Abstract
The authors consider the analysis of hierarchical longitudinal functional data based upon a functional principal components approach. In contrast to standard frequentist approaches to selecting the number of principal components, the authors do model averaging using a Bayesian formulation. A relatively straightforward reversible jump Markov Chain Monte Carlo formulation has poor mixing properties and in simulated data often becomes trapped at the wrong number of principal components. In order to overcome this, the authors show how to apply Stochastic Approximation Monte Carlo (SAMC) to this problem, a method that has the potential to explore the entire space and does not become trapped in local extrema. The combination of reversible jump methods and SAMC in hierarchical longitudinal functional data is simplified by a polar coordinate representation of the principal components. The approach is easy to implement and does well in simulated data in determining the distribution of the number of principal components, and in terms of its frequentist estimation properties. Empirical applications are also presented.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 256-270 |
| Number of pages | 15 |
| Journal | Canadian Journal of Statistics |
| Volume | 38 |
| Issue number | 2 |
| DOIs | |
| State | Published - Jun 2010 |
| Externally published | Yes |
Bibliographical note
KAUST Repository Item: Exported on 2020-10-01Acknowledged KAUST grant number(s): KUS-CI-016-04
Acknowledgements: We wish to thank the editor and a referee for their detailed reading of the original manuscript and their many suggestions that led to a significant improvement in the paper. We also thank the participants of the International Symposium in Statistics on Inferences in Generalized Linear Longitudinal Mixed Models, whose comments led us to rethink important parts of this work. Martinez was supported by a post-doctoral training grant from the National Cancer Institute (R25T-CA90301), Carroll's research was supported by a grant from the National Cancer Institute (CA57030), Liang's research was supported by a grant from the National Science Foundation (DMS-0706755) and Zhou was supported by a grant from the National Science Foundation (DMS-0907170). Both Carroll and Liang were also supported by Award Number KUS-CI-016-04, made by King Abdullah University of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.