I'm not sure that curve means what you think it means: Toward a [more] realistic understanding of the role of eye-movement generation in the Visual World Paradigm.

The Visual World Paradigm (VWP) is a powerful experimental paradigm for language research. Listeners respond to speech in a "visual world" containing potential referents of the speech. Fixations to these referents provides insight into the preliminary states of language processing as decisions unfold. The VWP has become the dominant paradigm in psycholinguistics and extended to every level of language, development, and disorders. Part of its impact is the impressive data visualizations which reveal the millisecond-by-millisecond time course of processing, and advances have been made in developing new analyses that precisely characterize this time course. All theoretical and statistical approaches make the tacit assumption that the time course of fixations is closely related to the underlying activation in the system. However, given the serial nature of fixations and their long refractory period, it is unclear how closely the observed dynamics of the fixation curves are actually coupled to the underlying dynamics of activation. I investigated this assumption with a series of simulations. Each simulation starts with a set of true underlying activation functions and generates simulated fixations using a simple stochastic sampling procedure that respects the sequential nature of fixations. I then analyzed the results to determine the conditions under which the observed fixations curves match the underlying functions, the reliability of the observed data, and the implications for Type I error and power. These simulations demonstrate that even under the simplest fixation-based models, observed fixation curves are systematically biased relative to the underlying activation functions, and they are substantially noisier, with important implications for reliability and power. I then present a potential generative model that may ultimately overcome many of these issues.