@article{RabeChandraKruegeletal.2021,
  author    = {Rabe, Maximilian Michael and Chandra, Johan and Kr{\"u}gel, Andr{\´e} and Seelig, Stefan A. and Vasishth, Shravan and Engbert, Ralf},
  title     = {A bayesian approach to dynamical modeling of eye-movement control in reading of normal, mirrored, and scrambled texts},
  series = {Psychological Review},
  volume    = {128},
  journal   = {Psychological Review},
  number    = {5},
  publisher = {American Psychological Association},
  address   = {Washington},
  issn      = {0033-295X},
  doi       = {10.1037/rev0000268},
  pages     = {803 -- 823},
  year      = {2021},
  abstract  = {In eye-movement control during reading, advanced process-oriented models have been developed to reproduce behavioral data. So far, model complexity and large numbers of model parameters prevented rigorous statistical inference and modeling of interindividual differences. Here we propose a Bayesian approach to both problems for one representative computational model of sentence reading (SWIFT; Engbert et al., Psychological Review, 112, 2005, pp. 777-813). We used experimental data from 36 subjects who read the text in a normal and one of four manipulated text layouts (e.g., mirrored and scrambled letters). The SWIFT model was fitted to subjects and experimental conditions individually to investigate between- subject variability. Based on posterior distributions of model parameters, fixation probabilities and durations are reliably recovered from simulated data and reproduced for withheld empirical data, at both the experimental condition and subject levels. A subsequent statistical analysis of model parameters across reading conditions generates model-driven explanations for observable effects between conditions.},
  language  = {en}
}
@inproceedings{Engbert2012,
  author    = {Engbert, Ralf},
  title     = {A computational model of microsaccadic responses to shifts of covert attention},
  series = {Perception},
  volume    = {41},
  booktitle = {Perception},
  publisher = {Sage Publ.},
  address   = {London},
  issn      = {0301-0066},
  pages     = {55 -- 55},
  year      = {2012},
  language  = {en}
}
@article{EngbertLongtinKliegl2002,
  author    = {Engbert, Ralf and Longtin, Andre and Kliegl, Reinhold},
  title     = {A dynamical model of saccade generation in reading based on spatially distributed lexical processing},
  year      = {2002},
  language  = {en}
}
@article{EngelmannVasishthEngbertetal.2013,
  author    = {Engelmann, Felix and Vasishth, Shravan and Engbert, Ralf and Kliegl, Reinhold},
  title     = {A framework for modeling the interaction of syntactic processing and eye movement control},
  series = {Topics in cognitive science},
  volume    = {5},
  journal   = {Topics in cognitive science},
  number    = {3},
  publisher = {Wiley-Blackwell},
  address   = {Hoboken},
  issn      = {1756-8757},
  doi       = {10.1111/tops.12026},
  pages     = {452 -- 474},
  year      = {2013},
  abstract  = {We explore the interaction between oculomotor control and language comprehension on the sentence level using two well-tested computational accounts of parsing difficulty. Previous work (Boston, Hale, Vasishth, \& Kliegl, 2011) has shown that surprisal (Hale, 2001; Levy, 2008) and cue-based memory retrieval (Lewis \& Vasishth, 2005) are significant and complementary predictors of reading time in an eyetracking corpus. It remains an open question how the sentence processor interacts with oculomotor control. Using a simple linking hypothesis proposed in Reichle, Warren, and McConnell (2009), we integrated both measures with the eye movement model EMMA (Salvucci, 2001) inside the cognitive architecture ACT-R (Anderson et al., 2004). We built a reading model that could initiate short Time Out regressions (Mitchell, Shen, Green, \& Hodgson, 2008) that compensate for slow postlexical processing. This simple interaction enabled the model to predict the re-reading of words based on parsing difficulty. The model was evaluated in different configurations on the prediction of frequency effects on the Potsdam Sentence Corpus. The extension of EMMA with postlexical processing improved its predictions and reproduced re-reading rates and durations with a reasonable fit to the data. This demonstration, based on simple and independently motivated assumptions, serves as a foundational step toward a precise investigation of the interaction between high-level language processing and eye movement control.},
  language  = {en}
}
