Covariate adjusted functional principal components analysis for longitudinal data

TL;DR

This paper introduces two covariate-adjusted functional principal component analysis methods for longitudinal data, accommodating measurement errors and irregular sampling, with theoretical and empirical performance evaluations.

Contribution

It develops novel FPCA approaches that incorporate covariate effects into mean and covariance functions, extending existing methods to handle complex longitudinal data structures.

Findings

Both methods effectively adjust for covariates in FPCA.

The fully covariate-adjusted approach is more data-adaptive but computationally intensive.

Simulation and real data demonstrate the methods' advantages over traditional FPCA.

Abstract

Classical multivariate principal component analysis has been extended to functional data and termed functional principal component analysis (FPCA). Most existing FPCA approaches do not accommodate covariate information, and it is the goal of this paper to develop two methods that do. In the first approach, both the mean and covariance functions depend on the covariate $Z$ and time scale $t$ while in the second approach only the mean function depends on the covariate $Z$. Both new approaches accommodate additional measurement errors and functional data sampled at regular time grids as well as sparse longitudinal data sampled at irregular time grids. The first approach to fully adjust both the mean and covariance functions adapts more to the data but is computationally more intensive than the approach to adjust the covariate effects on the mean function only. We develop general asymptotic theory for both approaches and compare their performance numerically through simulation studies and a data set.