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.
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
pe <- make_eeg(n_time = 5000, n_channels = 4, sr = 500)
gc_df <- eegGrangerCausality(pe, order = 5, band = c(8, 13))
head(gc_df)
#> from_channel to_channel gc_value
#> 1 Fp1 Fp2 0.08458763
#> 2 Fp1 F7 0.06416600
#> 3 Fp1 F3 0.07524694
#> 4 Fp2 Fp1 0.17008322
#> 5 Fp2 F7 0.04102852
#> 6 Fp2 F3 0.15872682