@article{MalemShinitskiOpperReichetal.2020,
  author    = {Malem-Shinitski, Noa and Opper, Manfred and Reich, Sebastian and Schwetlick, Lisa and Seelig, Stefan A. and Engbert, Ralf},
  title     = {A mathematical model of local and global attention in natural scene viewing},
  series = {PLoS Computational Biology : a new community journal},
  volume    = {16},
  journal   = {PLoS Computational Biology : a new community journal},
  number    = {12},
  publisher = {PLoS},
  address   = {San Fransisco},
  issn      = {1553-734X},
  doi       = {10.1371/journal.pcbi.1007880},
  pages     = {21},
  year      = {2020},
  abstract  = {Author summary <br /> Switching between local and global attention is a general strategy in human information processing. We investigate whether this strategy is a viable approach to model sequences of fixations generated by a human observer in a free viewing task with natural scenes. Variants of the basic model are used to predict the experimental data based on Bayesian inference. Results indicate a high predictive power for both aggregated data and individual differences across observers. The combination of a novel model with state-of-the-art Bayesian methods lends support to our two-state model using local and global internal attention states for controlling eye movements. <br /> Understanding the decision process underlying gaze control is an important question in cognitive neuroscience with applications in diverse fields ranging from psychology to computer vision. The decision for choosing an upcoming saccade target can be framed as a selection process between two states: Should the observer further inspect the information near the current gaze position (local attention) or continue with exploration of other patches of the given scene (global attention)? Here we propose and investigate a mathematical model motivated by switching between these two attentional states during scene viewing. The model is derived from a minimal set of assumptions that generates realistic eye movement behavior. We implemented a Bayesian approach for model parameter inference based on the model's likelihood function. In order to simplify the inference, we applied data augmentation methods that allowed the use of conjugate priors and the construction of an efficient Gibbs sampler. This approach turned out to be numerically efficient and permitted fitting interindividual differences in saccade statistics. Thus, the main contribution of our modeling approach is two-fold; first, we propose a new model for saccade generation in scene viewing. Second, we demonstrate the use of novel methods from Bayesian inference in the field of scan path modeling.},
  language  = {en}
}
@article{KruegelEngbert2014,
  author    = {Kruegel, Andre and Engbert, Ralf},
  title     = {A model of saccadic landing positions in reading under the influence of sensory noise},
  series = {Visual cognition},
  volume    = {22},
  journal   = {Visual cognition},
  number    = {3-4},
  publisher = {Routledge, Taylor \& Francis Group},
  address   = {Abingdon},
  issn      = {1350-6285},
  doi       = {10.1080/13506285.2014.894166},
  pages     = {334 -- 353},
  year      = {2014},
  language  = {en}
}
@article{HerrmannMetzlerEngbert2017,
  author    = {Herrmann, Carl J. J. and Metzler, Ralf and Engbert, Ralf},
  title     = {A self-avoiding walk with neural delays as a model of fixational eye movements},
  series = {Scientific reports},
  volume    = {7},
  journal   = {Scientific reports},
  publisher = {Nature Publ. Group},
  address   = {London},
  issn      = {2045-2322},
  doi       = {10.1038/s41598-017-13489-8},
  pages     = {17},
  year      = {2017},
  abstract  = {Fixational eye movements show scaling behaviour of the positional mean-squared displacement with a characteristic transition from persistence to antipersistence for increasing time-lag. These statistical patterns were found to be mainly shaped by microsaccades (fast, small-amplitude movements). However, our re-analysis of fixational eye-movement data provides evidence that the slow component (physiological drift) of the eyes exhibits scaling behaviour of the mean-squared displacement that varies across human participants. These results suggest that drift is a correlated movement that interacts with microsaccades. Moreover, on the long time scale, the mean-squared displacement of the drift shows oscillations, which is also present in the displacement auto-correlation function. This finding lends support to the presence of time-delayed feedback in the control of drift movements. Based on an earlier non-linear delayed feedback model of fixational eye movements, we propose and discuss different versions of a new model that combines a self-avoiding walk with time delay. As a result, we identify a model that reproduces oscillatory correlation functions, the transition from persistence to antipersistence, and microsaccades.},
