An illustration of the effect of non-decision time on the threshold value on the final stopping point.

The illustration of the evidence accumulation process in the fixed threshold diffusion model (left panel; bu(t) = −bl(t) = θ) and hyperbolic collapsing threshold diffusion model (right panel; ).

Illustration of the non-decision time-informed diffusion model.

The HMP analysis method extracts the timing of cognitive states in each trial from EEG signals. Then, the decision time is considered the duration between the cognitive states that determines the decision process, such as the N200 latency, which marks the end of perceptual encoding (Nunez et al., 2019), and the peak of central parietal positivity, which indicates the end of the decision process (O’Connell et al., 2012) — see also Weindel et al. (2025) for a detailed discussion. Subtracting the decision time from the response time gives an approximation of non-decision time in each trial. The extracted non-decision time measurements are employed to constrain the non-decision time parameter in the CT-DDM.

R2 values measuring the agreement between estimated and ground truth threshold parameters in exponential (left) and hyperbolic (right) collapsing threshold models.

Estimated versus ground truth parameter values for two modeling approaches.

The top two rows show parameter recovery for models estimated without additional constraints (“Uninformed”), while the bottom two rows show recovery for joint models that incorporate additional non-decision time observations (“NDT-informed”). Each point represents a recovered parameter estimate plotted against its corresponding true data-generating value. Rows correspond to different functional forms of threshold (i.e., Exponential and Hyperbolic). Dashed diagonal lines indicate perfect recovery.

Illustration of the sensitivity of parameter estimation to the number of trials in the NDT-informed models.

R2 values measure the agreement between estimated and ground truth parameters of the exponential (left) and hyperbolic (right) collapsing threshold models.

Illustration of sensitivity of parameter estimation to the noise level in the non-decision time observations.

R2 values measuring the agreement between estimated and ground truth parameters of the exponential (left) and hyperbolic (right) collapsing threshold models.

Estimated versus true parameter values for cross-fitting of CT-DDM on FT-DDM with across-trial variability in drift rate.

In each panel except the rightmost one, each point represents a recovered parameter estimate plotted against its corresponding true data-generating value, and the dashed diagonal line indicates perfect recovery. The right column illustrates the density of the estimated decay rate parameter (λ). Rows correspond to different functional forms of threshold (i.e., Exponential and Hyperbolic).

The event sequence and timing of each event estimated by the HMP method averaged over all participants (Weindel et al., 2025).

The mean estimated parameters and goodness of fit results for Study 1.

The estimated threshold dynamics from NDT-informed CT-DDMs for individuals in Study 1.

The first row illustrates the estimated hyperbolic threshold dynamics, and the second row illustrates the estimated exponential threshold dynamics. The left column shows the threshold dynamics in the speed condition, and the right column shows the accuracy condition. Each gray line corresponds to a subject. The blue line corresponds to the average group level.

Prediction of best-fitting models against empirical data for speed (top row) and accuracy (bottom row) conditions in Study 1.

In each panel, the x-axis represents the response time quantiles in seconds, and the y-axis represents the cumulative choice proportion.

The event sequence and timing of each event estimated by the HMP method for Accuracy (top) and Speed (bottom) conditions averaged over all participants (Weindel et al., 2024).

The mean estimated parameters and goodness of fit results for Study 2.

The estimated threshold dynamics from NDT-informed CT-DDMs for individuals in Study 2.

The first row illustrates the estimated hyperbolic threshold dynamics, and the second row illustrates the estimated exponential threshold dynamics. The left column shows the threshold dynamics in the speed condition, and the right column shows the accuracy condition. Each gray line corresponds to a subject. The blue line corresponds to the average group level.

Prediction of best-fitting models against empirical data for speed (top row) and accuracy (bottom row) conditions in Study 2.

In each panel, the x-axis represents the response time quantiles in seconds, and the y-axis represents the cumulative choice proportion.

R2 values measuring the agreement between estimated and ground truth threshold parameters in exponential (left) and hyperbolic (right) collapsing boundary models.

Estimated vs. true parameter values for two modeling approaches.

The top two rows show parameter recovery for models estimated without additional constraints (“Uninformed”), while the bottom two rows show recovery for joint models that incorporate additional non-decision time observations (“NDT informed”). Each point represents a recovered parameter estimate plotted against its corresponding true data-generating value. Rows correspond to different functional forms (Exponential and Hyperbolic). Dashed diagonal lines indicate perfect recovery.

R2 values measuring the agreement between estimated and ground truth parameters in exponential (left) and hyperbolic (right) collapsing threshold diffusion models as a function of bias in non-decision time measurements.

The correlation values measuring the agreement between estimated and ground truth parameters in exponential (left) and hyperbolic (right) collapsing threshold diffusion models as a function of bias in non-decision time measurements.

The effect of bias in non-decision time measurements on starting threshold (upper panels) and decay rate (lower panels) parameters for exponential (left panels) and hyperbolic (right panels) collapsing threshold diffusion models.

The estimated threshold dynamics from uninformed CT-DDMs for individuals in Study 1.

The first row illustrates the estimated hyperbolic threshold dynamics, and the second row illustrates the estimated exponential threshold dynamics. The left column shows the threshold dynamics in the speed condition, and the right column shows the accuracy condition. Each gray line corresponds to a subject. The blue line corresponds to the average group level.

The estimated threshold dynamics from uninformed CT-DDMs for individuals in Study 2.

The first row illustrates the estimated hyperbolic threshold dynamics, and the second row illustrates the estimated exponential threshold dynamics. The left column shows the threshold dynamics in the speed condition, and the right column shows the accuracy condition. Each gray line corresponds to a subject. The blue line corresponds to the average group level.

Posterior prediction of uninformed FT-DDM against empirical data for speed (left panel) and accuracy (right row) conditions in Study 1.

In each panel, the x-axis represents the response time quantiles in seconds, and the y-axis represents the cumulative choice proportion.

Posterior prediction of uninformed FT-DDM against empirical data for speed (left panel) and accuracy (right row) conditions in Study 2.

In each panel, the x-axis represents the response time quantiles in seconds, and the y-axis represents the cumulative choice proportion.

R2 values measuring the agreement between estimated and ground truth threshold parameters in exponential (left) and hyperbolic (right) collapsing boundary circular diffusion models.

Estimated vs. true parameter values for two modeling approaches based on the CT-CDM.

The top two rows show parameter recovery for models estimated without additional constraints (“Uninformed”), while the bottom two rows show recovery for joint models that incorporate additional non-decision time observations (“NDT-informed”). Each point represents a recovered parameter estimate plotted against its corresponding true data-generating value. Rows correspond to different functional forms (Exponential and Hyperbolic). Dashed diagonal lines indicate perfect recovery.