TY - JOUR
T1 - A random covariance model for bi-level graphical modeling with application to resting-state fMRI data
AU - Zhang, Lin
AU - DiLernia, Andrew
AU - Quevedo, Karina
AU - Camchong, Jazmin
AU - Lim, Kelvin
AU - Pan, Wei
N1 - Publisher Copyright:
© 2020 The International Biometric Society
PY - 2021/12
Y1 - 2021/12
N2 - We consider a novel problem, bi-level graphical modeling, in which multiple individual graphical models can be considered as variants of a common group-level graphical model and inference of both the group- and individual-level graphical models is of interest. Such a problem arises from many applications, including multi-subject neuro-imaging and genomics data analysis. We propose a novel and efficient statistical method, the random covariance model, to learn the group- and individual-level graphical models simultaneously. The proposed method can be nicely interpreted as a random covariance model that mimics the random effects model for mean structures in linear regression. It accounts for similarity between individual graphical models, identifies group-level connections that are shared by individuals, and simultaneously infers multiple individual-level networks. Compared to existing multiple graphical modeling methods that only focus on individual-level graphical modeling, our model learns the group-level structure underlying the multiple individual graphical models and enjoys computational efficiency that is particularly attractive for practical use. We further define a measure of degrees-of-freedom for the complexity of the model useful for model selection. We demonstrate the asymptotic properties of our method and show its finite-sample performance through simulation studies. Finally, we apply the method to our motivating clinical data, a multi-subject resting-state functional magnetic resonance imaging dataset collected from participants diagnosed with schizophrenia, identifying both individual- and group-level graphical models of functional connectivity.
AB - We consider a novel problem, bi-level graphical modeling, in which multiple individual graphical models can be considered as variants of a common group-level graphical model and inference of both the group- and individual-level graphical models is of interest. Such a problem arises from many applications, including multi-subject neuro-imaging and genomics data analysis. We propose a novel and efficient statistical method, the random covariance model, to learn the group- and individual-level graphical models simultaneously. The proposed method can be nicely interpreted as a random covariance model that mimics the random effects model for mean structures in linear regression. It accounts for similarity between individual graphical models, identifies group-level connections that are shared by individuals, and simultaneously infers multiple individual-level networks. Compared to existing multiple graphical modeling methods that only focus on individual-level graphical modeling, our model learns the group-level structure underlying the multiple individual graphical models and enjoys computational efficiency that is particularly attractive for practical use. We further define a measure of degrees-of-freedom for the complexity of the model useful for model selection. We demonstrate the asymptotic properties of our method and show its finite-sample performance through simulation studies. Finally, we apply the method to our motivating clinical data, a multi-subject resting-state functional magnetic resonance imaging dataset collected from participants diagnosed with schizophrenia, identifying both individual- and group-level graphical models of functional connectivity.
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U2 - 10.1111/biom.13364
DO - 10.1111/biom.13364
M3 - Article
C2 - 32865813
AN - SCOPUS:85090763324
SN - 0006-341X
VL - 77
SP - 1385
EP - 1396
JO - Biometrics
JF - Biometrics
IS - 4
ER -