title: Is First-Order Vector Autoregressive Model Optimal for fMRI Data?
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 data sets depending on different data dimensions, subjects, tasks, and experimental designs. In addition, the classical information criteria (IC) used (e.g., the Akaike IC (AIC)) are biased and inappropriate for the high-dimensional fMRI data typically with a 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 data set--with varying time series dimensions obtained from distinct functional brain networks. We use a more balanced criterion, Kullback's IC (KIC) based on Kullback's symmetric divergence combining two directed divergences. We also consider the bias-corrected versions (AICc and KICc) to improve 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 overfitting, with KICc performing the best. Results on real data show that orders greater than one were selected by all criteria across all data sets for the small to moderate dimensions, particularly 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.
authors.affiliation: Center for Biomedical Engineering, Universiti Teknologi Malaysia, 81310 Skudai, Johor, Malaysia cmting@utm.my.
authors.forename: Chee-Ming
authors.initials: CM
authors.lastname: Ting
authors.affiliation: Department of Electrical and Electronic Engineering, University of Melbourne, Victoria 3010, Australia Abd-krim.seghouane@unimelb.edu.au.
authors.forename: Abd-Krim
authors.initials: AK
authors.lastname: Seghouane
authors.affiliation: College of Engineering and Computer Science, Australian National University, Canberra ACT 0200, Australia Usman.Khalid@nicta.com.au.
authors.forename: Muhammad Usman
authors.initials: MU
authors.lastname: Khalid
authors.affiliation: Center for Biomedical Engineering, Universiti Teknologi Malaysia, 81310 Skudai, Johor, Malaysia hussain@fke.utm.my.
authors.forename: Sh-Hussain
authors.initials: ShH
authors.lastname: Salleh
mesh_terms: D000465:Algorithms; D001921:Brain / Q000098:blood supply*; D001931:Brain Mapping; D006225:Hand; D006801:Humans; D007091:Image Processing, Computer-Assisted; D008279:Magnetic Resonance Imaging / Q000379:methods; D008959:Models, Neurological; D009068:Movement; D010100:Oxygen / Q000097:blood; D011597:Psychomotor Performance; D012146:Rest
chemical_list: D010100:Oxygen