WALD-EM: Wald accumulation for locations and durations of eye movements.

Abstract

Describing, analyzing and explaining patterns in eye movement behavior is crucial for understanding visual perception. Further, eye movements are increasingly used in informing cognitive process models. In this article, we start by reviewing basic characteristics and desiderata for models of eye movements. Specifically, we argue that there is a need for models combining spatial and temporal aspects of eye-tracking data (i.e., fixation durations and fixation locations), that formal models derived from concrete theoretical assumptions are needed to inform our empirical research, and custom statistical models are useful for detecting specific empirical phenomena that are to be explained by said theory.In this article, we develop a conceptual model of eye movements, or specifically, fixation durations and fixation locations, and from it derive a formal statistical model -meeting our goal of crafting a model useful in both the theoretical and empirical research cycle. We demonstrate the use of the model on an example of infant natural scene viewing, to show that the model is able to explain different features of the eye movement data, and to showcase how to identify that the model needs to be adapted if it does not agree with the data. We conclude with discussion of potential future avenues for formal eye movement models.

A dynamical scan-path model for task-dependence during scene viewing.

“…The likelihood function plays an important role for combined modeling of fixation durations and fixation locations (e.g., Engbert et al, 2022; Schütt et al, 2017). To our knowledge, the first study using spatiotemporal likelihood inference in scene viewing was published by Kucharsky et al (2021), in line with conceptual work for eye movements in reading by Seelig et al (2020). Kucharsky et al’s (2021) WALD-EM model combines a standard information accumulation process for saccade timing with a spatial component.…”

“…To our knowledge, the first study using spatiotemporal likelihood inference in scene viewing was published by Kucharsky et al (2021), in line with conceptual work for eye movements in reading by Seelig et al (2020). Kucharsky et al’s (2021) WALD-EM model combines a standard information accumulation process for saccade timing with a spatial component. Similar to our results, WALD-EM was demonstrated to successfully reproduce several key aspects of eye-movements statistics including interindividual differences.…”

“…L. Smith & Ratcliff, 2004) generates qualitatively very similar distributions. The WALD-EM model by Kucharsky et al (2021) assumes a WALD (inverse Gaussian) distribution, which gives a comparable goodness of fit to the experimental data. Thus, the total duration of each fixation is generated by sampling from the γ distribution.…”

“…This is particularly desirable in models with a complex likelihood structure, where posteriors may be multimodal or when we are interested in how much the data constrain the parameters (Gelman et al, 2013; Schad et al, 2021). Past studies have yielded promising results when applying Bayesian methods to dynamical cognitive models (e.g., Kucharsky et al, 2021; Rabe et al, 2021; Schütt et al, 2017; Seelig et al, 2020). For example, model parameters could be estimated for single participants, which was impossible before.…”

Objects guide human gaze behavior in dynamic real-world scenes

“…A few models exist that simultaneously account for when and where the eyes move when exploring static scenes. Kucharsky et al (2021) argue for the need for models that combine the spatial and temporal aspects of gaze behavior and present the WALD-EM model. They introduced a spatiotemporal likelihood function to statistically model fixation positions and fixation durations, which are assumed to follow a WALD (inverse Gaussian) distribution, simultaneously and were successful in 2/29 reproducing many aspects of scanpath statistics.…”