EEG Spectral Granger Causality

Computes spectral Granger causality between all EEG channel pairs by fitting bivariate autoregressive (AR) models using Yule-Walker equations and computing the transfer function in the frequency domain. Unlike coherence-based measures, Granger causality is directional: GC from channel A to channel B is generally different from GC from B to A.

Usage

eegGrangerCausality(x, order = 5, band = NULL, assay_name = NULL)

Arguments

x: A PhysioExperiment object with EEG data (2D: time x channels).
order: Integer AR model order for the bivariate model (default: 5).
band: Numeric vector of length 2 specifying the frequency band in Hz over which to average GC. If NULL, returns the average over all positive frequencies.
assay_name: Name of the input assay. If NULL, the default assay is used.

Value

A data.frame with columns:

from_channel: Character or integer identifier of the source channel.
to_channel: Character or integer identifier of the target channel.
gc_value: Numeric Granger causality value (>= 0). Higher values indicate stronger directed influence.

Details

The spectral Granger causality from channel x to channel y at frequency f is defined as: $$GC_{x \to y}(f) = \log(S_{yy}(f) / (S_{yy}(f) - |H_{xy}(f)|^2 \cdot \Sigma_{xx}))$$

References

Lachaux, J. P., et al. (1999). Measuring phase synchrony in brain signals. Human Brain Mapping, 8(4), 194-208.

Granger, C. W. J. (1969). Investigating causal relations by econometric models and cross-spectral methods. Econometrica, 37(3), 424-438.

Examples

if (FALSE) { # \dontrun{
pe <- make_eeg(n_time = 5000, n_channels = 4, sr = 500)
gc_df <- eegGrangerCausality(pe, order = 5, band = c(8, 13))
head(gc_df)
} # }