Towards Detecting Connectivity in EEG: A Comparative Study of Parameters of Effective Connectivity Measures on Simulated Data

We compare the performance of many effective connectivity measures in detecting statistically significant causal connections between time series drawn from linear and nonlinear coupled systems. Fifteen measures are compared, drawn from two families (information theoretic, and frequency- and time-based multivariate autoregressive models), including common and uncommon measures. Measures were tested on simulated data from three systems: three coupled Hénon maps; a multivariate autoregressive (MVAR) model with and without EEG as an exogenous input; and simulated EEG. Comparisons focus on the effective of parameter choices, e.g. maximum model order or maximum number of lags, for different lengths of data. Performance varies with dataset, and no measure was outstanding for all datasets. Strong performance is obtained where the measure’s model and data source match (eg MVAR model, or frequency domain measures with narrowband data). When there is no match, information theoretic measures and Copula Granger causality generally perform best.

[1]  M. Eichler.  Graphical modelling of multivariate time series , 2006, math/0610654.

[2]  L. Baccalá,et al.  Overcoming the limitations of correlation analysis for many simultaneously processed neural structures. , 2001, Progress in brain research.

[3]  Schreiber,et al.  Measuring information transfer , 2000, Physical review letters.

[4]  S. Frenzel,et al.  Partial mutual information for coupling analysis of multivariate time series. , 2007, Physical review letters.

[5]  R. Andrzejak,et al.  Detection of weak directional coupling: phase-dynamics approach versus state-space approach. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  Matthäus Staniek,et al.  Symbolic transfer entropy. , 2008, Physical review letters.

[7]  S. Bressler,et al.  Granger Causality: Basic Theory and Application to Neuroscience , 2006, q-bio/0608035.

[8]  James Theiler,et al.  Testing for nonlinearity in time series: the method of surrogate data , 1992 .

[9]  Dimitris Kugiumtzis,et al.  Partial transfer entropy on rank vectors , 2013, ArXiv.

[10]  Albert Y. Zomaya,et al.  Local information transfer as a spatiotemporal filter for complex systems. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  M. Kaminski,et al.  Granger causality and information flow in multivariate processes. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  Hualou Liang,et al.  A copula approach to assessing Granger causality , 2014, NeuroImage.

[13]  C. Granger.  Testing for causality: a personal viewpoint , 1980 .

[14]  Karl J. Friston,et al.  Evaluation of different measures of functional connectivity using a neural mass model , 2004, NeuroImage.

[15]  Anthony R. McIntosh,et al.  Confounding Effects of Phase Delays on Causality Estimation , 2013, PloS one.

[16]  H. Marko,et al.  The Bidirectional Communication Theory - A Generalization of Information Theory , 1973, IEEE Transactions on Communications.

[17]  S. Bressler,et al.  Frequency decomposition of conditional Granger causality and application to multivariate neural field potential data , 2006, Journal of Neuroscience Methods.

[18]  Luiz A. Baccalá,et al.  Partial directed coherence: a new concept in neural structure determination , 2001, Biological Cybernetics.

[19]  Anil K. Seth,et al.  The MVGC multivariate Granger causality toolbox: A new approach to Granger-causal inference , 2014, Journal of Neuroscience Methods.

[20]  Giandomenico Nollo,et al.  Multivariate Frequency Domain Analysis of Causal Interactions in Physiological Time Series , 2011 .

[21]  K. Kendrick,et al.  Partial Granger causality—Eliminating exogenous inputs and latent variables , 2008, Journal of Neuroscience Methods.

[22]  C. Granger.  Investigating Causal Relations by Econometric Models and Cross-Spectral Methods , 1969 .

[23]  Santiago Collavini,et al.  Assessing effective connectivity in epileptogenic networks. A model-based simulation approach , 2013 .

[24]  J. Geweke,et al.  Measures of Conditional Linear Dependence and Feedback between Time Series , 1984 .

[25]  Solomon Kullback,et al.  Information Theory and Statistics , 1960 .

[26]  Mingzhou Ding,et al.  Evaluating causal relations in neural systems: Granger causality, directed transfer function and statistical assessment of significance , 2001, Biological Cybernetics.

[27]  J. Geweke,et al.  Measurement of Linear Dependence and Feedback between Multiple Time Series , 1982 .