@misc{HohensteinMatuschekKliegl2016,
  author    = {Hohenstein, Sven and Matuschek, Hannes and Kliegl, Reinhold},
  title     = {Linked linear mixed models},
  series = {Postprints der Universit{\"a}t Potsdam Humanwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam Humanwissenschaftliche Reihe},
  number    = {552},
  issn      = {1866-8364},
  doi       = {10.25932/publishup-42828},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-428281},
  pages     = {15},
  year      = {2016},
  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{KlieglWeiDambacheretal.2011,
  author    = {Kliegl, Reinhold and Wei, Ping and Dambacher, Michael and Yan, Ming and Zhou, Xiaolin},
  title     = {Experimental effects and individual differences in linear mixed models estimating the relationship between spatial, object, and attraction effects in visual attention},
  series = {Frontiers in psychology},
  volume    = {2},
  journal   = {Frontiers in psychology},
  publisher = {Frontiers Research Foundation},
  address   = {Lausanne},
  issn      = {1664-1078},
  doi       = {10.3389/fpsyg.2010.00238},
  pages     = {12},
  year      = {2011},
  abstract  = {Linear mixed models (LMMs) provide a still underused methodological perspective on combining experimental and individual-differences research. Here we illustrate this approach with two-rectangle cueing in visual attention (Egly et al., 1994). We replicated previous experimental cue-validity effects relating to a spatial shift of attention within an object (spatial effect), to attention switch between objects (object effect), and to the attraction of attention toward the display centroid (attraction effect), also taking into account the design-inherent imbalance of valid and other trials. We simultaneously estimated variance/covariance components of subject-related random effects for these spatial, object, and attraction effects in addition to their mean reaction times (RTs). The spatial effect showed a strong positive correlation with mean RT and a strong negative correlation with the attraction effect. The analysis of individual differences suggests that slow subjects engage attention more strongly at the cued location than fast subjects. We compare this joint LMM analysis of experimental effects and associated subject-related variances and correlations with two frequently used alternative statistical procedures.},
  language  = {en}
}
@misc{KlieglWeiDambacheretal.2011,
  author    = {Kliegl, Reinhold and Wei, Ping and Dambacher, Michael and Yan, Ming and Zhou, Xiaolin},
  title     = {Experimental effects and individual differences in linear mixed models: Estimating the relationship between spatial, object, and attraction effects in visual attention},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-56859},
  year      = {2011},
  abstract  = {Linear mixed models (LMMs) provide a still underused methodological perspective on combining experimental and individual-differences research. Here we illustrate this approach with two-rectangle cueing in visual attention (Egly et al., 1994). We replicated previous experimental cue-validity effects relating to a spatial shift of attention within an object (spatial effect), to attention switch between objects (object effect), and to the attraction of attention toward the display centroid (attraction effect), also taking into account the design-inherent imbalance of valid and other trials. We simultaneously estimated variance/covariance components of subject-related random effects for these spatial, object, and attraction effects in addition to their mean reaction times (RTs). The spatial effect showed a strong positive correlation with mean RT and a strong negative correlation with the attraction effect. The analysis of individual differences suggests that slow subjects engage attention more strongly at the cued location than fast subjects. We compare this joint LMM analysis of experimental effects and associated subject-related variances and correlations with two frequently used alternative statistical procedures},
  language  = {en}
}