Weighted phase-lag index estimator (raw and debiased)

Computes the weighted phase-lag index (wPLI) and its unbiased (debiased) estimator from the imaginary part of a cross-spectrum, following Vinck et al. (2011, Eq. 6). This is the single source of the wPLI debiasing math shared by PhysioEEG (eegWPLI) and PhysioCrossModal (weightedPLI), so the two agree exactly on identical input.

Usage

wpliEstimate(imag, debiased = TRUE)

Arguments

imag

Numeric vector of imaginary cross-spectrum values.

debiased

Logical; also compute the debiased estimator (default TRUE).

Value

A list with wpli (raw wPLI, from 0 to 1), wpli_debiased (the debiased estimator, or NA if debiased = FALSE or fewer than two values), and n (the number of values used).

Details

The estimators, over the imaginary cross-spectrum values \(X_j\) (one per window, taper, or time sample), are $$\mathrm{wPLI} = \frac{|\sum_j X_j|}{\sum_j |X_j|}$$ $$\mathrm{debiased\ wPLI} = \frac{(\sum_j X_j)^2 - \sum_j X_j^2}{(\sum_j |X_j|)^2 - \sum_j X_j^2}.$$ The debiased numerator and denominator subtract the diagonal self-terms, so the estimator is unbiased: for independent signals it is distributed around 0 rather than being inflated toward positive values.

References

Vinck, M., Oostenveld, R., van Wingerden, M., Battaglia, F., & Pennartz, C.M.A. (2011). "An improved index of phase-synchronization for electrophysiological data in the presence of volume-conduction, noise and sample-size bias." NeuroImage, 55(4), 1548-1565. doi:10.1016/j.neuroimage.2011.01.055

Examples

set.seed(1)
wpliEstimate(rnorm(500))
#> $wpli
#> [1] 0.02835767
#> 
#> $wpli_debiased
#> [1] -0.002410649
#> 
#> $n
#> [1] 500
#>