Causality analysis of neural connectivity: Critical examination of existing methods and advances of new methods

Sanqing Hu, Guojun Dai, Gregory A. Worrell, Qionghai Dai, Hualou Liang

Research output: Contribution to journalReview articlepeer-review

45 Scopus citations


Granger causality (GC) is one of the most popular measures to reveal causality influence of time series and has been widely applied in economics and neuroscience. Especially, its counterpart in frequency domain, spectral GC, as well as other Granger-like causality measures have recently been applied to study causal interactions between brain areas in different frequency ranges during cognitive and perceptual tasks. In this paper, we show that: 1) GC in time domain cannot correctly determine how strongly one time series influences the other when there is directional causality between two time series, and 2) spectral GC and other Granger-like causality measures have inherent shortcomings and/or limitations because of the use of the transfer function (or its inverse matrix) and partial information of the linear regression model. On the other hand, we propose two novel causality measures (in time and frequency domains) for the linear regression model, called new causality and new spectral causality, respectively, which are more reasonable and understandable than GC or Granger-like measures. Especially, from one simple example, we point out that, in time domain, both new causality and GC adopt the concept of proportion, but they are defined on two different equations where one equation (for GC) is only part of the other (for new causality), thus the new causality is a natural extension of GC and has a sound conceptual/theoretical basis, and GC is not the desired causal influence at all. By several examples, we confirm that new causality measures have distinct advantages over GC or Granger-like measures. Finally, we conduct event-related potential causality analysis for a subject with intracranial depth electrodes undergoing evaluation for epilepsy surgery, and show that, in the frequency domain, all measures reveal significant directional event-related causality, but the result from new spectral causality is consistent with event-related timefrequency power spectrum activity. The spectral GC as well as other Granger-like measures are shown to generate misleading results. The proposed new causality measures may have wide potential applications in economics and neuroscience.

Original languageEnglish (US)
Article number5751700
Pages (from-to)829-844
Number of pages16
JournalIEEE Transactions on Neural Networks
Issue number6
StatePublished - Jun 2011


  • Event-related potential
  • Granger or Granger-like causality
  • linear regression model
  • new causality
  • power spectrum

ASJC Scopus subject areas

  • Software
  • Computer Science Applications
  • Computer Networks and Communications
  • Artificial Intelligence


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