A note on the phase locking value and its properties

We investigate the properties of the Phase Locking Value (PLV) and the Phase Lag Index (PLI) as metrics for quantifying interactions in bivariate local field potential (LFP), electroencephalography (EEG) and magnetoencephalography (MEG) data. In particular we describe the relationship between nonparametric estimates of PLV and PLI and the parameters of two distributions that can both be used to model phase interactions. The first of these is the von Mises distribution, for which the sample PLV is a maximum likelihood estimator. The second is the relative phase distribution associated with bivariate circularly symmetric complex Gaussian data. We derive an explicit expression for the PLV for this distribution and show that it is a function of the cross-correlation between the two signals. We compare the bias and variance of the sample PLV and the PLV computed from the cross-correlation. We also show that both the von Mises and Gaussian models are suitable for representing relative phase in application to LFP data from a visually-cued motor study in macaque. We then compare results using the two different PLV estimators and conclude that, for this data, the sample PLV provides equivalent information to the cross-correlation of the two complex time series.