A pairwise interaction model for multivariate functional and longitudinal data

Jeng-Min Chiou and Hans-Georg Müller

Biometrika, 2016, vol. 103, issue 2, 377-396

Abstract: Functional data vectors consisting of samples of multivariate data where each component is a random function are encountered increasingly often but have not yet been comprehensively investigated. We introduce a simple pairwise interaction model that leads to an interpretable and straightforward decomposition of multivariate functional data and of their variation into component-specific processes and pairwise interaction processes. The latter quantify the degree of pairwise interactions between the components of the functional data vectors, while the component-specific processes reflect the functional variation of a particular functional vector component that cannot be explained by the other components. Thus the proposed model provides an extension of the usual notion of a covariance or correlation matrix for multivariate vector data to functional data vectors and generates an interpretable functional interaction map. The decomposition provided by the model can also serve as a basis for subsequent analysis, such as study of the network structure of functional data vectors. The decomposition of the total variance into componentwise and interaction contributions can be quantified by an $R^2$-like decomposition. We provide consistency results for the proposed methods and illustrate the model by applying it to sparsely sampled longitudinal data from the Baltimore Longitudinal Study of Aging, examining the relationships between body mass index and blood fats.

Date: 2016
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://hdl.handle.net/10.1093/biomet/asw007 (application/pdf)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:oup:biomet:v:103:y:2016:i:2:p:377-396.

Ordering information: This journal article can be ordered from
https://academic.oup.com/journals

Access Statistics for this article

Biometrika is currently edited by Paul Fearnhead

More articles in Biometrika from Biometrika Trust Oxford University Press, Great Clarendon Street, Oxford OX2 6DP, UK.
Bibliographic data for series maintained by Oxford University Press ().