Joint modelling of paired sparse functional data using principal components

• 成果类型: Article
• 署名作者: Zhou, Lan; Huang, Jianhua Z.; Carroll, Raymond J.
• 署名单位: Texas A&M University System; Texas A&M University College Station
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asn035
• 发表日期: 2008
• 页码: 601619
• 关键词: varying-coefficient models; immunological responses; longitudinal data

摘要

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.