Statistical Modelling 23 (4) (2024), 303326
Multivariate functional additive mixed models
Alexander Volkmann,
School of Business and Economics,
Humboldt-Universitäat zu Berlin,
Germany.
e-mail: alexander.volkmann@hu-berlin.de
Almond Stöcker,
School of Business and Economics,
Humboldt-Universität zu Berlin,
Germany.
Fabian Scheipl,
Department of Statistics,
Ludwig-Maximilians-Universität
Müunchen,
Germany.
Sonja Greven,
School of Business and Economics,
Humboldt-Universität zu Berlin,
Germany.
Abstract:
Multivariate functional data can be intrinsically multivariate like movement trajectories
in 2D or complementary such as precipitation, temperature and wind speeds over time at a given
weather station. We propose a multivariate functional additive mixed model (multiFAMM) and show
its application to both data situations using examples from sports science (movement trajectories
of snooker players) and phonetic science (acoustic signals and articulation of consonants). The
approach includes linear and nonlinear covariate effects and models the dependency structure
between the dimensions of the responses using multivariate functional principal component analysis.
Multivariate functional random intercepts capture both the auto-correlation within a given function
and cross-correlations between the multivariate functional dimensions. They also allow us to model
between-function correlations as induced by, for example, repeated measurements or crossed study
designs. Modelling the dependency structure between the dimensions can generate additional insight
into the properties of the multivariate functional process, improves the estimation of random effects,
and yields corrected confidence bands for covariate effects. Extensive simulation studies indicate that
a multivariate modelling approach is more parsimonious than fitting independent univariate models
to the data while maintaining or improving model fit.
Keywords:
Functional additive mixed model; multivariate functional principal components;
multivariate functional data; snooker trajectories; speech production
Downloads:
Data and R Code, Supplementary material.
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