Reportedly, coherence-based metrics are primarily influenced by linearity in phase. However, Klein et al report that coherence is also:
... very sensitive to fluctuations of linearity in phase, relatively less so to nonlinear fluctuations of amplitude and completely insensitive to linear fluctuations in amplitude. How much both types of linearity contribute to the final measure, however, remains somewhat unclear and, therefore, some authors have argued that amplitude should not contribute to the final measure at all, using a "phase locking value" instead,which is essentially the square root of (4) with all the moduli set to 1
without citing papers that prove the sensitivity of coherence with non-linear amplitude fluctuations.
Does this stand and if yes, are there any papers supporting it?