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Even though human experience unfolds continuously in time, it is not strictly linear; instead, it entails cascading processes building hierarchical cognitive structures. For instance, during speech perception, humans transform a continuously varying acoustic signal into phonemes, words, and meaning, and these levels all have distinct but interdependent temporal structures. Time-lagged regression usingtemporal response functions (TRFs) has recently emerged as a promising tool for disentangling electrophysiological brain responses related to such complex models of perception. Here, we introduce the Eelbrain Python toolkit, which makes this kind of analysis easy and accessible. We demonstrate its use, using continuous speech as a sample paradigm, with a freely available EEG dataset of audiobook listening. A companion GitHub repository provides the complete source code for the analysis, from raw data to group-level statistics. More generally, we advocate a hypothesis-driven approach in which the experimenter specifies a hierarchy of time-continuous representations that are hypothesized to have contributed to brain responses, and uses those as predictor variables for the electrophysiological signal. This is analogous to a multiple regression problem, but with the addition of a time dimension. TRF analysis decomposes the brain signal into distinct responses associated with the different predictor variables by estimating a multivariate TRF (mTRF), quantifying the influence of each predictor on brain responses as a function of time(-lags). This allows asking two questions about the predictor variables: (1) Is there a significant neural representation corresponding to this predictor variable? And if so, (2) what are the temporal characteristics of the neural response associated with it? Thus, different predictor variables can be systematically combined and evaluated to jointly model neural processing at multiple hierarchical levels. We discuss applications of this approach, including the potential for linking algorithmic/representational theories at different cognitive levels to brain responses through computational models with appropriate linking hypotheses. 

When listening to speech, our brain responses time lock to acoustic events in the stimulus. Recent studies have also reported that cortical responses track linguistic representations of speech. However, tracking of these representations is often described without controlling for acoustic properties. Therefore, the response to these linguistic representations might reflect unaccounted acoustic processing rather than language processing. Here, we evaluated the potential of several recently proposed linguistic representations as neural markers of speech comprehension. To do so, we investigated EEG responses to audiobook speech of 29 participants (22 females). We examined whether these representations contribute unique information over and beyond acoustic neural tracking and each other. Indeed, not all of these linguistic representations were significantly tracked after controlling for acoustic properties. However, phoneme surprisal, cohort entropy, word surprisal, and word frequency were all significantly tracked over and beyond acoustic properties. We also tested the generality of the associated responses by training on one story and testing on another. In general, the linguistic representations are tracked similarly across different stories spoken by different readers. These results suggests that these representations characterize the processing of the linguistic content of speech. SIGNIFICANCE STATEMENT For clinical applications, it would be desirable to develop a neural marker of speech comprehension derived from neural responses to continuous speech. Such a measure would allow for behavior-free evaluation of speech understanding; this would open doors toward better quantification of speech understanding in populations from whom obtaining behavioral measures may be difficult, such as young children or people with cognitive impairments, to allow better targeted interventions and better fitting of hearing devices.