Electronic Journal of Statistics

Longitudinal functional principal component analysis

Sonja Greven, Ciprian Crainiceanu, Brian Caffo, and Daniel Reich

Full-text: Open access

Abstract

We introduce models for the analysis of functional data observed at multiple time points. The dynamic behavior of functional data is decomposed into a time-dependent population average, baseline (or static) subject-specific variability, longitudinal (or dynamic) subject-specific variability, subject-visit-specific variability and measurement error. The model can be viewed as the functional analog of the classical longitudinal mixed effects model where random effects are replaced by random processes. Methods have wide applicability and are computationally feasible for moderate and large data sets. Computational feasibility is assured by using principal component bases for the functional processes. The methodology is motivated by and applied to a diffusion tensor imaging (DTI) study designed to analyze differences and changes in brain connectivity in healthy volunteers and multiple sclerosis (MS) patients. An R implementation is provided.

Article information

Source
Electron. J. Statist. Volume 4 (2010), 1022-1054.

Dates
First available in Project Euclid: 12 October 2010

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1286889183

Digital Object Identifier
doi:10.1214/10-EJS575

Mathematical Reviews number (MathSciNet)
MR2727452

Zentralblatt MATH identifier
1329.62334

Keywords
Diffusion tensor imaging functional data analysis Karhunen-Loève expansion longitudinal data analysis mixed effects model

Citation

Greven, Sonja; Crainiceanu, Ciprian; Caffo, Brian; Reich, Daniel. Longitudinal functional principal component analysis. Electron. J. Statist. 4 (2010), 1022--1054. doi:10.1214/10-EJS575. https://projecteuclid.org/euclid.ejs/1286889183


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