(Kelly et al., 2021; Steinemann et al., 2018), further emphasizing the functional dissociation between decision making and motor preparation. Fitting GCDF variants that incorporate urgency mechanisms is beyond the scope of the present work and should be conducted in tandem with an electrophysiological investigation of motor preparation.

Although GCDF showed a good fit to data used to constrain parameter estimation, it provided a mixed predictive account of the remaining data. The model captured the mean latency of the first partial EMG burst in Experiments 1 and 2 but systematically overestimated this latency by about 100 ms in Experiments 3 and 4. We cannot exclude the possibility that a set of parameters could have better captured the partial burst latency data had we considered these data in parameter estimation. Alternatively, variations in EMG signal quality across experiments may have contributed to this pattern of results, as the percentage of rejected trials was larger on average in Experiments 3 (12.41%) and 4 (10.4%) compared to Experiments 1 (7.5%) and 2 (2.7%). Therefore, the data from Experiments 3 and 4 might incorporate a larger amount of artifactual partial EMG bursts.

Besides the mean latency of partial EMG bursts, GCDF provided a mixed pre-
dictive account of the between-trial correlation between PMT and MT. In general, model
predictions showed more dispersion compared to observed data at the individual level, but
this phenomenon is likely explained by noise in EMG onset detection. However, the model
systematically overestimated the correlation averaged across subjects in Experiments 3 and
4, and the easiest condition of Experiment 1. One may argue that this discrepancy be-
tween data and model predictions speaks against the model architecture, as the filtering
mechanism at the motor preparation level flattens out random fluctuations of the evidence
accumulation signal and increases the predicted correlation between PMT and MT at the
single-trial level. Once again, we cannot exclude the possibility that a set of parameters
could have better captured the between-trial correlation between PMT and MT had we
considered these data in parameter estimation. Alternatively, it is important to remember
that the filtering mechanism (regulated by the leak parameter) interacts in complex ways
with drift rate and between-trial variability in drift rate (see Appendix D). This interaction
is problematic because GCDF variants used in Experiments 3 and 4 do not incorporate rep-
resentational assumptions that specify how drift rate distributions arise from the stimuli. In
addition, although the linear relationship between motion coherence and drift rate provided
a good fit to data from Experiment 1 (see also Palmer et al., 2005; Ratcliff and McKoon,
2008), a more complex representational assumption has recently been proposed for the ran-
dom dot motion task (Smith and Lilburn, 2020). Consequently, discrepancies between data
and model predictions may stem from a misspecification of drift rate distributions.

More generally, these findings highlight the need of considering predecisional pro-
cessing stages when modeling motor phenomena. This need is further highlighted by the
lexical decision data from Experiment 4. The word frequency effect has been successfully
modeled by assuming that word frequency modulates drift rate (Ratcliff et al., 2004), mean
nondecision time (Donkin et al., 2009; Gomez and Perea, 2014), and between-trial vari-
ability in drift rate (Tillman et al., 2017). Within the framework of GCDF, the decrease
of drift rate as word frequency decreases should increase the predicted mean MT. Con-
trary to this prediction, we found an inverted U-shape relationship between mean MT and
word frequency. Specifically, mean MT showed an initial increase from high frequency to
medium frequency words, followed by a decrease for low and very-low frequency words. At
(Kelly et al., 2021; Steinemann et al., 2018), further emphasizing the functional dissociation between decision making and motor preparation. Fitting GCDF variants that incorporate urgency mechanisms is beyond the scope of the present work and should be conducted in tandem with an electrophysiological investigation of motor preparation.

Although GCDF showed a good fit to data used to constrain parameter estimation, it provided a mixed predictive account of the remaining data. The model captured the mean latency of the first partial EMG burst in Experiments 1 and 2 but systematically overestimated this latency by about 100 ms in Experiments 3 and 4. We cannot exclude the possibility that a set of parameters could have better captured the partial burst latency data had we considered these data in parameter estimation. Alternatively, variations in EMG signal quality across experiments may have contributed to this pattern of results, as the percentage of rejected trials was larger on average in Experiments 3 (12.41%) and 4 (10.4%) compared to Experiments 1 (7.5%) and 2 (2.7%). Therefore, the data from Experiments 3 and 4 might incorporate a larger amount of artifactual partial EMG bursts.

Besides the mean latency of partial EMG bursts, GCDF provided a mixed pre-
dictive account of the between-trial correlation between PMT and MT. In general, model
predictions showed more dispersion compared to observed data at the individual level, but
this phenomenon is likely explained by noise in EMG onset detection. However, the model
systematically overestimated the correlation averaged across subjects in Experiments 3 and
4, and the easiest condition of Experiment 1. One may argue that this discrepancy be-
tween data and model predictions speaks against the model architecture, as the filtering
mechanism at the motor preparation level flattens out random fluctuations of the evidence
accumulation signal and increases the predicted correlation between PMT and MT at the
single-trial level. Once again, we cannot exclude the possibility that a set of parameters
could have better captured the between-trial correlation between PMT and MT had we
considered these data in parameter estimation. Alternatively, it is important to remember
that the filtering mechanism (regulated by the leak parameter) interacts in complex ways
with drift rate and between-trial variability in drift rate (see Appendix D). This interaction
is problematic because GCDF variants used in Experiments 3 and 4 do not incorporate rep-
resentational assumptions that specify how drift rate distributions arise from the stimuli. In
addition, although the linear relationship between motion coherence and drift rate provided
a good fit to data from Experiment 1 (see also Palmer et al., 2005; Ratcliff and McKoon,
2008), a more complex representational assumption has recently been proposed for the ran-
dom dot motion task (Smith and Lilburn, 2020). Consequently, discrepancies between data
and model predictions may stem from a misspecification of drift rate distributions.

More generally, these findings highlight the need of considering predecisional pro-
cessing stages when modeling motor phenomena. This need is further highlighted by the
lexical decision data from Experiment 4. The word frequency effect has been successfully
modeled by assuming that word frequency modulates drift rate (Ratcliff et al., 2004), mean
nondecision time (Donkin et al., 2009; Gomez and Perea, 2014), and between-trial vari-
ability in drift rate (Tillman et al., 2017). Within the framework of GCDF, the decrease
of drift rate as word frequency decreases should increase the predicted mean MT. Con-
trary to this prediction, we found an inverted U-shape relationship between mean MT and
word frequency. Specifically, mean MT showed an initial increase from high frequency to
medium frequency words, followed by a decrease for low and very-low frequency words. At
first glance, this result speaks against the architecture of GCDF. However, the model does not incorporate assumptions regarding how the drift rate is computed in this task, so the origin of the problem is unclear. It would be useful to connect models of lexical access (e.g., Grainger, 2018; Houghton, 2018; McClelland and Rumelhart, 1981) to GCDF to shed light on this issue.

