Electronic Journal of Statistics

Functional models for longitudinal data with covariate dependent smoothness

David K. Mensah, David J. Nott, Linda S. L. Tan, and Lucy Marshall

Full-text: Open access

Abstract

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.

Article information

Source
Electron. J. Statist., Volume 10, Number 1 (2016), 527-549.

Dates
Received: July 2014
First available in Project Euclid: 4 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1457123505

Digital Object Identifier
doi:10.1214/16-EJS1113

Mathematical Reviews number (MathSciNet)
MR3471987

Zentralblatt MATH identifier
1332.62136

Keywords
Functional data Gaussian processes longitudinal data variational Bayes

Citation

Mensah, David K.; Nott, David J.; Tan, Linda S. L.; Marshall, Lucy. Functional models for longitudinal data with covariate dependent smoothness. Electron. J. Statist. 10 (2016), no. 1, 527--549. doi:10.1214/16-EJS1113. https://projecteuclid.org/euclid.ejs/1457123505


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