Statistical Modelling 16 (1) (2016), 67–88

Functional linear mixed models for irregularly or sparsely sampled data

Jona Cederbaum
Department of Statistics,
Faculty of Mathematics,
Computer Science and Statistics,
Ludwig-Maximilians-University,
Munich,
Germany


Marianne Pouplier
Department of Phonetics and Speech Processing,
Faculty of Languages and Literature,
Ludwig-Maximilians-University,
Munich,
Germany


Phil Hoole
Department of Phonetics and Speech Processing,
Faculty of Languages and Literature,
Ludwig-Maximilians-University,
Munich,
Germany


Sonja Greven
Department of Statistics,
Faculty of Mathematics,
Computer Science and Statistics,
Ludwig-Maximilians-University,
Munich,
Germany
e-mail: Sonja.Greven@stat.uni-muenchen.de

Abstract:

We propose an estimation approach to analyse correlated functional data, which are observed on unequal grids or even sparsely. The model we use is a functional linear mixed model, a functional analogue of the linear mixed model. Estimation is based on dimension reduction via functional principal component analysis and on mixed model methodology. Our procedure allows the decomposition of the variability in the data as well as the estimation of mean effects of interest, and borrows strength across curves. Confidence bands for mean effects can be constructed conditionally on estimated principal components. We provide R-code implementing our approach in an online appendix. The method is motivated by and applied to data from speech production research.

Keywords:

functional additive mixed models; Dependent functional data; functional principal component analysis; penalized splines; speech production.

Downloads:

Example data and code in zipped archive.
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