Multi-Level Dynamical Parameter Estimation: Hypothesis Testing with Dynamical Systems

The practice of dynamical modeling of perception-action behavior has lagged behind the proliferation of the dynamical perspective. Two methodological roadblocks to dynamical modeling are discussed. First, parameter selection is difficult with current tools. Second, it is unclear what role models have in the larger scientific project beyond their use as descriptions or proofs of concept. In this dissertation, a new parameter selection method is developed to address these issues, Multi-Level Dynamical Parameter Estimation (MLDPE). Like its precursor DPE, MLDPE uses an extended Luenberger observer to stabilize the synchronization manifold in combined model-data space. MLDPE also embeds a regression model into the parameter-selection process, allowing for parameter values to vary systematically as a function of both fixed and random effects. In this way, it allows for parameter dynamics to be used as dependent variables in experimental research. The method is tested with three experiments. In Experiment 1, a model of steering dynamics was fit to data while allowing preferred walking speed to vary by participant. In this case, the limitations of local search were encountered due to non-smooth functions in the model equations. Experiments 2 and 3 demonstrated the use of fixed effects in MLDPE, using data collected in a driving simulator with a braking task. Experiment 2 showed that changing the context of the task Henry S. Harrison — University of Connecticut, 2017 from a race to a safety test produced predictable changes in parameter values. Experiment 3 tested the effects of distraction on braking, replicating previous results and describing them in terms of parameter dynamics. Thus, MLDPE is able to select parameters using multiple observations of a system, unlike previous methods. Additionally, it is able to detect changes in dynamics across these observations. This method allows dynamical models to be used in a traditional experimental research program. Possible applications and limitations of the method are discussed. Multi-level Dynamical Parameter Estimation: Hypothesis Testing with Dynamical Systems