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Dynamical models of cognition play an increasingly important role in driving theoretical and experimental research in psychology. Therefore, parameter estimation, model analysis and comparison of dynamical models are of essential importance. In this article, we propose a maximum likelihood approach for model analysis in a fully dynamical framework that includes time-ordered experimental data. Our methods can be applied to dynamical models for the prediction of discrete behavior (e.g., movement onsets); in particular, we use a dynamical model of saccade generation in scene viewing as a case study for our approach. For this model, the likelihood function can be computed directly by numerical simulation, which enables more efficient parameter estimation including Bayesian inference to obtain reliable estimates and corresponding credible intervals. Using hierarchical models inference is even possible for individual observers. Furthermore, our likelihood approach can be used to compare different models. In our example, the dynamical framework is shown to outperform nondynamical statistical models. Additionally, the likelihood based evaluation differentiates model variants, which produced indistinguishable predictions on hitherto used statistics. Our results indicate that the likelihood approach is a promising framework for dynamical cognitive models.
Bottom-up and top-down as well as low-level and high-level factors influence where we fixate when viewing natural scenes. However, the importance of each of these factors and how they interact remains a matter of debate. Here, we disentangle these factors by analyzing their influence over time. For this purpose, we develop a saliency model that is based on the internal representation of a recent early spatial vision model to measure the low-level, bottom-up factor. To measure the influence of high-level, bottom-up features, we use a recent deep neural network-based saliency model. To account for top-down influences, we evaluate the models on two large data sets with different tasks: first, a memorization task and, second, a search task. Our results lend support to a separation of visual scene exploration into three phases: the first saccade, an initial guided exploration characterized by a gradual broadening of the fixation density, and a steady state that is reached after roughly 10 fixations. Saccade-target selection during the initial exploration and in the steady state is related to similar areas of interest, which are better predicted when including high-level features. In the search data set, fixation locations are determined predominantly by top-down processes. In contrast, the first fixation follows a different fixation density and contains a strong central fixation bias. Nonetheless, first fixations are guided strongly by image properties, and as early as 200 ms after image onset, fixations are better predicted by high-level information. We conclude that any low-level, bottom-up factors are mainly limited to the generation of the first saccade. All saccades are better explained when high-level features are considered, and later, this high-level, bottom-up control can be overruled by top-down influences.