文章基本信息

标题：Functional models for longitudinal data with covariate dependent smoothness
本地全文：下载
作者：David K. Mensah ; David J. Nott ; Linda S. L. Tan 等
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2016
卷号：10
期号：1
页码：527-549
DOI：10.1214/16-EJS1113
语种：English
出版社：Institute of Mathematical Statistics
摘要：This paper considers functional models for longitudinal data with subject and group specific trends modelled using Gaussian processes. Fitting Gaussian process regression models is a computationally challenging task, and various sparse approximations to Gaussian processes have been considered in the literature to ease the computational burden. This manuscript builds on a fast non-standard variational approximation which uses a sparse spectral representation and is able to treat uncertainty in the covariance function hyperparameters. This allows fast variational computational methods to be extended to models where there are many functions to be estimated and where there is a hierarchical model involving the covariance function parameters. The main goal of this paper is to implement this idea in the context of functional models for longitudinal data by allowing individual specific smoothness related to covariates for different subjects. Understanding the relationship of smoothness to individual specific covariates is of great interest in some applications. The methods are illustrated with simulated data and a dataset of streamflow curves generated by a rainfall runoff model, and compared with MCMC. It is also shown how these methods can be used to obtain good proposal distributions for MCMC analyses.