Functional CAR Models for Large Spatially Correlated Functional Datasets

Lin Zhang, Veerabhadran Baladandayuthapani, Hongxiao Zhu, Keith A. Baggerly, Tadeusz Majewski, Bogdan A. Czerniak, Jeffrey S. Morris

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Abstract

We develop a functional conditional autoregressive (CAR) model for spatially correlated data for which functions are collected on areal units of a lattice. Our model performs functional response regression while accounting for spatial correlations with potentially nonseparable and nonstationary covariance structure, in both the space and functional domains. We show theoretically that our construction leads to a CAR model at each functional location, with spatial covariance parameters varying and borrowing strength across the functional domain. Using basis transformation strategies, the nonseparable spatial-functional model is computationally scalable to enormous functional datasets, generalizable to different basis functions, and can be used on functions defined on higher dimensional domains such as images. Through simulation studies, we demonstrate that accounting for the spatial correlation in our modeling leads to improved functional regression performance. Applied to a high-throughput spatially correlated copy number dataset, the model identifies genetic markers not identified by comparable methods that ignore spatial correlations. Supplementary materials for this article are available online.

Original languageEnglish (US)
Pages (from-to)772-786
Number of pages15
JournalJournal of the American Statistical Association
Volume111
Issue number514
DOIs
StatePublished - Apr 2 2016

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Keywords

  • Conditional autoregressive model
  • Functional data analysis
  • Functional regression
  • Spatial functional data
  • Whole-organ histology and genetic maps

Cite this

Zhang, L., Baladandayuthapani, V., Zhu, H., Baggerly, K. A., Majewski, T., Czerniak, B. A., & Morris, J. S. (2016). Functional CAR Models for Large Spatially Correlated Functional Datasets. Journal of the American Statistical Association, 111(514), 772-786. https://doi.org/10.1080/01621459.2015.1042581