Apart from the unexpected word frequency effect on mean MT, EMG findings were remarkably consistent across experiments, suggesting that GCDF generalizes across cognitive domains. Both mean PMT and mean MT increased as choice difficulty increased. The increase of mean MT as choice difficulty increased was caused by a decrease in the rising slope of the neural drive, as suggested by our analysis of full-wave rectified EMG signals. This important aspect of the data was nicely captured by GCDF because the neural drive predicted by the model reflects evidence-dependent dynamics of the underlying motor preparation signal. Partial bursts were also observed in the EMG data of each subject of each experiment. The proportion of correct trials containing at least one partial EMG burst during PMT and the mean latency of the first partial burst increased as choice difficulty increased. Interestingly, the proportion of correct trials in which the first partial burst was located in the same EMG channel as the response was systematically larger than the proportion of correct trials in which the first partial burst was located in the opposite EMG channel. Within the framework of GCDF, this finding is explained by the same mechanism that captures the relative proportion of correct and incorrect responses. Putting aside between-trial variability in model components, errors are produced by noise in the evidence accumulated at each time step. Although part of this noise is flattened out during motor preparation, the predicted proportion of errors is smaller than the proportion of correct responses, so long as the drift rate is not null.

## Comparisons With GCD

As predicted, GCDF captured the data with a relatively low level of leakage, indicating that the evidence accumulation variable is smoothed at the motor preparation level. This finding suggests that the smoothing mechanism adds to a GCD description of the data. Model selection statistics (AIC and BIC) further showed that the additional complexity of GCDF was justified in light of the (large) improvement in fit quality. Both AIC and BIC statistics favored GCDF over GCD for 90/90 participants (raw models) and 89/90 (full models). These findings provide decisive evidence for GCDF. Interestingly, the difference in model selection statistics between raw and full models was much larger for GCD than for GCDF, suggesting that between-trial variability in GCD components has a major impact on the fit quality of the model, contrary to GCDF. Still, the AIC (BIC) statistic favored the raw GCDF over the full GCD for 67(70)/90 subjects. Although between-trial variability in processing components is plausible, we believe that a large contribution of between-trial variability to the fit quality of a model is problematic, as there is generally no explanation of why this variability occurs or why it has the parametric form researchers assume to represent it. In this view, between-trial variability essentially corresponds to adding a random component to the model without any strong theoretical motivation for it rather than to improve the fit quality (Evans, Tillman, and Wagenmakers, 2020). Consequently, we consider our findings regarding between-trial variability as additional evidence for GCDF.

In its raw form, GCD grossly overestimated the proportion of trials containing at
first glance, this result speaks against the architecture of GCDF. However, the model does
not incorporate assumptions regarding how the drift rate is computed in this task, so the
origin of the problem is unclear. It would be useful to connect models of lexical access (e.g.,
Grainger, 2018; Houghton, 2018; McClelland and Rumelhart, 1981) to GCDF to shed light
on this issue.

Apart from the unexpected word frequency effect on mean MT, EMG findings
were remarkably consistent across experiments, suggesting that GCDF generalizes across
cognitive domains. Both mean PMT and mean MT increased as choice difficulty increased.
The increase of mean MT as choice difficulty increased was caused by a decrease in the
rising slope of the neural drive, as suggested by our analysis of full-wave rectified EMG
signals. This important aspect of the data was nicely captured by GCDF because the neural
drive predicted by the model reflects evidence-dependent dynamics of the underlying motor
preparation signal. Partial bursts were also observed in the EMG data of each subject of
each experiment. The proportion of correct trials containing at least one partial EMG burst
during PMT and the mean latency of the first partial burst increased as choice difficulty
increased. Interestingly, the proportion of correct trials in which the first partial burst
was located in the same EMG channel as the response was systematically larger than the
proportion of correct trials in which the first partial burst was located in the opposite EMG
channel. Within the framework of GCDF, this finding is explained by the same mechanism
that captures the relative proportion of correct and incorrect responses. Putting aside
between-trial variability in model components, errors are produced by noise in the evidence
accumulated at each time step. Although part of this noise is flattened out during motor
preparation, the predicted proportion of errors is smaller than the proportion of correct
responses, so long as the drift rate is not null.

Comparisons With GCD

As predicted, GCDF captured the data with a relatively low level of leakage, indi-
cating that the evidence accumulation variable is smoothed at the motor preparation level.
This finding suggests that the smoothing mechanism adds to a GCD description of the data.
Model selection statistics (AIC and BIC) further showed that the additional complexity of
GCDF was justified in light of the (large) improvement in fit quality. Both AIC and BIC
statistics favored GCDF over GCD for 90/90 participants (raw models) and 89/90 (full
models). These findings provide decisive evidence for GCDF. Interestingly, the difference
in model selection statistics between raw and full models was much larger for GCD than for
GCDF, suggesting that between-trial variability in GCD components has a major impact
on the fit quality of the model, contrary to GCDF. Still, the AIC (BIC) statistic favored the
raw GCDF over the full GCD for 67(70)/90 subjects. Although between-trial variability
in processing components is plausible, we believe that a large contribution of between-trial
variability to the fit quality of a model is problematic, as there is generally no explanation
of why this variability occurs or why it has the parametric form researchers assume to rep-
resent it. In this view, between-trial variability essentially corresponds to adding a random
component to the model without any strong theoretical motivation for it rather than to im-
prove the fit quality (Evans, Tillman, and Wagenmakers, 2020). Consequently, we consider
our findings regarding between-trial variability as additional evidence for GCDF.

In its raw form, GCD grossly overestimated the proportion of trials containing at
least one partial EMG burst, especially when the first partial burst was located in the same EMG channel as the response. The full GCD provided a better account of these proportions by using a very small response threshold (Experiment 1) or by combining high drift rates with a high between-trial variability in drift rates (Experiments 2-4; see Tables 1 and 2). However, both processing schemes resulted in predicted MTs that were too fast compared to observed MTs. The model compensated this problem by increasing the contribution of residual motor latencies to predicted MTs (parameters *Tr* and *sTr*), but this compensation had two negative consequences. First, the model was not able to capture large effects of choice difficulty on mean MT, such as those observed in Experiment 1. Second, the model was not able to capture the right-skewed shape of MT distributions because between-trial variability in residual motor latencies added to predicted MTs is uniformly distributed, an (arbitrary) assumption inherited from the diffusion decision model (Ratcliff and Rouder, 1998).

