期刊
STATISTICAL MODELLING
卷 17, 期 1-2, 页码 1-35出版社
SAGE PUBLICATIONS LTD
DOI: 10.1177/1471082X16681317
关键词
functional additive mixed model; Functional data; functional principal components; GAMLSS; gradient boosting; penalized splines
资金
- German Research Foundation (DFG) through Emmy Noether grant [GR 3793/1-1]
Researchers are increasingly interested in regression models for functional data. This article discusses a comprehensive framework for additive (mixed) models for functional responses and/or functional covariates based on the guiding principle of reframing functional regression in terms of corresponding models for scalar data, allowing the adaptation of a large body of existing methods for these novel tasks. The framework encompasses many existing as well as new models. It includes regression for generalized' functional data, mean regression, quantile regression as well as generalized additive models for location, shape and scale (GAMLSS) for functional data. It admits many flexible linear, smooth or interaction terms of scalar and functional covariates as well as (functional) random effects and allows flexible choices of basesparticularly splines and functional principal componentsand corresponding penalties for each term. It covers functional data observed on common (dense) or curve-specific (sparse) grids. Penalized-likelihood-based and gradient-boosting-based inference for these models are implemented in R packages refund and FDboost, respectively. We also discuss identifiability and computational complexity for the functional regression models covered. A running example on a longitudinal multiple sclerosis imaging study serves to illustrate the flexibility and utility of the proposed model class. Reproducible code for this case study is made available online.
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