Multivariate Granger causality: An estimation framework based on factorization of the spectral density matrix

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 371, Issue 1997, 2013, Pages

  Wen, Xiaotong ^a   Rangarajan, Govindan ^b   Ding, Mingzhou ^a  

^a University of Florida   (United States)

^b INDIAN INSTITUTE OF SCIENCE   (India)

Author keywords

Factorization; Granger causality; Multivariate; Spectral density matrix

Indexed keywords

BRAIN; ESTIMATION; FACTORIZATION;

AUTO REGRESSIVE MODELS; CURRENT ESTIMATION; DIRECTIONAL INTERACTIONS; FUNCTIONAL IMAGING; GRANGER CAUSALITY; MULTI-ELECTRODE; MULTIVARIATE; SPECTRAL DENSITY MATRIX;

STATISTICAL TESTS;

ANIMAL; ARTICLE; BIOLOGICAL MODEL; BRAIN; BRAIN MAPPING; COMPUTER SIMULATION; FACTORIAL ANALYSIS; FACTORIZATION; GRANGER CAUSALITY; HUMAN; METHODOLOGY; MULTIVARIATE; MULTIVARIATE ANALYSIS; NERVE CELL NETWORK; PHYSIOLOGY; REGRESSION ANALYSIS; SPECTRAL DENSITY MATRIX; STATISTICAL MODEL; SYNAPTIC TRANSMISSION;

FACTORIZATION; GRANGER CAUSALITY; MULTIVARIATE; SPECTRAL DENSITY MATRIX;

ANIMALS; BRAIN; BRAIN MAPPING; COMPUTER SIMULATION; FACTOR ANALYSIS, STATISTICAL; HUMANS; MODELS, NEUROLOGICAL; MODELS, STATISTICAL; MULTIVARIATE ANALYSIS; NERVE NET; REGRESSION ANALYSIS; SYNAPTIC TRANSMISSION;

EID: 84880528896     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2011.0610     Document Type: Article

References (36)

