Not all fixations are created equal: The benefits of using ex-Gaussian modeling of fixation durations

Abstract

Various cognitive and perceptual factors have been shown to modulate the duration of fixations during visual exploration of complex scenes. The majority of these studies have only considered the mean of the distribution of fixation durations. However, this distribution is skewed to the right, so that an increase in the mean may be driven by a lengthening of all fixations (i.e., a right shift of the whole distribution) or only the relatively longer ones (i.e., a longer right tail of the distribution). To determine which factor is at play, the distribution can be modeled with an ex-Gaussian distribution, which is a convolution of a Gaussian and an exponential distribution. Here we demonstrate the usefulness of applying the ex-Gaussian model to empirical distributions of fixation durations and the reliability of its parameters across time. We demonstrate how the ex-Gaussian model had advantages over exclusive consideration of the mean, by showing that an increase in the mean can stem from specific changes in the components of the ex-Gaussian distribution. Specifically, the type of image leads to a change in the Gaussian component alone, indicating a right shift of the main mass of the distribution. By contrast, familiarity with the inspected image modifies the exponential component, and results in a more specific modulation of a subset of relatively long fixations. Hence, estimating the ex-Gaussian parameters may provide novel insights into the underlying processes that determine fixation duration and can contribute to the future development of process-based computational models of gaze behavior.

An updating-based working memory load alters the dynamics of eye movements but not their spatial extent during free viewing of natural scenes

“…However, participants’ individual fixation duration distributions displayed significant rightward skew, such that there was a tail of longer fixation durations in each participant’s distribution. This skewness of fixation distributions is consistently observed in eye-movement research, and one response is to fit ex-Gaussian distributions to individual participants’ fixation duration distributions (Guy et al, 2020 ). An ex-Gaussian distribution is produced by combining a normal and an exponential distribution, such that the normal distribution is given a more heavily weighted rightward tail.…”

Measuring the double-drift illusion and its resets with hand trajectories

“…An alternative to the gamma distribution, the ex-Gaussian (e.g. Matzke & Wagenmakers, 2009 ; Guy, Lancry-Dayan, & Pertzov, 2020 ), could be a more realistic alternative but does not fit the data as well. In any case, the process that actually leads to resets remains to be seen in future work.…”

Measuring the double-drift illusion and its resets with hand trajectories

“…An alternative to the gamma distribution, the ex-Gaussian (e.g. Matzke & Wagenmakers, 2009;Guy et al, 2020), could be a more realistic alternative but does not fit the data as well. In any case, the process that actually leads to resets remains to be seen in future work.…”