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2015 ; 24
(2
): 477-501
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Functional Additive Mixed Models
#MMPMID26347592
Scheipl F
; Staicu AM
; Greven S
J Comput Graph Stat
2015[Apr]; 24
(2
): 477-501
PMID26347592
show ga
We propose an extensive framework for additive regression models for correlated
functional responses, allowing for multiple partially nested or crossed
functional random effects with flexible correlation structures for, e.g.,
spatial, temporal, or longitudinal functional data. Additionally, our framework
includes linear and nonlinear effects of functional and scalar covariates that
may vary smoothly over the index of the functional response. It accommodates
densely or sparsely observed functional responses and predictors which may be
observed with additional error and includes both spline-based and functional
principal component-based terms. Estimation and inference in this framework is
based on standard additive mixed models, allowing us to take advantage of
established methods and robust, flexible algorithms. We provide easy-to-use open
source software in the pffr() function for the R-package refund. Simulations show
that the proposed method recovers relevant effects reliably, handles small sample
sizes well and also scales to larger data sets. Applications with spatially and
longitudinally observed functional data demonstrate the flexibility in modeling
and interpretability of results of our approach.