1. Valdes-Sosa PA, Sanchez-Bornot JM, Lage-Castellanos A, Vega-Hernandez M, Bosch- Bayard J, Melie-Garcia L, Canales-Rodriguez E. 2005 Estimating brain functional connectivity with sparse multivariate autoregression. Phil. Trans. R. Soc. B 360, 969-981. (doi:10.1098/rstb.2005.1654). (Pubitemid 41672858)
2. Ding M, Chen Y, Bressler SL. 2006 Granger causality: basic theory and applications to neuroscience. In Handbook of time series analysis (eds B Schelter, M Winterhalder, J Timmer), pp. 437-460. Weinheim, Germany:Wiley-VCH Verlag.
3. Bollimunta A, Chen Y, Schroeder CE, Ding M. 2008 Neuronal mechanisms of cortical alpha oscillations in awake-behaving macaques. J. Neurosci. 28, 9976-9988. (doi:10.1523/JNEUROSCI.2699-08.2008).
4. Goebel R, Roebroeck A, Kim D-S, Formisano E. 2003 Investigating directed cortical interactions in time-resolved fMRI data using vector autoregressive modeling and Granger causality mapping. Magn. Reson. Imaging 21, 1251-1261. (doi:10.1016/j.mri.2003.08.026). (Pubitemid 38199731)
5. Hesse W, Möller E, Arnold M, Schack B. 2003 The use of time-variant EEG Granger causality for inspecting directed interdependencies of neural assemblies. J. Neurosci.Methods 124, 27-44. (doi:10.1016/S0165-0270(02)00366-7). (Pubitemid 36315806)
6. Kaminski M, Ding M, Truccolo WA, Bressler SL. 2001 Evaluating causal relations in neural systems: Granger causality, directed transfer function and statistical assessment of significance. Biol. Cybern. 85, 145-157. (doi:10.1007/s004220000235). (Pubitemid 33605209)
7. Nedungadi A, Rangarajan G, Jain N, Ding M. 2009 Analyzing multiple spike trains with nonparametricGranger causality. J. Comp. Neurosci. 27, 55-64. (doi:10.1007/s10827-008-0126-2).
8. Roebroeck A, Formisano E, Goebel R. 2005 Mapping directed influence over the brain using Granger causality and fMRI. Neuroimage 25, 230-242. (doi:10.1016/j.neuroimage.2004.11.017). (Pubitemid 40289151)
9. Schelter B, Winterhalder M, Eichler M, Peifer M, Hellwig B, Guschlbauer B, Lücking CH, Dahlhaus R, Timmer J. 2006 Testing for directed influences among neural signals using partial directed coherence. J. Neurosci. Methods 152, 210-219. (doi:10.1016/j.jneumeth.2005.09.001). (Pubitemid 43343492)
10. Wen X, Yao L, Liu Y, Ding M. 2012 Causal interactions in attention networks predict behavioral performance. J. Neurosci. 32, 1284-1292. (doi:10.1523/JNEUROSCI.2817-11.2012).
11. Seth AK. 2005 Causal connectivity of evolved neural networks during behavior. Netw. Comp. Neural Syst. 16, 35-54. (doi:10.1080/09548980500238756). (Pubitemid 43982148)
12. Baccala LA, Sameshima K. 2001 Partial directed coherence: A new concept in neural structure determination. Biol. Cybern. 84, 463-474. (doi:10.1007/PL00007990). (Pubitemid 33605196)
13. Astolfi L et al. 2005 Assessing cortical functional connectivity by linear inverse estimation and directed transfer function: simulations and application to real data. Clin. Neurophysiol. 116, 920-932. (doi:10.1016/j. clinph.2004.10.012). (Pubitemid 40432010)
14. Brovelli A, Ding M, Ledberg A, Chen Y, Nakamura R, Bressler SL. 2004 Beta oscillations in a large-scale sensorimotor cortical network: directional influences revealed by Granger causality. Proc. Natl Acad. Sci. USA 101, 9849-9854. (doi:10.1073/pnas.0308538101). (Pubitemid 38869325)
15. Chen Y, Bressler SL, Ding M. 2006 Stochastic modeling of neurobiological time series: power, coherence, Granger causality, and separation of evoked responses from ongoing activity. Chaos 16, 026113. (doi:10.1063/1.2208455). (Pubitemid 44000356)
16. Chen YH, Bressler SL, Ding MZ. 2006 Frequency decomposition of conditional Granger causality and application to multivariate neural field potential data. J. Neurosci. Methods 150, 228-237. (doi:10.1016/j.jneumeth.2005. 06.011). (Pubitemid 43144459)
17. Blinowska KJ, Kus R, Kaminski M. 2004 Granger causality and information flow in multivariate processes. Phys. Rev. E 70, 05d0902. (doi:10.1103/PhysRevE. 70.050902). (Pubitemid 40108202)
18. Deshpande G, Laconte S, James GA, Peltier S, Hu X. 2009 Multivariate Granger causality analysis of fMRI data. Hum. Brain Mapp. 30, 1361-1373. (doi:10.1002/hbm.20606).
19. Mader W, Feess D, Lange R, Saur D, Glauche V, Weiller C, Timmer J, Schelter B. 2008 On the detection of direct directed information flow in fMRI. IEEE J. Sel. Top. Signal Process 2, 965-974. (doi:10.1109/JSTSP.2008.2008260).
20. Schelter B, Timmer J, Eichlere M. 2009 Assessing the strength of directed influences among neural signals using renormalized partial directed coherence. J. Neurosci. Methods 179, 121-130. (doi:10.1016/j.jneumeth.2009.01.006).
21. Wiener N. 1956 The theory of prediction. In Modern mathematics for the engineer (ed. EF Beckenbach), pp. 165-190. New York, NY: McGraw-Hill.
22. Granger C. 1969 Investigating causal relations by econometric models and cross-spectral methods. Econometrica 37, 424-438. (doi:10.2307/1912791).
23. Geweke J. 1982 Measurement of linear dependence and feedback between multiple time series. J. Am. Stat. Assoc. 77, 304-313. (doi:10.1080/01621459. 1982.10477803).
24. Geweke J. 1984 Measures of conditional linear dependence and feedback between time series. J. Am. Stat. Assoc. 79, 907-915. (doi:10.1080/01621459. 1984.10477110).
25. Jenkins GM, Watts DG. 1968 Spectral analysis and its applications. San Francisco, CA: Holden- Day.
26. Wilson GT. 1972 The factorization of matricial spectral densities. SIAM J. Appl. Math. 23, 420-426. (doi:10.1137/0123044).
27. Dhamala M, Rangarajan G, Ding MZ. 2008 Estimating Granger causality from Fourier and wavelet transforms of time series data. Phys. Rev. Lett. 100, 018701. (doi:10.1103/PhysRevLett.100.018701). (Pubitemid 351388395)
28. Dhamala M, Rangarajan G, Ding MZ. 2008 Analyzing information flow in brain networks with nonparametric Granger causality. NeuroImage 41, 354-362. (doi:10.1016/j.neuroimage.2008.02.020).
29. Thomson DJ. 1982 Spectrum estimation and harmonic analysis. Proc. IEEE 70, 1055-1096. (doi:10.1109/PROC.1982.12433).
30. Walden AT. 2000 A unified view of multitaper spectral estimation. Biometrika 87, 767-788. (doi:10.1093/biomet/87.4.767).
31. Corbetta M, Patel G, Shulman GL. 2008 The reorienting system of the human brain: from environment to theory of mind. Neuron 58, 306-324. (doi:10.1016/j.neuron.2008.04.017). (Pubitemid 351615192)
32. Dosenbach NU et al. 2006 A core system for the implementation of task sets. Neuron 50, 799-812. (doi:10.1016/j.neuron.2006.04.031). (Pubitemid 43775735)
33. Faes L, Pinna GD, Porta A, Maestri R, Nollo G. 2004 Surrogate data analysis for assessing the significance of the coherence function. IEEE Trans. Biomed. Eng. 51, 1156-1166. (doi:10.1109/TBME.2004.827271). (Pubitemid 38787922)
34. Faes L, Porta A, Nollo G. 2010 Testing frequency-domain causality in multivariate time series. IEEE Trans. Biomed. Eng. 57, 1897-1906. (doi:10.1109/TBME.2010.2042715).
35. Bressler SL, Tang W, Sylvester C, Shulman G, Corbetta M. 2008 Top-down control of human visual cortex by frontal and parietal cortex in anticipatory visual spatial attention. J. Neurosci. 28, 10056-10061. (doi:10.1523/JNEUROSCI. 1776-08.2008).
36. Cohen JD, Botvinick M, Carter CS. 2000 Anterior cingulate and prefrontal cortex: who's in control? Nat. Neurosci. 3, 421-423. (doi:10.1038/74783). (Pubitemid 30495619)