Regression models for functional data, i.e., scalar-on-function, function-on-scalar and function-on-function regression models, are fitted by a component-wise gradient boosting algorithm.
Sarah Brockhaus, David Ruegamer and Almond Stoecker
This package is intended to fit regression models with functional variables. It is possible to fit models with functional response and/or functional covariates, resulting in scalar-on-function, function-on-scalar and function-on-function regression. Furthermore, the package can be used to fit density-on-scalar regression models. Details on the functional regression models that can be fitted with FDboost can be found in Brockhaus et al. (2015, 2017, 2018) and Ruegamer et al. (2018). A hands-on tutorial for the package can be found in Brockhaus, Ruegamer and Greven (2020), see <doi:10.18637/jss.v094.i10>. For density-on-scalar regression models see Maier et al. (2021).
Using component-wise gradient boosting as fitting procedure, FDboost relies on the R package mboost (Hothorn et al., 2017). A comprehensive tutorial to mboost is given in Hofner et al. (2014).
The main fitting function is FDboost.
The model complexity is controlled by the number of boosting iterations (mstop).
Like the fitting procedures in mboost, the function FDboost DOES NOT
select an appropriate stopping iteration. This must be chosen by the user.
The user can determine an adequate stopping iteration by resampling methods like
cross-validation or bootstrap.
This can be done using the function applyFolds.
Aside from common effect surface plots, tensor product factorization via the
function factorize presents an alternative tool for visualization
of estimated effects for non-linear function-on-scalar models
(Stoecker, Steyer and Greven (2022), https://arxiv.org/abs/2109.02624).
After factorization, effects are decomposed multiple scalar effects into
functional main effect directions, which can be separately plotted allowing to
visualize more complex effect structures.
Brockhaus, S., Ruegamer, D. and Greven, S. (2020): Boosting Functional Regression Models with FDboost. Journal of Statistical Software, 94(10), 1–50. <doi:10.18637/jss.v094.i10>
Brockhaus, S., Scheipl, F., Hothorn, T. and Greven, S. (2015): The functional linear array model. Statistical Modelling, 15(3), 279-300.
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), 913-926.
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, 665-686.
Hothorn T., Buehlmann P., Kneib T., Schmid M., and Hofner B. (2017). mboost: Model-Based Boosting, R package version 2.8-1, https://cran.r-project.org/package=mboost
Hofner, B., Mayr, A., Robinzonov, N., Schmid, M. (2014). Model-based Boosting in R: A Hands-on Tutorial Using the R Package mboost. Computational Statistics, 29, 3-35. https://cran.r-project.org/package=mboost/vignettes/mboost_tutorial.pdf
Maier, E.-M., Stoecker, A., Fitzenberger, B., Greven, S. (2021): Additive Density-on-Scalar Regression in Bayes Hilbert Spaces with an Application to Gender Economics. arXiv preprint arXiv:2110.11771.
Ruegamer D., Brockhaus, S., Gentsch K., Scherer, K., Greven, S. (2018). Boosting factor-specific functional historical models for the detection of synchronization in bioelectrical signals. Journal of the Royal Statistical Society: Series C (Applied Statistics), 67, 621-642.
Stoecker A., Steyer L., Greven S. (2022): Functional Additive Models on Manifolds of Planar Shapes and Forms. arXiv preprint arXiv:2109.02624.
FDboost for the main fitting function and
applyFolds for model tuning via resampling methods.