  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 conditional on estimated principal components. We provide
R-code implementing our approach. The method is motivated by and applied to
data from speech production research.
