TY - JOUR
T1 - Functional CAR Models for Large Spatially Correlated Functional Datasets
AU - Zhang, Lin
AU - Baladandayuthapani, Veerabhadran
AU - Zhu, Hongxiao
AU - Baggerly, Keith A.
AU - Majewski, Tadeusz
AU - Czerniak, Bogdan A.
AU - Morris, Jeffrey S.
N1 - Publisher Copyright:
© 2016, © American Statistical Association.
PY - 2016/4/2
Y1 - 2016/4/2
N2 - 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.
AB - 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.
KW - Conditional autoregressive model
KW - Functional data analysis
KW - Functional regression
KW - Spatial functional data
KW - Whole-organ histology and genetic maps
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U2 - 10.1080/01621459.2015.1042581
DO - 10.1080/01621459.2015.1042581
M3 - Article
C2 - 28018013
AN - SCOPUS:84983348732
SN - 0162-1459
VL - 111
SP - 772
EP - 786
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
IS - 514
ER -