@misc{HohensteinMatuschekKliegl2017,
  author    = {Hohenstein, Sven and Matuschek, Hannes and Kliegl, Reinhold},
  title     = {Linked linear mixed models: A joint analysis of fixation locations and fixation durations in natural reading},
  series = {Psychonomic bulletin \& review : a journal of the Psychonomic Society},
  volume    = {24},
  journal   = {Psychonomic bulletin \& review : a journal of the Psychonomic Society},
  publisher = {Springer},
  address   = {New York},
  issn      = {1069-9384},
  doi       = {10.3758/s13423-016-1138-y},
  pages     = {637 -- 651},
  year      = {2017},
  abstract  = {The complexity of eye-movement control during reading allows measurement of many dependent variables, the most prominent ones being fixation durations and their locations in words. In current practice, either variable may serve as dependent variable or covariate for the other in linear mixed models (LMMs) featuring also psycholinguistic covariates of word recognition and sentence comprehension. Rather than analyzing fixation location and duration with separate LMMs, we propose linking the two according to their sequential dependency. Specifically, we include predicted fixation location (estimated in the first LMM from psycholinguistic covariates) and its associated residual fixation location as covariates in the second, fixation-duration LMM. This linked LMM affords a distinction between direct and indirect effects (mediated through fixation location) of psycholinguistic covariates on fixation durations. Results confirm the robustness of distributed processing in the perceptual span. They also offer a resolution of the paradox of the inverted optimal viewing position (IOVP) effect (i.e., longer fixation durations in the center than at the beginning and end of words) although the opposite (i.e., an OVP effect) is predicted from default assumptions of psycholinguistic processing efficiency: The IOVP effect in fixation durations is due to the residual fixation-location covariate, presumably driven primarily by saccadic error, and the OVP effect (at least the left part of it) is uncovered with the predicted fixation-location covariate, capturing the indirect effects of psycholinguistic covariates. We expect that linked LMMs will be useful for the analysis of other dynamically related multiple outcomes, a conundrum of most psychonomic research.},
  language  = {en}
}
@article{KlieglHohensteinYanetal.2013,
  author    = {Kliegl, Reinhold and Hohenstein, Sven and Yan, Ming and McDonald, Scott A.},
  title     = {How preview space/time translates into preview cost/benefit for fixation durations during reading},
  series = {The quarterly journal of experimental psychology},
  volume    = {66},
  journal   = {The quarterly journal of experimental psychology},
  number    = {3},
  publisher = {Wiley},
  address   = {Hove},
  issn      = {1747-0218},
  doi       = {10.1080/17470218.2012.658073},
  pages     = {581 -- 600},
  year      = {2013},
  abstract  = {Eye-movement control during reading depends on foveal and parafoveal information. If the parafoveal preview of the next word is suppressed, reading is less efficient. A linear mixed model (LMM) reanalysis of McDonald (2006) confirmed his observation that preview benefit may be limited to parafoveal words that have been selected as the saccade target. Going beyond the original analyses, in the same LMM, we examined how the preview effect (i.e., the difference in single-fixation duration, SFD, between random-letter and identical preview) depends on the gaze duration on the pretarget word and on the amplitude of the saccade moving the eye onto the target word. There were two key results: (a) The shorter the saccade amplitude (i.e., the larger preview space), the shorter a subsequent SFD with an identical preview; this association was not observed with a random-letter preview. (b) However, the longer the gaze duration on the pretarget word, the longer the subsequent SFD on the target, with the difference between random-letter string and identical previews increasing with preview time. A third patternincreasing cost of a random-letter string in the parafovea associated with shorter saccade amplitudeswas observed for target gaze durations. Thus, LMMs revealed that preview effects, which are typically summarized under preview benefit, are a complex mixture of preview cost and preview benefit and vary with preview space and preview time. The consequence for reading is that parafoveal preview may not only facilitate, but also interfere with lexical access.},
  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}
}