Hierarchical vector auto-regressive models and their applications to multi-subject effective connectivity

Cristina Gorrostieta, Mark Fiecas, Hernando Ombao*, Erin Burke, Steven Cramer

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

32 Scopus citations


Vector auto-regressive (VAR) models typically form the basis for constructing directed graphical models for investigating connectivity in a brain network with brain regions of interest (ROIs) as nodes. There are limitations in the standard VAR models. The number of parameters in the VAR model increases quadratically with the number of ROIs and linearly with the order of the model and thus due to the large number of parameters, the model could pose serious estimation problems. Moreover, when applied to imaging data, the standard VAR model does not account for variability in the connectivity structure across all subjects. In this paper, we develop a novel generalization of the VAR model that overcomes these limitations. To deal with the high dimensionality of the parameter space, we propose a Bayesian hierarchical framework for the VAR model that will account for both temporal correlation within a subject and between subject variation. Our approach uses prior distributions that give rise to estimates that correspond to penalized least squares criterion with the elastic net penalty. We apply the proposed model to investigate differences in effective connectivity during a hand grasp experiment between healthy controls and patients with residual motor deficit following a stroke.

Original languageEnglish (US)
Article number159
JournalFrontiers in Computational Neuroscience
Issue numberNOV
StatePublished - Nov 12 2013
Externally publishedYes


  • Brain effective connectivity
  • Elastic net
  • Functional magnetic resonance imaging
  • Hierarchical models
  • Multivariate time series
  • Stroke
  • Vector auto-regressive model

ASJC Scopus subject areas

  • Neuroscience (miscellaneous)
  • Cellular and Molecular Neuroscience


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