Neurophysiological Implementation, Theoretical Limitations, and Possible
Model Extensions

As detailed in the general introduction, properties of motor preparation and ex-
ecution, uncovered by neurophysiological studies, are not accounted for by current RT
models such as the diffusion model (Ratcliff, 1978; Ratcliff et al., 2016), the leaky com-
peting accumulator (Usher and McClelland, 2001), the linear ballistic accumulator (Brown
and Heathcote, 2008), racing diffusion models (Ratcliff et al., 2003; Tillman et al., 2020),
and Poisson counter models (Ratcliff and Smith, 2004; Vickers, 1970). In this respect, we
believe that the models proposed by Servant et al. (2015, 2021), Verdonck et al. (2021), and
their development and integration through GCDF constitute a major theoretical advance
in the field, as they offer a mechanistic explanation to the interplay between decision and
motor processes.

The diffusion decision process has been the object of several neurocomputational
characterizations and has been hypothesized to arise from recurrent loops within neural
networks (Smith and McKenzie, 2011; Wang, 2002; Wong and Wang, 2006). Interestingly,
recurrent neural networks have also been used to approximate Kalman-Bucy filters (Denève
et al., 2007), paving the way for a joint characterization of decision and motor preparation
processes at the neural circuit level. At the systems level, we believe that future empirical
tests of GCDF would benefit from a combination of EEG and EMG recordings. Although
the application of a low-pass filter during EEG signal processing precludes a precise test of
the Kalman-Bucy filter hypothesis at the motor preparation level, averaged model trajecto-
ries at decision making and motor preparation levels computed from best fitting parameters
could be compared to CPP and effector-selective motor preparation EEG activities, respec-
tively. Some parameters of the model could also be constrained to match corresponding
electrical signatures (Kelly et al., 2021).

Additional constraints to GCDF could also arise from a more detailed analysis
of partial EMG bursts at the motor execution level. Some trials contain more than one
partial burst during PMT, and these additional bursts could be considered in the model-
ing. In particular, the co-occurrence of two partial bursts in left and right EMG channels
would suggest some degree of independence between accumulators. We note, however, that
more detailed EMG analyses entail an increased sensitivity to potentially artifactual elec-
least one partial EMG burst, especially when the first partial burst was located in the same EMG channel as the response. The full GCD provided a better account of these proportions by using a very small response threshold (Experiment 1) or by combining high drift rates with a high between-trial variability in drift rates (Experiments 2-4; see Tables 1 and 2). However, both processing schemes resulted in predicted MTs that were too fast compared to observed MTs. The model compensated this problem by increasing the contribution of residual motor latencies to predicted MTs (parameters *Tr* and *sTr*), but this compensation had two negative consequences. First, the model was not able to capture large effects of choice difficulty on mean MT, such as those observed in Experiment 1. Second, the model was not able to capture the right-skewed shape of MT distributions because between-trial variability in residual motor latencies added to predicted MTs is uniformly distributed, an (arbitrary) assumption inherited from the diffusion decision model (Ratcliff and Rouder, 1998).

Neurophysiological Implementation, Theoretical Limitations, and Possible
Model Extensions

As detailed in the general introduction, properties of motor preparation and ex-
ecution, uncovered by neurophysiological studies, are not accounted for by current RT
models such as the diffusion model (Ratcliff, 1978; Ratcliff et al., 2016), the leaky com-
peting accumulator (Usher and McClelland, 2001), the linear ballistic accumulator (Brown
and Heathcote, 2008), racing diffusion models (Ratcliff et al., 2003; Tillman et al., 2020),
and Poisson counter models (Ratcliff and Smith, 2004; Vickers, 1970). In this respect, we
believe that the models proposed by Servant et al. (2015, 2021), Verdonck et al. (2021), and
their development and integration through GCDF constitute a major theoretical advance
in the field, as they offer a mechanistic explanation to the interplay between decision and
motor processes.

The diffusion decision process has been the object of several neurocomputational
characterizations and has been hypothesized to arise from recurrent loops within neural
networks (Smith and McKenzie, 2011; Wang, 2002; Wong and Wang, 2006). Interestingly,
recurrent neural networks have also been used to approximate Kalman-Bucy filters (Denève
et al., 2007), paving the way for a joint characterization of decision and motor preparation
processes at the neural circuit level. At the systems level, we believe that future empirical
tests of GCDF would benefit from a combination of EEG and EMG recordings. Although
the application of a low-pass filter during EEG signal processing precludes a precise test of
the Kalman-Bucy filter hypothesis at the motor preparation level, averaged model trajecto-
ries at decision making and motor preparation levels computed from best fitting parameters
could be compared to CPP and effector-selective motor preparation EEG activities, respec-
tively. Some parameters of the model could also be constrained to match corresponding
electrical signatures (Kelly et al., 2021).

Additional constraints to GCDF could also arise from a more detailed analysis
of partial EMG bursts at the motor execution level. Some trials contain more than one
partial burst during PMT, and these additional bursts could be considered in the model-
ing. In particular, the co-occurrence of two partial bursts in left and right EMG channels
would suggest some degree of independence between accumulators. We note, however, that
more detailed EMG analyses entail an increased sensitivity to potentially artifactual elec-
trical activities. In addition, partial EMG bursts might be followed by a refractory period. Consequently, the analysis and modeling of trials with multiple partial bursts represent an important challenge for future work.

Beyond the basic mechanisms that drive the time course of decision making, motor preparation, and motor execution processes, we believe that future developments of GCDF would benefit from model-based investigations of more complex relationships between decision and motor processes. For example, decisions are often taken well before being expressed behaviorally. This scenario is involved when voters have to choose a candidate. It is currently outside the scope of GCDF, as the model does not specify the relationship between memory and decision/motor processes. The choice might be categorically retrieved from memory and transmitted to the motor system. Consequently, effector-selective motor preparation EEG activities and EMG signals should not be modulated by the quality of evidence. However, this hypothetical processing scheme may vary as a function of the temporal delay between decision and motor processes and foreknowledge of the stimulus-response mapping (Twomey et al., 2016).

Another scenario that deserves additional scrutiny concerns continuous movement reports. Similar to EMG findings, reaching trajectories are modulated by perceptual and cognitive factors (e.g., Buc Calderon et al., 2015; Kinder et al., 2022; Song and Nakayama, 2009; Sullivan et al., 2015). However, the application of GCDF to choice reaching tasks is not straightforward. Reaching movements engage a complex pattern of neuromuscular activity, making EMG recordings and analyses challenging. One way to reduce this complexity is to model reaching movements at the level of kinematic motor primitives, hypothetical building blocks that can be combined to construct motion (for reviews, see Flash and Hochner, 2005; Giszter, 2015; Latash, 2020). Despite their apparent continuity, reaching movements appear to be composed of discrete submovements. Friedman et al. (2013) hypothesized that an intermittent motor control process probes the state of accumulated evidence at discrete time points to determine submovements and showed good fits of this model to arm movement trajectories in a variant of the random dot motion task. The relationship between this intermittent motor control process, motor preparation, and EMG activity remains to be elucidated.

