Functional Linear Mixed Models for Irregularly or Sparsely Sampled Data

TL;DR

This paper introduces a functional linear mixed model approach for analyzing irregularly or sparsely sampled correlated functional data, enabling variability decomposition, mean effect estimation, and confidence band construction.

Contribution

It presents a novel estimation method combining functional principal component analysis with mixed model techniques for sparse and irregular data.

Findings

Effective decomposition of variability in sparse functional data

Ability to estimate mean effects with confidence bands

Application to speech production research data

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 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.