  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. Here 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 non-dynamical 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.