To conclude, the present EMG investigations in choice RT tasks add to a growing body of behavioral and neurophysiological evidence that suggests that the motor system can have systematic effects that are computationally related to central decision processes. These effects are important to complete the story of how our choices are reflected in our actions. The proposed GCDF offers a new framework to understand this relationship.

## References

* Boehm, U., Annis, J., Frank, M. J., Hawkins, G. E., Heathcote, A., Kellen, D., Krypotos, A.-M., Lerche, V., Logan, G. D., Palmeri, T. J., van Ravenzwaaij, D., Servant, M., Singmann, H., Starns, J. J., Voss, A., Wiecki, T. V., Matzke, D., & Wagenmakers, E.-J. (2018). Estimating across-trial variability parameters of the Diffusion Decision Model: Expert advice and recommendations. *Journal of Mathematical Psychology, 87*, 46–75. https://doi.org/10.1016/j.jmp.2018.09.004
trical activities. In addition, partial EMG bursts might be followed by a refractory period. Consequently, the analysis and modeling of trials with multiple partial bursts represent an important challenge for future work.

Beyond the basic mechanisms that drive the time course of decision making, motor preparation, and motor execution processes, we believe that future developments of GCDF would benefit from model-based investigations of more complex relationships between decision and motor processes. For example, decisions are often taken well before being expressed behaviorally. This scenario is involved when voters have to choose a candidate. It is currently outside the scope of GCDF, as the model does not specify the relationship between memory and decision/motor processes. The choice might be categorically retrieved from memory and transmitted to the motor system. Consequently, effector-selective motor preparation EEG activities and EMG signals should not be modulated by the quality of evidence. However, this hypothetical processing scheme may vary as a function of the temporal delay between decision and motor processes and foreknowledge of the stimulus-response mapping (Twomey et al., 2016).

Another scenario that deserves additional scrutiny concerns continuous movement reports. Similar to EMG findings, reaching trajectories are modulated by perceptual and cognitive factors (e.g., Buc Calderon et al., 2015; Kinder et al., 2022; Song and Nakayama, 2009; Sullivan et al., 2015). However, the application of GCDF to choice reaching tasks is not straightforward. Reaching movements engage a complex pattern of neuromuscular activity, making EMG recordings and analyses challenging. One way to reduce this complexity is to model reaching movements at the level of kinematic motor primitives, hypothetical building blocks that can be combined to construct motion (for reviews, see Flash and Hochner, 2005; Giszter, 2015; Latash, 2020). Despite their apparent continuity, reaching movements appear to be composed of discrete submovements. Friedman et al. (2013) hypothesized that an intermittent motor control process probes the state of accumulated evidence at discrete time points to determine submovements and showed good fits of this model to arm movement trajectories in a variant of the random dot motion task. The relationship between this intermittent motor control process, motor preparation, and EMG activity remains to be elucidated.

To conclude, the present EMG investigations in choice RT tasks add to a growing body of behavioral and neurophysiological evidence that suggests that the motor system can have systematic effects that are computationally related to central decision processes. These effects are important to complete the story of how our choices are reflected in our actions. The proposed GCDF offers a new framework to understand this relationship.

## References

* Boehm, U., Annis, J., Frank, M. J., Hawkins, G. E., Heathcote, A., Kellen, D., Krypotos, A.-M., Lerche, V., Logan, G. D., Palmeri, T. J., van Ravenzwaaij, D., Servant, M., Singmann, H., Starns, J. J., Voss, A., Wiecki, T. V., Matzke, D., & Wagenmakers, E.-J. (2018). Estimating across-trial variability parameters of the Diffusion Decision Model: Expert advice and recommendations. *Journal of Mathematical Psychology, 87*, 46-75. https://doi.org/10.1016/j.jmp.2018.09.004
Bogacz, R., Brown, E., Moehlis, J., Holmes, P., & Cohen, J. D. (2006). The physics of optimal decision making: A formal analysis of models of performance in two-alternative forced-choice tasks. *Psychological Review*, *113*(4), 700–765. https://doi.org/10.1037/0033-295X.113.4.700

Boik, R. J. (1981). A priori tests in repeated measures designs: Effects of nonsphericity [Place: Germany Publisher: Springer]. *Psychometrika*, *46*(3), 241–255. https://doi.org/10.1007/BF02293733

Botwinick, J., & Thompson, L. W. (1966). Premotor and motor components of reaction time. *Journal of Experimental Psychology*, *71*(1), 9–15. https://doi.org/10.1037/h0022634

Brown, S. D., & Heathcote, A. (2008). The simplest complete model of choice response time: Linear ballistic accumulation. *Cognitive Psychology*, *57*(3), 153–178. https://doi.org/10.1016/j.cogpsych.2007.12.002

Buc Calderon, C., Verguts, T., & Gevers, W. (2015). Losing the boundary: Cognition biases action well after action selection [Place: US Publisher: American Psychological Association]. *Journal of Experimental Psychology: General*, *144*, 737–743. https://doi.org/10.1037/xge0000087

Calderón, J. C., Bolaños, P., & Caputo, C. (2014). The excitation–contraction coupling mechanism in skeletal muscle. *Biophysical Reviews*, *6*(1), 133–160. https://doi.org/10.1007/s12551-013-0135-x

Cavanagh, P. R., & Komi, P. V. (1979). Electromechanical delay in human skeletal muscle under concentric and eccentric contractions. *European Journal of Applied Physiology and Occupational Physiology*, *42*(3), 159–163. https://doi.org/10.1007/BF00431022

Churchland, A. K., Kiani, R., & Shadlen, M. N. (2008). Decision-making with multiple alternatives. *Nature neuroscience*, *11*(6), 693–702. https://doi.org/10.1038/nn.2123

Cisek, P. (2007). Cortical mechanisms of action selection: The affordance competition hypothesis. *Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences*, 362(1485), 1585–1599. https://doi.org/10.1098/rstb.2007.2054

Cisek, P., & Kalaska, J. F. (2010). Neural mechanisms for interacting with a world full of action choices. *Annual Review of Neuroscience*, *33*, 269–298. https://doi.org/10.1146/annurev.neuro.051508.135409

Cisek, P., Puskas, G. A., & El-Murr, S. (2009). Decisions in changing conditions: The urgency-gating model. *The Journal of Neuroscience: The Official Journal of the Society for Neuroscience*, *29*(37), 11560–11571. https://doi.org/10.1523/JNEUROSCI.1844-09.2009

Coles, M. G. H., Gratton, G., Bashore, T. R., Eriksen, C. W., & Donchin, E. (1985). A psychophysiological investigation of the continuous flow model of human information processing [Place: US Publisher: American Psychological Association]. *Journal of Experimental Psychology: Human Perception and Performance*, *11*(5), 529–553. https://doi.org/10.1037/0096-1523.11.5.529

