Journal
BIOMETRIKA
Volume 95, Issue 3, Pages 601-619Publisher
OXFORD UNIV PRESS
DOI: 10.1093/biomet/asn035
Keywords
functional data; longitudinal data; mixed-effects model; penalized spline; principal component; reduced-rank model
Funding
- NCI NIH HHS [R37 CA057030-20, R37 CA057030] Funding Source: Medline
- NATIONAL CANCER INSTITUTE [R37CA057030] Funding Source: NIH RePORTER
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We propose a modelling framework to study the relationship between two paired longitudinally observed variables. The data for each variable are viewed as smooth curves measured at discrete time-points plus random errors. While the curves for each variable are summarized using a few important principal components, the association of the two longitudinal variables is modelled through the association of the principal component scores. We use penalized splines to model the mean curves and the principal component curves, and cast the proposed model into a mixed-effects model framework for model fitting, prediction and inference. The proposed method can be applied in the difficult case in which the measurement times are irregular and sparse and may differ widely across individuals. Use of functional principal components enhances model interpretation and improves statistical and numerical stability of the parameter estimates.
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