Joint modelling of paired sparse functional data using principal components
Joint modelling of paired sparse functional data using principal components
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DOI：
10.1093/biomet/asn035
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发表时间：
2008-09-01
期刊：
影响因子：
2.7
通讯作者：
Carroll, Raymond J.
中科院分区：
文献类型：
--
作者：
Zhou, Lan;Huang, Jianhua Z.;Carroll, Raymond J.
我们提出了一个建模框架来研究两个配对纵向观察变量之间的关系。每个变量的数据被视为在离散时间点加上随机误差测量的平滑曲线。虽然每个变量的曲线是使用几个重要的主成分来总结的，但两个纵向变量的关联是通过主成分分数的关联来建模的。我们使用惩罚样条对平均曲线和主成分曲线进行建模，并将所提出的模型转化为混合效应模型框架，用于模型拟合、预测和推理。所提出的方法可以应用于测量时间不规则且稀疏并且个体之间可能存在很大差异的困难情况。函数主成分的使用增强了模型解释并提高了参数估计的统计和数值稳定性。
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.