Functional Additive Mixed Models

Journal of Computational and Graphical Statistics : a Joint Publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America
Fabian ScheiplSonja Greven

Abstract

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.

References

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Citations

Aug 23, 2016·Journal of the Royal Statistical Society. Series C, Applied Statistics·Jeff Goldsmith, Tomoko Kitago
Nov 26, 2015·Stat : the ISI's Journal for Rapid Dissemination of Statistics Research·So Young Park, Ana-Maria Staicu
May 18, 2016·Stat : the ISI's Journal for Rapid Dissemination of Statistics Research·Julia WrobelJeff Goldsmith
Dec 13, 2017·Statistics in Medicine·Andrew LerouxWilliam Checkley
May 8, 2018·Statistics in Medicine·Clemontina A DavenportVeerabhadran Baladandayuthapani
Aug 11, 2017·Biometrical Journal. Biometrische Zeitschrift·Meike KöhlerSonja Greven
Jan 14, 2020·Journal of the Royal Statistical Society. Series C, Applied Statistics·Ana-Maria StaicuEric van Heugten
May 7, 2019·Journal of the American Statistical Association·S LuoH Zhu
Jun 27, 2019·Journal of the American Statistical Association·Wonyul LeeJeffrey S Morris
May 20, 2020·Statistics in Biosciences·Jihui LeeJeff Goldsmith
Sep 29, 2020·Journal of the American Statistical Association·Hojin YangJeffrey S Morris
Oct 17, 2017·Biostatistics·So Young ParkCiprian M Crainiceanu
Oct 12, 2018·Statistics in Medicine·Meike KöhlerSonja Greven
Jan 31, 2017·Biometrics·Antonio GasparriniMichael G Kenward
May 22, 2018·Journal of Computational and Graphical Statistics : a Joint Publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America·Janet S KimDavid Ruppert
Feb 17, 2018·Statistics and Computing·Luo XiaoCiprian Crainiceanu
Aug 27, 2019·Journal of the American Statistical Association·Yakuan ChenR Todd Ogden
Sep 3, 2017·The Journal of the Acoustical Society of America·Marianne PouplierSonja Greven
Nov 13, 2018·Journal of the American Statistical Association·Daniel BackenrothTomoko Kitago
Sep 27, 2016·Computational Statistics & Data Analysis·Jan GertheissAna-Maria Staicu
Apr 2, 2021·Biometrics·Ruiyan Luo, Xin Qi
Dec 7, 2021·Statistical Methods in Medical Research·Bo Chen, Wei Xu

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Methods Mentioned

BETA
imaging technique

Software Mentioned

R package refund
MATLAB
pffr
R
package
WFMM
R Development Core Team
fda
R package
mgcv

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