Linear manifold modelling of multivariate functional data
Jeng-Min Chiou, Hans-Georg Müller
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2014 · Volume 76 · Issue 3
Abstract
Multivariate functional data are increasingly encountered in data analysis, whereas statistical models for such data are not well developed yet. Motivated by a case-study where one aims to quantify the relationship between various longitudinally recorded behaviour intensities forDrosophilaflies, we propose a functional linear manifold model. This model reflects the functional dependence between the components of multivariate random processes and is defined through data-determined linear combinations of the multivariate component trajectories, which are characterized by a set of varying-coefficient functions. The time varying linear relationships that govern the components of multivariate random functions yield insights about the underlying processes and also lead to noise-reduced representations of the multivariate component trajectories. The functional linear manifold model proposed is put to the task for an analysis of longitudinally observed behavioural patterns of flying, feeding, walking and resting over the lifespan ofDrosophilaflies and is also investigated in simulations.
Keywords
Behaviour, Drosophila, Functional data analysis, Longitudinal data, Multivariate random functions, Principal component analysis
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