A study of problems encountered in Granger causality analysis from a neuroscience perspective

Abstract

, we misunderstood the method described in Barnett and Seth (25) to compute the conditional Granger causality. We realize now that the spectral factorization method they describe can be used to obtain the conditional Granger causality with a single model fit, which would avoid the computational problems associated with separate model fits. We apologize for this error." Granger causality methods were developed to analyze the flow of information between time series. These methods have become more widely applied in neuroscience. Frequency-domain causality measures, such as those of Geweke, as well as multivariate methods, have particular appeal in neuroscience due to the prevalence of oscillatory phenomena and highly multivariate experimental recordings. Despite its widespread application in many fields, there are ongoing concerns regarding the applicability of Granger causality methods in neuroscience. When are these methods appropriate? How reliably do they recover the system structure underlying the observed data? What do frequency-domain causality measures tell us about the functional properties of oscillatory neural systems? In this paper, we analyze fundamental properties of Granger-Geweke (GG) causality, both computational and conceptual. Specifically, we show that (i) GG causality estimates can be either severely biased or of high variance, both leading to spurious results; (ii) even if estimated correctly, GG causality estimates alone are not interpretable without examining the component behaviors of the system model; and (iii) GG causality ignores critical components of a system's dynamics. Based on this analysis, we find that the notion of causality quantified is incompatible with the objectives of many neuroscience investigations, leading to highly counterintuitive and potentially misleading results. Through the analysis of these problems, we provide important conceptual clarification of GG causality, with implications for other related causality approaches and for the role of causality analyses in neuroscience as a whole.Granger causality | time series analysis | neural oscillations | connectivity | system identification G ranger causality is a statistical tool developed to analyze the flow of information between time series. Neuroscientists have applied Granger causality methods to diverse sources of data, including electroencephalography (EEG), magnetoencephalography (MEG), functional magnetic resonance imaging (fMRI), and local field potentials (LFP). These studies have investigated functional neural systems at scales of organization from the cellular level (1-3) to whole-brain network activity (4), under a range of conditions, including sensory stimuli (5-7), varying levels of consciousness (8-10), cognitive tasks (11), and pathological states (12, 13). In such analyses, the time series data are interpreted to reflect neural activity from a particular source, and Granger causality is used to characterize the directionality, directness, and dynamics of influence between sources.Oscillations are a ...

Thalamocortical synchronization during induction and emergence from propofol-induced unconsciousness

“…In particular, whereas cortical inhibitory networks can generate β oscillations (26) that slow to α frequencies with increasing inhibitory tone (13), propofol-induced α oscillations appear to become coherent through the functional influence of the thalamus (14). We must emphasize, however, that the presence of thalamocortical coherence implies only an interaction between the two areas, and cannot convey directional influences, which would require the application of different analysis methods that can be challenging to interpret (27). During emergence, these propofol-induced dynamics dissipated, but with a trajectory that differed from that observed during induction.…”

“…Electroencephalogram (EEG) recordings in humans during gradual induction of unconsciousness with propofol show the appearance of frontal β oscillations (15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30) at the onset of sedation, followed by the appearance of coherent frontal α (8-12 Hz) oscillations (7)(8)(9)(10) and widespread slow (0.1-1 Hz) and δ (1-4 Hz) oscillations (7,11,12) when subjects no longer respond to sensory stimuli. Biophysical models of neuronal dynamics have shown that whereas α and β oscillations can be generated by propofol's actions in cortex alone (13), coherent α oscillations require the participation of both thalamus and cortex (14).…”

Modulation of network‐to‐network connectivity via spike‐timing‐dependent noninvasive brain stimulation

“…Specifically, A ! In recent years, criticism about pairwise GC analysis has been growing (Smith, 2012;Barnett et al, 2017), leading to the development of newer approaches for information flow estimation such as the one implemented in the present investigation (Stokes & Purdon, 2017;Faes, Stramaglia, & Marinazzo, 2017;Seth et al, 2013). The method applied here stem from Granger Causality (GC) analysis, and it is based on the concepts of predictability and precedence: variable A is said to modulate variable B if the past behavior of A contains information that helps predict the future behavior of B over and above information already in the past of B.…”

Neural correlates of time distortion in a preaction period

“…In a time window of 800–900 ms, we found significant causality from alpha power to the ERFs (Granger coefficient = 0.161, corrected p = .0064), while causality from the ERFs to alpha power was nonsignificant (Granger coefficient = 0.05, uncorrected p = .09). Those results suggested that a dissociation of ERFs between F‐A and F‐NA trials (beginning from 890 ms) resulted from temporal dynamics of alpha rhythm in the same time window (800–900 ms), although results of the Granger causality analysis should be interpreted cautiously (Stokes & Purdon, ).…”