Higher-order EEG microstate syntax and surrogate testing

Higher-order syntax properties of EEG microstate sequences offer insight into the transition dynamics of functional brain networks. We here define higher-order syntax as microstate sequence properties that are not explained by the first-order transition matrix, and we postulate three requirements that surrogate data should fulfill to provide a null hypothesis for higher-order syntax tests. We then compare two general approaches to surrogate data generation that have been used in microstate research, (a) surrogates from a first-order Markov chain model, and, (b) surrogates obtained from sequence shuffling. There are two different ways of representing microstate sequences, and syntax analyses can be applied to both, continuous microstate sequences, where each time sample is assigned the nearest microstate cluster, or to jump sequences which record only non-identical transitions by removing adjacent duplicates. We show that jump sequences have at least first-order syntax properties, whereas continuous sequences allow for zero-order and first-order surrogates. Markov chain generated surrogates fulfill the three requirements, i.e. they preserve the microstate distribution and transition matrix, and have no higher-order properties. Jump sequence shuffling, on the other hand, yields first-order surrogates whose first-order parameters are markedly different from the original sequence. Using a large open-access resting-state EEG dataset we show that jump sequence shuffling almost certainly produces microstate word probabilities that are significantly different from first-order expected word frequencies, erroneously indicating higher-order syntax properties. Markov chain surrogates reproduce the expected word probabilities of first-order sequences and correctly reject higher-order syntax properties in these cases. We conclude that jump sequence shuffling does not produce adequate surrogates for higher-order syntax investigations. The proposed Markov chain generative method for surrogate data synthesis is computationally efficient and allows the generation of surrogate sequences of arbitrary length, whereas shuffling can lead to sequences that are shorter than the original sequence and have variable length. Sample code in Python and MATLAB is provided.