Dehaene, S. (2003). The neural basis of the Weber-Fechner law: A logarithmic mental number line. *Trends in Cognitive Sciences*, *7*(4), 145–147. https://doi.org/10.1016/S1364-6613(03)00055-X

de Jong, R., Wierda, M., Mulder, G., & Mulder, L. J. (1988). Use of partial stimulus information in response processing [Place: US Publisher: American Psychological Association].
Bogacz, R., Brown, E., Moehlis, J., Holmes, P., & Cohen, J. D. (2006). The physics of optimal decision making: A formal analysis of models of performance in two-alternative forced-choice tasks. *Psychological Review*, *113*(4), 700-765. https://doi.org/10.1037/0033-295X.113.4.700

Boik, R. J. (1981). A priori tests in repeated measures designs: Effects of nonsphericity [Place: Germany Publisher: Springer]. *Psychometrika*, *46*(3), 241-255. https://doi.org/10.1007/BF02293733

Botwinick, J., & Thompson, L. W. (1966). Premotor and motor components of reaction time. *Journal of Experimental Psychology*, *71*(1), 9-15. https://doi.org/10.1037/h0022634

Brown, S. D., & Heathcote, A. (2008). The simplest complete model of choice response time: Linear ballistic accumulation. *Cognitive Psychology*, *57*(3), 153-178. https://doi.org/10.1016/j.cogpsych.2007.12.002

Buc Calderon, C., Verguts, T., & Gevers, W. (2015). Losing the boundary: Cognition biases action well after action selection [Place: US Publisher: American Psychological Association]. *Journal of Experimental Psychology: General*, *144*, 737-743. https://doi.org/10.1037/xge0000087

Calderón, J. C., Bolaños, P., & Caputo, C. (2014). The excitation-contraction coupling mechanism in skeletal muscle. *Biophysical Reviews*, *6*(1), 133-160. https://doi.org/10.1007/s12551-013-0135-x

Cavanagh, P. R., & Komi, P. V. (1979). Electromechanical delay in human skeletal muscle under concentric and eccentric contractions. *European Journal of Applied Physiology and Occupational Physiology*, *42*(3), 159-163. https://doi.org/10.1007/BF00431022

Churchland, A. K., Kiani, R., & Shadlen, M. N. (2008). Decision-making with multiple alternatives. *Nature neuroscience*, *11*(6), 693-702. https://doi.org/10.1038/nn.2123

Cisek, P. (2007). Cortical mechanisms of action selection: The affordance competition hypothesis. *Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences*, *362*(1485), 1585-1599. https://doi.org/10.1098/rstb.2007.2054

Cisek, P., & Kalaska, J. F. (2010). Neural mechanisms for interacting with a world full of action choices. *Annual Review of Neuroscience*, *33*, 269-298. https://doi.org/10.1146/annurev.neuro.051508.135409

Cisek, P., Puskas, G. A., & El-Murr, S. (2009). Decisions in changing conditions: The urgency-gating model. *The Journal of Neuroscience: The Official Journal of the Society for Neuroscience*, *29*(37), 11560-11571. https://doi.org/10.1523/JNEUROSCI.1844-09.2009

Coles, M. G. H., Gratton, G., Bashore, T. R., Eriksen, C. W., & Donchin, E. (1985). A psychophysiological investigation of the continuous flow model of human information processing [Place: US Publisher: American Psychological Association]. *Journal of Experimental Psychology: Human Perception and Performance*, *11*(5), 529-553. https://doi.org/10.1037/0096-1523.11.5.529

Dehaene, S. (2003). The neural basis of the Weber-Fechner law: A logarithmic mental number line. *Trends in Cognitive Sciences*, *7*(4), 145-147. https://doi.org/10.1016/S1364-6613(03)00055-X

de Jong, R., Wierda, M., Mulder, G., & Mulder, L. J. (1988). Use of partial stimulus information in response processing [Place: US Publisher: American Psychological Association].
ciation]. *Journal of Experimental Psychology: Human Perception and Performance*, **14**(4), 682-692. https://doi.org/10.1037/0096-1523.14.4.682

de Lange, F. P., Rahnev, D. A., Donner, T. H., & Lau, H. (2013). Prestimulus oscillatory activity over motor cortex reflects perceptual expectations. *The Journal of Neuroscience: The Official Journal of the Society for Neuroscience*, **33**(4), 1400–1410.
https://doi.org/10.1523/JNEUROSCI.1094-12.2013

Denève, S., Duhamel, J.-R., & Pouget, A. (2007). Optimal sensorimotor integration in recurrent cortical networks: A neural implementation of Kalman filters. *The Journal of Neuroscience: The Official Journal of the Society for Neuroscience*, **27**(21), 5744–5756. https://doi.org/10.1523/JNEUROSCI.3985-06.2007

Dideriksen, J. L., & Farina, D. (2019). Amplitude cancellation influences the association between frequency components in the neural drive to muscle and the rectified EMG signal [Publisher: Public Library of Science]. *PLOS Computational Biology*, **15**(5), e1006985. https://doi.org/10.1371/journal.pcbi.1006985

Ditterich, J. (2006). Stochastic models of decisions about motion direction: Behavior and physiology. *Neural Networks: The Official Journal of the International Neural Network Society*, **19**(8), 981–1012. https://doi.org/10.1016/j.neunet.2006.05.042

Donders, F. C. (1969). On the speed of mental processes. *Acta Psychologica*, **30**, 412–431.
https://doi.org/10.1016/0001-6918(69)90065-1

Donkin, C., Brown, S., Heathcote, A., & Andrews, S. (2009). Non-Decision Time Effects in the Lexical Decision Task. *Proceedings of the Annual Meeting of the Cognitive Science Society*, **31**. Retrieved August 4, 2022, from https://escholarship.org/uc/item/07q9n3tq

Donner, T. H., Siegel, M., Fries, P., & Engel, A. K. (2009). Buildup of choice-predictive activity in human motor cortex during perceptual decision making. *Current biology: CB*, **19**(18), 1581–1585. https://doi.org/10.1016/j.cub.2009.07.066

Ebbesen, C. L., & Brecht, M. (2017). Motor cortex — to act or not to act? [Number: 11
Publisher: Nature Publishing Group]. *Nature Reviews Neuroscience*, **18**(11), 694–
705. https://doi.org/10.1038/nrn.2017.119

Eriksen, C. W., & Schultz, D. W. (1979). Information processing in visual search: A continuous flow conception and experimental results. *Perception & Psychophysics*, **25**(4), 249–263. https://doi.org/10.3758/bf03198804

