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Is First-Order Vector Autoregressive Model Optimal for fMRI Data?
Neural Computation (2015)
  • Chee-Ming Ting
  • Abd-Krim Seghouane
  • Muhammad Usman Khalid
  • Sh-Hussain Salleh
Abstract
We consider the problem of selecting the optimal orders of vector autoregressive (VAR) models for fMRI data. Many previous studies used model-order of one and ignored that it may vary considerably across datasets depending on different data dimensions, subjects, tasks and experimental designs. Besides, the classical information criteria (IC) used, e.g. the Akaike IC (AIC) are biased and inappropriate for the high-dimensional fMRI data typically with small sample size. We examine the mixed results on the optimal VAR orders for fMRI, especially the validity of the order-one hypothesis by a comprehensive evaluation using different model selection criteria, over three typical data types: a resting-state, an event-related-design and a block-design dataset, with varying time-series dimensions obtained from distinct functional brain networks. We use a more balanced criterion, the Kullback’s IC (KIC) based on a Kullback’s symmetric divergence combining two directed divergences. We also consider the bias-corrected versions (AICc and KICc) to improve the VAR model-selection in small samples. Simulation results show better small-sample selection performance of the proposed criteria over the classical ones. Both bias-corrected ICs provide more accurate and consistent model order choices than their biased counterparts which suffer from over-fitting, with KICc performing the best. Results on real data show that orders greater than one were selected by all criteria across all datasets, for the small to moderate dimensions, particular from small specific networks such as the resting-state default mode network and the task-related motor networks. Whereas, low orders close to one but not necessarily one were chosen for the large dimensions of full-brain networks.
Keywords
  • fMRI,
  • vector autoregressive models,
  • model selection,
  • AIC,
  • Kullback information criterion
Publication Date
2015
Publisher Statement
This is a preprint, or manuscript version of an article which has been accepted for publication in Neural Computation, 2015
Citation Information
Chee-Ming Ting, Abd-Krim Seghouane, Muhammad Usman Khalid and Sh-Hussain Salleh. "Is First-Order Vector Autoregressive Model Optimal for fMRI Data?" Neural Computation (2015)
Available at: http://works.bepress.com/chee-ming_ting/14/