Kneib, T. and Schmid, M. (2012): Generalized additive models for location, scale and shape for highdimensional data  a flexible approach based on boosting. Journal of the Royal Statistical Society: Series C (Applied Statistics), 61(3), 403427.
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(3), 507554.
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, 673687.
Note that FDboostLSS
calls FDboost
directly.
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  ########### simulate Gaussian scalaronfunction data
n < 500 ## number of observations
G < 120 ## number of observations per functional covariate
set.seed(123) ## ensure reproducibility
z < runif(n) ## scalar covariate
z < z  mean(z)
s < seq(0, 1, l=G) ## index of functional covariate
## generate functional covariate
if(require(splines)){
x < t(replicate(n, drop(bs(s, df = 5, int = TRUE) %*% runif(5, min = 1, max = 1))))
}else{
x < matrix(rnorm(n*G), ncol = G, nrow = n)
}
x < scale(x, center = TRUE, scale = FALSE) ## center x per observation point
mu < 2 + 0.5*z + (1/G*x) %*% sin(s*pi)*5 ## true functions for expectation
sigma < exp(0.5*z  (1/G*x) %*% cos(s*pi)*2) ## for standard deviation
y < rnorm(mean = mu, sd = sigma, n = n) ## draw respone y_i ~ N(mu_i, sigma_i)
## save data as list containing s as well
dat_list < list(y = y, z = z, x = I(x), s = s)
## model fit with noncyclic algorithm assuming Gaussian location scale model
m_boost < FDboostLSS(list(mu = y ~ bols(z, df = 2) + bsignal(x, s, df = 2, knots = 16),
sigma = y ~ bols(z, df = 2) + bsignal(x, s, df = 2, knots = 16)),
timeformula = NULL, data = dat_list, method = "noncyclic")
summary(m_boost)
## Not run:
if(require(gamboostLSS)){
## find optimal number of boosting iterations on a grid in 1:1000
## using 5fold bootstrap
## takes some time, easy to parallelize on Linux
set.seed(123)
cvr < cvrisk(m_boost, folds = cv(model.weights(m_boost[[1]]), B = 5),
grid = 1:1000, trace = FALSE)
## use model at optimal stopping iterations
m_boost < m_boost[mstop(cvr)] ## 832
## plot smooth effects of functional covariates for mu and sigma
par(mfrow = c(1,2))
plot(m_boost$mu, which = 2, ylim = c(0,5))
lines(s, sin(s*pi)*5, col = 3, lwd = 2)
plot(m_boost$sigma, which = 2, ylim = c(2.5,2.5))
lines(s, cos(s*pi)*2, col = 3, lwd = 2)
}
## End(Not run)

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