Tensor factorisations have proven useful to model amplitude and spectral information of brain recordings. Here, we assess the usefulness of tensor factorisations in the multiway analysis of other brain signal features in the context of complexity measures recently proposed to inspect multiscale dynamics. We consider the "refined composite multiscale entropy" (rcMSE), which computes entropy "profiles" showing levels of physiological complexity over temporal scales for individual signals. We compute the rcMSE of resting-state magnetoencephalogram (MEG) recordings from 36 patients with Alzheimer's disease and 26 control subjects. Instead of traditional simple visual examinations, we organise the entropy profiles as a three-way tensor to inspect relationships across temporal and spatial scales and subjects with multiway data analysis techniques based on PARAFAC and PARAFAC2 factorisations. A PARAFAC2 model with two factors was appropriate to account for the interactions in the entropy tensor between temporal scales and MEG channels for all subjects. Moreover, the PARAFAC2 factors had information related to the subjects' diagnosis, achieving a cross-validated area under the ROC curve of 0.77. This confirms the suitability of tensor factorisations to represent electrophysiological brain data efficiently despite the unsupervised nature of these techniques. This article is part of a Special Issue entitled 'Neural data analysis'.