Evans, N. J. (2019). A method, framework, and tutorial for efficiently simulating models of decision-making. *Behavior Research Methods*, **51**(5), 2390–2404. https://doi.org/10.3758/s13428-019-01219-z

Evans, N. J., Hawkins, G. E., & Brown, S. D. (2020). The role of passing time in decision-making [Place: US Publisher: American Psychological Association]. *Journal of Experimental Psychology: Learning, Memory, and Cognition*, **46**, 316–326. https://doi.org/10.1037/xlm0000725

Evans, N. J., Tillman, G., & Wagenmakers, E.-J. (2020). Systematic and random sources of variability in perceptual decision-making: Comment on Ratcliff, Voskuilen, and McKoon (2018). *Psychological Review*, **127**(5), 932–944. https://doi.org/10.1037/rev0000192
ciation]. *Journal of Experimental Psychology: Human Perception and Performance*, **14**(4), 682-692. https://doi.org/10.1037/0096-1523.14.4.682

de Lange, F. P., Rahnev, D. A., Donner, T. H., & Lau, H. (2013). Prestimulus oscillatory activity over motor cortex reflects perceptual expectations. *The Journal of Neuroscience: The Official Journal of the Society for Neuroscience*, **33**(4), 1400–1410.
https://doi.org/10.1523/JNEUROSCI.1094-12.2013

Denève, S., Duhamel, J.-R., & Pouget, A. (2007). Optimal sensorimotor integration in recurrent cortical networks: A neural implementation of Kalman filters. *The Journal of Neuroscience: The Official Journal of the Society for Neuroscience*, **27**(21), 5744–5756. https://doi.org/10.1523/JNEUROSCI.3985-06.2007

Dideriksen, J. L., & Farina, D. (2019). Amplitude cancellation influences the association between frequency components in the neural drive to muscle and the rectified EMG signal [Publisher: Public Library of Science]. *PLOS Computational Biology*, **15**(5), e1006985. https://doi.org/10.1371/journal.pcbi.1006985

Ditterich, J. (2006). Stochastic models of decisions about motion direction: Behavior and physiology. *Neural Networks: The Official Journal of the International Neural Network Society*, **19**(8), 981–1012. https://doi.org/10.1016/j.neunet.2006.05.042

Donders, F. C. (1969). On the speed of mental processes. *Acta Psychologica*, **30**, 412–431.
https://doi.org/10.1016/0001-6918(69)90065-1

Donkin, C., Brown, S., Heathcote, A., & Andrews, S. (2009). Non-Decision Time Effects in the Lexical Decision Task. *Proceedings of the Annual Meeting of the Cognitive Science Society*, **31**. Retrieved August 4, 2022, from https://escholarship.org/uc/item/07q9n3tq

Donner, T. H., Siegel, M., Fries, P., & Engel, A. K. (2009). Buildup of choice-predictive activity in human motor cortex during perceptual decision making. *Current biology: CB*, **19**(18), 1581–1585. https://doi.org/10.1016/j.cub.2009.07.066

Ebbesen, C. L., & Brecht, M. (2017). Motor cortex — to act or not to act? [Number: 11
Publisher: Nature Publishing Group]. *Nature Reviews Neuroscience*, **18**(11), 694–
705. https://doi.org/10.1038/nrn.2017.119

Eriksen, C. W., & Schultz, D. W. (1979). Information processing in visual search: A continuous flow conception and experimental results. *Perception & Psychophysics*, **25**(4), 249–263. https://doi.org/10.3758/bf03198804

Evans, N. J. (2019). A method, framework, and tutorial for efficiently simulating models of decision-making. *Behavior Research Methods*, **51**(5), 2390–2404. https://doi.org/10.3758/s13428-019-01219-z

Evans, N. J., Hawkins, G. E., & Brown, S. D. (2020). The role of passing time in decision-making [Place: US Publisher: American Psychological Association]. *Journal of Experimental Psychology: Learning, Memory, and Cognition*, **46**, 316–326. https://doi.org/10.1037/xlm0000725

Evans, N. J., Tillman, G., & Wagenmakers, E.-J. (2020). Systematic and random sources of variability in perceptual decision-making: Comment on Ratcliff, Voskuilen, and McKoon (2018). *Psychological Review*, **127**(5), 932–944. https://doi.org/10.1037/rev0000192
Evans, N. J., & Wagenmakers, E.-J. (2020). Evidence accumulation models: Current limitations and future directions. *The Quantitative Methods for Psychology, 16*, 73-90.

Farina, D., Holobar, A., Merletti, R., & Enoka, R. M. (2010). Decoding the neural drive to muscles from the surface electromyogram. *Clinical Neurophysiology: Official Journal of the International Federation of Clinical Neurophysiology, 121*(10), 1616-1623.
https://doi.org/10.1016/j.clinph.2009.10.040

Filimon, F., Philiastides, M. G., Nelson, J. D., Kloosterman, N. A., & Heekeren, H. R. (2013). How Embodied Is Perceptual Decision Making? Evidence for Separate Processing of Perceptual and Motor Decisions. *The Journal of Neuroscience, 33*(5), 2121-2136. https://doi.org/10.1523/JNEUROSCI.2334-12.2013

Flash, T., & Hochner, B. (2005). Motor primitives in vertebrates and invertebrates. *Current Opinion in Neurobiology, 15*(6), 660-666. https://doi.org/10.1016/j.conb.2005.10.011

Forstmann, B. U., Ratcliff, R., & Wagenmakers, E.-J. (2016). Sequential Sampling Models in Cognitive Neuroscience: Advantages, Applications, and Extensions. *Annual Review of Psychology, 67*, 641-666. https://doi.org/10.1146/annurev-psych-122414-033645

Frank, M. J. (2011). Computational models of motivated action selection in corticostriatal circuits. *Current Opinion in Neurobiology, 21*(3), 381-386. https://doi.org/10.1016/j.conb.2011.02.013

Freedman, D. J., & Assad, J. A. (2016). Neuronal Mechanisms of Visual Categorization: An Abstract View on Decision Making. *Annual Review of Neuroscience, 39*, 129-147.
https://doi.org/10.1146/annurev-neuro-071714-033919

Friedman, J., Brown, S., & Finkbeiner, M. (2013). Linking cognitive and reaching trajectories via intermittent movement control. *Journal of Mathematical Psychology, 57*(3), 140-151. https://doi.org/10.1016/j.jmp.2013.06.005

Giszter, S. F. (2015). Motor primitives–new data and future questions. *Current Opinion in Neurobiology, 33*, 156–165. https://doi.org/10.1016/j.conb.2015.04.004

Glickman, M., Moran, R., & Usher, M. (2022). Evidence integration and decision confidence are modulated by stimulus consistency. *Nature Human Behaviour, 6*(7), 988-999.
https://doi.org/10.1038/s41562-022-01318-6

