Description Details Author(s) References See Also Examples

Boosting methods for fitting generalized additive models for location, scale and shape (GAMLSS).

This package uses boosting algorithms for fitting GAMLSS (generalized
additive models for location, scale and shape). For information on
GAMLSS theory see Rigby and Stasinopoulos (2005), or the information
provided at http://gamlss.org. For a tutorial on
`gamboostLSS`

see Hofner et al. (2015). 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`

.

The fitting methods `glmboostLSS`

and
`gamboostLSS`

, are alternatives for the algorithms
provided with `gamlss`

in the `gamlss`

package. They offer shrinkage of effect estimates, intrinsic variable
selecion and model choice for potentially high-dimensional data
settings.

`glmboostLSS`

(for linear effects) and
`gamboostLSS`

(for smooth effects) depend on their
analogous companions `glmboost`

and
`gamboost`

for generalized additive models
(contained in package `mboost`

, see Hothorn et al. 2010,
2015) and are similar in their usage.

The package includes some pre-defined GAMLSS distributions, but the
user can also specify new distributions with `Families`

.

A wide range of different base-learners is available for covariate
effects (see `baselearners`

) including linear
(`bols`

), non-linear (`bbs`

), random (`brandom`

) or
spatial effects (`bspatial`

or Markov random fields `bmrf`

).
Each bease-learner can be included seperately for each predictor. The
selection of base-learnes is crucial as it implies the kind of effect
the covariate has on each distribution parameter in the final GAMLSS.

Benjamin Hofner, Andreas Mayr, Nora Fenske, Janek Thomas, Matthias Schmid

Maintainer: Benjamin Hofner <[email protected]>

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.

Stasinopoulos, D. M. and R. A. Rigby (2007). Generalized additive models for location scale and shape (GAMLSS) in R. Journal of Statistical Software 23(7).

Buehlmann, P. and Hothorn, T. (2007). Boosting algorithms: Regularization, prediction and model fitting. Statistical Science, 22(4), 477–505.

Hothorn, T., Buehlmann, P., Kneib, T., Schmid, M. and Hofner, B. (2010). Model-based boosting 2.0. Journal of Machine Learning Research 11(Aug), 2109-2113.

Hothorn, T., Buehlmann, P., Kneib, T., Schmid, M. and Hofner, B. (2015). mboost: Model-based boosting. R package version 2.4-2. https://CRAN.R-project.org/package=mboost

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: http://arxiv.org/abs/1611.10171).

`gamboostLSS`

and `glmboostLSS`

for model
fitting. Available distributions (families) are documented here:
`Families`

.

See also the `mboost`

package for more on model-based boosting, or
the `gamlss`

package for the original GAMLSS
algorithms provided by Rigby and Stasinopoulos.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 | ```
# Generate covariates
x1 <- runif(100)
x2 <- runif(100)
eta_mu <- 2 - 2*x1
eta_sigma <- -1 + 2*x2
# Generate response: Negative Binomial Distribution
y <- numeric(100)
for( i in 1:100) y[i] <- rnbinom(1, size=exp(eta_sigma[i]), mu=exp(eta_mu[i]))
# Model fitting, 300 boosting steps, same formula for both distribution parameters
mod1 <- glmboostLSS( y ~ x1 + x2, families=NBinomialLSS(),
control=boost_control(mstop=300), center = TRUE)
# Shrinked effect estimates
coef(mod1, off2int=TRUE)
# Empirical risk with respect to mu
plot(risk(mod1)$mu)
# Empirical risk with respect to sigma
plot(risk(mod1)$sigma)
``` |

```
Loading required package: mboost
Loading required package: parallel
Loading required package: stabs
This is mboost 2.8-1. See 'package?mboost' and 'news(package = "mboost")'
for a complete list of changes.
Attaching package: 'gamboostLSS'
The following object is masked from 'package:stats':
model.weights
$mu
(Intercept) x1 x2
2.0711047 -1.8912525 -0.1614297
$sigma
(Intercept) x1 x2
-0.1696782 -0.4235348 0.8783971
```

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