Guo Wensheng
Department of Biostatistics and Epidemiology, University of Pennsylvania School of Medicine, Philadelphia, PA 19104-6021, USA.
Stat Methods Med Res. 2004 Feb;13(1):49-62. doi: 10.1191/0962280204sm352ra.
Data in many experiments arise as curves and therefore it is natural to use a curve as a basic unit in the analysis, which is termed functional data analysis (FDA). In longitudinal studies, recent developments in FDA have extended classical linear models and linear mixed effects models to functional linear models (also termed varying-coefficient models) and functional mixed effects models. In this paper we focus our review on the functional mixed effects models using smoothing splines, because functional linear models are special cases of this more general framework. Due to the connection between smoothing splines and linear mixed effects models, functional mixed effects models can be fitted using existing software such as SAS Proc Mixed. A case study is presented as an illustration.
许多实验中的数据呈现为曲线形式，因此在分析中以曲线作为基本单元是很自然的，这被称为函数数据分析（FDA）。在纵向研究中，FDA的最新进展已将经典线性模型和线性混合效应模型扩展到函数线性模型（也称为变系数模型）和函数混合效应模型。在本文中，我们将综述聚焦于使用平滑样条的函数混合效应模型，因为函数线性模型是这个更一般框架的特殊情况。由于平滑样条与线性混合效应模型之间的联系，函数混合效应模型可以使用诸如SAS Proc Mixed等现有软件进行拟合。文中给出了一个案例研究作为示例。