  language  = {en}
}
@article{RisseHohensteinKliegletal.2014,
  author    = {Risse, Sarah and Hohenstein, Sven and Kliegl, Reinhold and Engbert, Ralf},
  title     = {A theoretical analysis of the perceptual span based on SWIFT simulations of the n+2 boundary paradigm},
  series = {Visual cognition},
  volume    = {22},
  journal   = {Visual cognition},
  number    = {3-4},
  publisher = {Routledge, Taylor \& Francis Group},
  address   = {Abingdon},
  issn      = {1350-6285},
  doi       = {10.1080/13506285.2014.881444},
  pages     = {283 -- 308},
  year      = {2014},
  abstract  = {Eye-movement experiments suggest that the perceptual span during reading is larger than the fixated word, asymmetric around the fixation position, and shrinks in size contingent on the foveal processing load. We used the SWIFT model of eye-movement control during reading to test these hypotheses and their implications under the assumption of graded parallel processing of all words inside the perceptual span. Specifically, we simulated reading in the boundary paradigm and analysed the effects of denying the model to have valid preview of a parafoveal word n + 2 two words to the right of fixation. Optimizing the model parameters for the valid preview condition only, we obtained span parameters with remarkably realistic estimates conforming to the empirical findings on the size of the perceptual span. More importantly, the SWIFT model generated parafoveal processing up to word n + 2 without fitting the model to such preview effects. Our results suggest that asymmetry and dynamic modulation are plausible properties of the perceptual span in a parallel word-processing model such as SWIFT. Moreover, they seem to guide the flexible distribution of processing resources during reading between foveal and parafoveal words.},
  language  = {en}
}
@article{KrampeEngbertKliegl2001,
  author    = {Krampe, Ralf-Thomas and Engbert, Ralf and Kliegl, Reinhold},
  title     = {Age-specific problems in rhythmic timing},
  year      = {2001},
  language  = {en}
}
@article{EngbertMergenthalerSinnetal.2011,
  author    = {Engbert, Ralf and Mergenthaler, Konstantin and Sinn, Petra and Pikovskij, Arkadij},
  title     = {An integrated model of fixational eye movements and microsaccades},
  series = {Proceedings of the National Academy of Sciences of the United States of America},
  volume    = {108},
  journal   = {Proceedings of the National Academy of Sciences of the United States of America},
  number    = {39},
  publisher = {National Acad. of Sciences},
  address   = {Washington},
  issn      = {0027-8424},
  doi       = {10.1073/pnas.1102730108},
  pages     = {E765 -- E770},
  year      = {2011},
  abstract  = {When we fixate a stationary target, our eyes generate miniature (or fixational) eye movements involuntarily. These fixational eye movements are classified as slow components (physiological drift, tremor) and microsaccades, which represent rapid, small-amplitude movements. Here we propose an integrated mathematical model for the generation of slow fixational eye movements and microsaccades. The model is based on the concept of self-avoiding random walks in a potential, a process driven by a self-generated activation field. The self-avoiding walk generates persistent movements on a short timescale, whereas, on a longer timescale, the potential produces antipersistent motions that keep the eye close to an intended fixation position. We introduce microsaccades as fast movements triggered by critical activation values. As a consequence, both slow movements and microsaccades follow the same law of motion; i.e., movements are driven by the self-generated activation field. Thus, the model contributes a unified explanation of why it has been a long-standing problem to separate slow movements and microsaccades with respect to their motion-generating principles. We conclude that the concept of a self-avoiding random walk captures fundamental properties of fixational eye movements and provides a coherent theoretical framework for two physiologically distinct movement types.},
  language  = {en}
}