Glickman, M., & Usher, M. (2019). Integration to boundary in decisions between numerical sequences. *Cognition, 193*, 104022. https://doi.org/10.1016/j.cognition.2019.104022

Gold, J. I., & Shadlen, M. N. (2000). Representation of a perceptual decision in developing oculomotor commands. *Nature, 404*(6776), 390-394. https://doi.org/10.1038/35006062

Gold, J. I., & Shadlen, M. N. (2003). The Influence of Behavioral Context on the Representation of a Perceptual Decision in Developing Oculomotor Commands [Publisher: Society for Neuroscience Section: ARTICLE]. *Journal of Neuroscience, 23*(2), 632-651. https://doi.org/10.1523/JNEUROSCI.23-02-00632.2003

Gold, J. I., & Shadlen, M. N. (2007). The neural basis of decision making. *Annual Review of Neuroscience, 30*, 535-574. https://doi.org/10.1146/annurev.neuro.29.051605.113038

Gomez, P., & Perea, M. (2014). Decomposing encoding and decisional components in visual-word recognition: A diffusion model analysis. *Quarterly Journal of Experimental
Evans, N. J., & Wagenmakers, E.-J. (2020). Evidence accumulation models: Current limitations and future directions. *The Quantitative Methods for Psychology, 16*, 73-90.

Farina, D., Holobar, A., Merletti, R., & Enoka, R. M. (2010). Decoding the neural drive to muscles from the surface electromyogram. *Clinical Neurophysiology: Official Journal of the International Federation of Clinical Neurophysiology, 121*(10), 1616-1623.
https://doi.org/10.1016/j.clinph.2009.10.040

Filimon, F., Philiastides, M. G., Nelson, J. D., Kloosterman, N. A., & Heekeren, H. R. (2013). How Embodied Is Perceptual Decision Making? Evidence for Separate Processing of Perceptual and Motor Decisions. *The Journal of Neuroscience, 33*(5), 2121-2136. https://doi.org/10.1523/JNEUROSCI.2334-12.2013

Flash, T., & Hochner, B. (2005). Motor primitives in vertebrates and invertebrates. *Current Opinion in Neurobiology, 15*(6), 660-666. https://doi.org/10.1016/j.conb.2005.10.011

Forstmann, B. U., Ratcliff, R., & Wagenmakers, E.-J. (2016). Sequential Sampling Models in Cognitive Neuroscience: Advantages, Applications, and Extensions. *Annual Review of Psychology, 67*, 641-666. https://doi.org/10.1146/annurev-psych-122414-033645

Frank, M. J. (2011). Computational models of motivated action selection in corticostriatal circuits. *Current Opinion in Neurobiology, 21*(3), 381-386. https://doi.org/10.1016/j.conb.2011.02.013

Freedman, D. J., & Assad, J. A. (2016). Neuronal Mechanisms of Visual Categorization: An Abstract View on Decision Making. *Annual Review of Neuroscience, 39*, 129-147.
https://doi.org/10.1146/annurev-neuro-071714-033919

Friedman, J., Brown, S., & Finkbeiner, M. (2013). Linking cognitive and reaching trajectories via intermittent movement control. *Journal of Mathematical Psychology, 57*(3), 140-151. https://doi.org/10.1016/j.jmp.2013.06.005

Giszter, S. F. (2015). Motor primitives–new data and future questions. *Current Opinion in Neurobiology, 33*, 156–165. https://doi.org/10.1016/j.conb.2015.04.004

Glickman, M., Moran, R., & Usher, M. (2022). Evidence integration and decision confidence are modulated by stimulus consistency. *Nature Human Behaviour, 6*(7), 988-999.
https://doi.org/10.1038/s41562-022-01318-6

Glickman, M., & Usher, M. (2019). Integration to boundary in decisions between numerical sequences. *Cognition, 193*, 104022. https://doi.org/10.1016/j.cognition.2019.104022

Gold, J. I., & Shadlen, M. N. (2000). Representation of a perceptual decision in developing oculomotor commands. *Nature, 404*(6776), 390-394. https://doi.org/10.1038/35006062

Gold, J. I., & Shadlen, M. N. (2003). The Influence of Behavioral Context on the Representation of a Perceptual Decision in Developing Oculomotor Commands [Publisher: Society for Neuroscience Section: ARTICLE]. *Journal of Neuroscience, 23*(2), 632-651. https://doi.org/10.1523/JNEUROSCI.23-02-00632.2003

Gold, J. I., & Shadlen, M. N. (2007). The neural basis of decision making. *Annual Review of Neuroscience, 30*, 535-574. https://doi.org/10.1146/annurev.neuro.29.051605.113038

Gomez, P., & Perea, M. (2014). Decomposing encoding and decisional components in visual-word recognition: A diffusion model analysis. *Quarterly Journal of Experimental
*Psychology (2006)*, 67(12), 2455-2466. https://doi.org/10.1080/17470218.2014.937447

Grainger, J. (2018). Orthographic processing: A 'mid-level' vision of reading: The 44th Sir Frederic Bartlett Lecture. *Quarterly Journal of Experimental Psychology (2006)*, 71(2), 335-359. https://doi.org/10.1080/17470218.2017.1314515

Gratton, G., Coles, M. G., Sirevaag, E. J., Eriksen, C. W., & Donchin, E. (1988). Pre-and poststimulus activation of response channels: A psychophysiological analysis. *Journal of Experimental Psychology. Human Perception and Performance, 14*(3), 331-344. https://doi.org/10.1037//0096-1523.14.3.331

Hanks, T., Kiani, R., & Shadlen, M. N. (2014). A neural mechanism of speed-accuracy tradeoff in macaque area LIP. *eLife*, 3, e02260. https://doi.org/10.7554/eLife.02260

Hawkins, G. E., Forstmann, B. U., Wagenmakers, E.-J., Ratcliff, R., & Brown, S. D. (2015). Revisiting the evidence for collapsing boundaries and urgency signals in perceptual decision-making. *The Journal of Neuroscience: The Official Journal of the Society for Neuroscience*, 35(6), 2476-2484. https://doi.org/10.1523/JNEUROSCI.2410-14.2015

Hikosaka, O. (2007). GABAergic output of the basal ganglia. *Progress in Brain Research*, 160, 209-226. https://doi.org/10.1016/S0079-6123(06)60012-5

Houghton, G. (2018). Action and perception in literacy: A common-code for spelling and reading. *Psychological Review*, 125(1), 83-116. https://doi.org/10.1037/rev0000084

Kalman, R. E., & Bucy, R. S. (1961). New Results in Linear Filtering and Prediction Theory. *Journal of Basic Engineering*, 83(1), 95-108. https://doi.org/10.1115/1.3658902

