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WALD-EM: Wald Accumulation for Locations and Durations of Eye Movements

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.