TY - JOUR A1 - Herrmann, Carl J. J. A1 - Metzler, Ralf A1 - Engbert, Ralf T1 - A self-avoiding walk with neural delays as a model of fixational eye movements JF - Scientific reports N2 - 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. Y1 - 2017 U6 - https://doi.org/10.1038/s41598-017-13489-8 SN - 2045-2322 VL - 7 PB - Nature Publ. Group CY - London ER - TY - GEN A1 - Laubrock, Jochen A1 - Engbert, Ralf A1 - Cajar, Anke T1 - Gaze-contingent manipulation of the FVF demonstrates the importance of fixation duration for explaining search behavior T2 - Behavioral and brain sciences : an international journal of current research and theory with open peer commentary N2 - Hulleman & Olivers' (H&O's) model introduces variation of the functional visual field (FVF) for explaining visual search behavior. Our research shows how the FVF can be studied using gaze-contingent displays and how FVF variation can be implemented in models of gaze control. Contrary to H&O, we believe that fixation duration is an important factor when modeling visual search behavior. Y1 - 2017 U6 - https://doi.org/10.1017/S0140525X16000145 SN - 0140-525X SN - 1469-1825 VL - 40 SP - 31 EP - 32 PB - Cambridge Univ. Press CY - New York ER - TY - JOUR A1 - Meyberg, Susann A1 - Sinn, Petra A1 - Engbert, Ralf A1 - Sommer, Werner T1 - Revising the link between microsaccades and the spatial cueing of voluntary attention JF - Vision research : an international journal for functional aspects of vision. N2 - Microsaccades - i.e., small fixational saccades generated in the superior colliculus (SC) - have been linked to spatial attention. While maintaining fixation, voluntary shifts of covert attention toward peripheral targets result in a sequence of attention-aligned and attention-opposing microsaccades. In most previous studies the direction of the voluntary shift is signaled by a spatial cue (e.g., a leftwards pointing arrow) that presents the most informative part of the cue (e.g., the arrowhead) in the to-be attended visual field. Here we directly investigated the influence of cue position and tested the hypothesis that microsaccades align with cue position rather than with the attention shift. In a spatial cueing task, we presented the task-relevant part of a symmetric cue either in the to-be attended visual field or in the opposite field. As a result, microsaccades were still weakly related to the covert attention shift; however, they were strongly related to the position of the cue even if that required a movement opposite to the cued attention shift. Moreover, if microsaccades aligned with cue position, we observed stronger cueing effects on manual response times. Our interpretation of the data is supported by numerical simulations of a computational model of microsaccade generation that is based on SC properties, where we explain our findings by separate attentional mechanisms for cue localization and the cued attention shift. We conclude that during cueing of voluntary attention, microsaccades are related to both - the overt attentional selection of the task-relevant part of the cue stimulus and the subsequent covert attention shift.(C) 2017 Elsevier Ltd. All rights reserved. KW - Endogenous attention KW - Visual search KW - Fixational eye movements KW - Posner cueing KW - Superior colliculus KW - Computational modelling Y1 - 2017 U6 - https://doi.org/10.1016/j.visres.2017.01.001 SN - 0042-6989 SN - 1878-5646 VL - 133 SP - 47 EP - 60 PB - Elsevier CY - Oxford ER - TY - JOUR A1 - Rothkegel, Lars Oliver Martin A1 - Trukenbrod, Hans Arne A1 - Schütt, Heiko Herbert A1 - Wichmann, Felix A. A1 - Engbert, Ralf T1 - Temporal evolution of the central fixation bias in scene viewing JF - Journal of vision N2 - When watching the image of a natural scene on a computer screen, observers initially move their eyes toward the center of the image—a reliable experimental finding termed central fixation bias. This systematic tendency in eye guidance likely masks attentional selection driven by image properties and top-down cognitive processes. Here, we show that the central fixation bias can be reduced by delaying the initial saccade relative to image onset. In four scene-viewing experiments we manipulated observers' initial gaze position and delayed their first saccade by a specific time interval relative to the onset of an image. We analyzed the distance to image center over time and show that the central fixation bias of initial fixations was significantly reduced after delayed saccade onsets. We additionally show that selection of the initial saccade target strongly depended on the first saccade latency. A previously published model of saccade generation was extended with a central activation map on the initial fixation whose influence declined with increasing saccade latency. This extension was sufficient to replicate the central fixation bias from our experiments. Our results suggest that the central fixation bias is generated by default activation as a response to the sudden image onset and that this default activation pattern decreases over time. Thus, it may often be preferable to use a modified version of the scene viewing paradigm that decouples image onset from the start signal for scene exploration to explicitly reduce the central fixation bias. KW - eye movements KW - dynamic models KW - visual scanpath KW - visual attention Y1 - 2017 U6 - https://doi.org/10.1167/17.13.3 SN - 1534-7362 VL - 17 SP - 1626 EP - 1638 PB - Association for Research in Vision and Opthalmology CY - Rockville ER - TY - JOUR A1 - Schütt, Heiko Herbert A1 - Rothkegel, Lars Oliver Martin A1 - Trukenbrod, Hans Arne A1 - Reich, Sebastian A1 - Wichmann, Felix A. A1 - Engbert, Ralf T1 - Likelihood-based parameter estimation and comparison of dynamical cognitive models JF - Psychological Review N2 - Dynamical models of cognition play an increasingly important role in driving theoretical and experimental research in psychology. Therefore, parameter estimation, model analysis and comparison of dynamical models are of essential importance. In this article, we propose a maximum likelihood approach for model analysis in a fully dynamical framework that includes time-ordered experimental data. Our methods can be applied to dynamical models for the prediction of discrete behavior (e.g., movement onsets); in particular, we use a dynamical model of saccade generation in scene viewing as a case study for our approach. For this model, the likelihood function can be computed directly by numerical simulation, which enables more efficient parameter estimation including Bayesian inference to obtain reliable estimates and corresponding credible intervals. Using hierarchical models inference is even possible for individual observers. Furthermore, our likelihood approach can be used to compare different models. In our example, the dynamical framework is shown to outperform nondynamical statistical models. Additionally, the likelihood based evaluation differentiates model variants, which produced indistinguishable predictions on hitherto used statistics. Our results indicate that the likelihood approach is a promising framework for dynamical cognitive models. KW - likelihood KW - model fitting KW - dynamical model KW - eye movements KW - model comparison Y1 - 2017 U6 - https://doi.org/10.1037/rev0000068 SN - 0033-295X SN - 1939-1471 VL - 124 IS - 4 SP - 505 EP - 524 PB - American Psychological Association CY - Washington ER -