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Lookup NU author(s): Dr Jian Shi, Dr Bo Wang
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Shi, Wang, Murray-Smith and Titterington (Biometrics 63:714-723, 2007) proposed a Gaussian process functional regression (GPFR) model to model functional response curves with a set of functional covariates. Two main problems are addressed by their method: modelling nonlinear and nonparametric regression relationship and modelling covariance structure and mean structure simultaneously. The method gives very good results for curve fitting and prediction but side-steps the problem of heterogeneity. In this paper we present a new method for modelling functional data with 'spatially' indexed data, i.e., the heterogeneity is dependent on factors such as region and individual patient's information. For data collected from different sources, we assume that the data corresponding to each curve (or batch) follows a Gaussian process functional regression model as a lower-level model, and introduce an allocation model for the latent indicator variables as a higher-level model. This higher-level model is dependent on the information related to each batch. This method takes advantage of both GPFR and mixture models and therefore improves the accuracy of predictions. The mixture model has also been used for curve clustering, but focusing on the problem of clustering functional relationships between response curve and covariates, i.e. the clustering is based on the surface shape of the functional response against the set of functional covariates. The model is examined on simulated data and real data. © 2008 Springer Science+Business Media, LLC.
Author(s): Shi JQ, Wang B
Publication type: Article
Publication status: Published
Journal: Statistics and Computing
Year: 2008
Volume: 18
Issue: 3
Pages: 267-283
Print publication date: 01/09/2008
ISSN (print): 0960-3174
ISSN (electronic): 1573-1375
Publisher: Springer New York LLC
URL: http://dx.doi.org/10.1007/s11222-008-9055-1
DOI: 10.1007/s11222-008-9055-1
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