Fig. 2: Influence of model variables for estimating behavioral model.

a Block diagram of our dynamical model—representing the brain—that models behavior to capture movement variability. Internal states are outlined by the dotted line to highlight its latent feedback structure in the model. b–d Examination of model variables for subject 6 reveals underlying dynamics from the internal states that lead to the improvement of estimated behavior from the model observed across all subjects. The black triangle marks trial 109. b Time-series of the observed (gray solid line) and estimated (black solid line) reaction time (RT) ± the 95% confidence interval (gray shaded area) over all trials for subject 6. The gray dotted line markers their average RT (1.07 s). c Time-series of the conditions (orange solid line) and states (purple solid line) over all trials for subject 6. The gray dotted line markers their average RT. Adding the conditions and states together yields the estimated RT in (b). d Time-series of the error state (blue solid line) and perturbed state (pink solid line) over all trials for subject 6. For demonstrative purposes, the states are not weighted but are scaled by their standard deviation. The gray dotted line marks 0. Adding the weighted combination of error and perturbed states together yields the states in (c). Goodness-of-fit for the (e) RT and (f) speed error (SE) models across all subjects measured using the coefficient of determination between the observed and estimated behavior, which ranges between 0% (worst) and 100% (best). We compared the behavioral models with internal states (With states) to a model with the same trial conditions but without internal states (Without states). Each marker is labeled by the subject it represents. Subject 6 is outlined in black. Adding internal states significantly improved the goodness-of-fit of the RT (two-tailed paired-sample t-test: t(9) = − 3.71, p = 0.0048) and SE (two-tailed paired-sample t-test: t(9) = − 5.62, p = 0.00032) model for all subjects, as larger values are better. Source data are provided as a Source Data file.