Phase Lag Index (PLI and wPLI)

The phase lag index measures the asymmetry of the distribution of instantaneous phase differences between two signals around zero: it is the absolute average of the sign of the imaginary part of the cross-spectrum. Because zero-lag mixing from volume conduction sits exactly at phase difference zero (or pi), it contributes no consistent sign and washes out, so a nonzero PLI reflects a consistently lagged, and therefore more plausibly genuine, interaction. PLI ranges from 0 to 1 and, unlike coherence, does not reward zero-lag coupling.

The weighted phase lag index (wPLI) refines this by weighting each contribution by the magnitude of the imaginary component, which strongly reduces the influence of phase differences near zero where small amounts of noise can flip the sign and inflate the raw PLI. wPLI is consequently less biased by noise and by small sample sizes and is a common default for scalp and source connectivity, though like all zero-lag-insensitive measures it is blind to true instantaneous coupling.