Kelly, S. P., Corbett, E. A., & O'Connell, R. G. (2021). Neurocomputational mechanisms of prior-informed perceptual decision-making in humans. *Nature Human Behaviour*, 5(4), 467-481. https://doi.org/10.1038/s41562-020-00967-9

Kelly, S. P., & O'Connell, R. G. (2013). Internal and External Influences on the Rate of Sensory Evidence Accumulation in the Human Brain. *Journal of Neuroscience*, 33(50), 19434-19441. https://doi.org/10.1523/JNEUROSCI.3355-13.2013

Keuleers, E., & Brysbaert, M. (2010). Wuggy: A multilingual pseudoword generator [Place: US Publisher: Psychonomic Society]. *Behavior Research Methods*, 42(3), 627-633. https://doi.org/10.3758/BRM.42.3.627

Kinder, K. T., Buss, A. T., & Tas, A. C. (2022). Tracking flanker task dynamics: Evidence for continuous attentional selectivity. *Journal of Experimental Psychology. Human Perception and Performance*, 48(7), 771-781. https://doi.org/10.1037/xhp0001023

Klein-Flügge, M. C., & Bestmann, S. (2012). Time-dependent changes in human corticospinal excitability reveal value-based competition for action during decision processing. *The Journal of Neuroscience: The Official Journal of the Society for Neuroscience*, 32(24), 8373-8382. https://doi.org/10.1523/JNEUROSCI.0270-12.2012

Laming, D. (1968). *Information theory of choice-reaction times*. Academic Press.

Latash, M. L. (2020). On Primitives in Motor Control. *Motor Control*, 24(2), 318-346. https://doi.org/10.1123/mc.2019-0099

Lemon, R. N. (2008). Descending pathways in motor control. *Annual Review of Neuroscience*, 31, 195-218. https://doi.org/10.1146/annurev.neuro.31.060407.125547
*Psychology (2006)*, 67(12), 2455-2466. https://doi.org/10.1080/17470218.2014.937447

Grainger, J. (2018). Orthographic processing: A 'mid-level' vision of reading: The 44th Sir Frederic Bartlett Lecture. *Quarterly Journal of Experimental Psychology (2006)*, 71(2), 335-359. https://doi.org/10.1080/17470218.2017.1314515

Gratton, G., Coles, M. G., Sirevaag, E. J., Eriksen, C. W., & Donchin, E. (1988). Pre-and poststimulus activation of response channels: A psychophysiological analysis. *Journal of Experimental Psychology. Human Perception and Performance, 14*(3), 331-344. https://doi.org/10.1037//0096-1523.14.3.331

Hanks, T., Kiani, R., & Shadlen, M. N. (2014). A neural mechanism of speed-accuracy tradeoff in macaque area LIP. *eLife*, 3, e02260. https://doi.org/10.7554/eLife.02260

Hawkins, G. E., Forstmann, B. U., Wagenmakers, E.-J., Ratcliff, R., & Brown, S. D. (2015). Revisiting the evidence for collapsing boundaries and urgency signals in perceptual decision-making. *The Journal of Neuroscience: The Official Journal of the Society for Neuroscience*, 35(6), 2476-2484. https://doi.org/10.1523/JNEUROSCI.2410-14.2015

Hikosaka, O. (2007). GABAergic output of the basal ganglia. *Progress in Brain Research*, 160, 209-226. https://doi.org/10.1016/S0079-6123(06)60012-5

Houghton, G. (2018). Action and perception in literacy: A common-code for spelling and reading. *Psychological Review*, 125(1), 83-116. https://doi.org/10.1037/rev0000084

Kalman, R. E., & Bucy, R. S. (1961). New Results in Linear Filtering and Prediction Theory. *Journal of Basic Engineering*, 83(1), 95-108. https://doi.org/10.1115/1.3658902

Kelly, S. P., Corbett, E. A., & O'Connell, R. G. (2021). Neurocomputational mechanisms of prior-informed perceptual decision-making in humans. *Nature Human Behaviour*, 5(4), 467-481. https://doi.org/10.1038/s41562-020-00967-9

Kelly, S. P., & O'Connell, R. G. (2013). Internal and External Influences on the Rate of Sensory Evidence Accumulation in the Human Brain. *Journal of Neuroscience*, 33(50), 19434-19441. https://doi.org/10.1523/JNEUROSCI.3355-13.2013

Keuleers, E., & Brysbaert, M. (2010). Wuggy: A multilingual pseudoword generator [Place: US Publisher: Psychonomic Society]. *Behavior Research Methods*, 42(3), 627-633. https://doi.org/10.3758/BRM.42.3.627

Kinder, K. T., Buss, A. T., & Tas, A. C. (2022). Tracking flanker task dynamics: Evidence for continuous attentional selectivity. *Journal of Experimental Psychology. Human Perception and Performance*, 48(7), 771-781. https://doi.org/10.1037/xhp0001023

Klein-Flügge, M. C., & Bestmann, S. (2012). Time-dependent changes in human corticospinal excitability reveal value-based competition for action during decision processing. *The Journal of Neuroscience: The Official Journal of the Society for Neuroscience*, 32(24), 8373-8382. https://doi.org/10.1523/JNEUROSCI.0270-12.2012

Laming, D. (1968). *Information theory of choice-reaction times*. Academic Press.

Latash, M. L. (2020). On Primitives in Motor Control. *Motor Control*, 24(2), 318-346. https://doi.org/10.1123/mc.2019-0099

Lemon, R. N. (2008). Descending pathways in motor control. *Annual Review of Neuroscience*, 31, 195-218. https://doi.org/10.1146/annurev.neuro.31.060407.125547
Logan, G. D., & Cowan, W. B. (1984). On the ability to inhibit thought and action: A theory of an act of control [Place: US Publisher: American Psychological Association]. *Psychological Review*, *91*(3), 295-327. https://doi.org/10.1037/0033-295X.91.3.295

Marr, D. (1982). *Vision: A computational investigation into the human representation and processing of visual information*. W.H. Freeman.

McClelland, J. L. (1979). On the time relations of mental processes: An examination of systems of processes in cascade [Place: US Publisher: American Psychological Association]. *Psychological Review*, *86*(4), 287-330. https://doi.org/10.1037/0033-295X.86.4.287

McClelland, J. L., & Rumelhart, D. E. (1981). An interactive activation model of context effects in letter perception: I. An account of basic findings [Place: US Publisher: American Psychological Association]. *Psychological Review*, *88*, 375-407. https://doi.org/10.1037/0033-295X.88.5.375

Mink, J. W. (1996). The basal ganglia: Focused selection and inhibition of competing motor programs. *Progress in Neurobiology*, *50*(4), 381-425. https://doi.org/10.1016/s0301-0082(96)00042-1

Murphy, P. R., Boonstra, E., & Nieuwenhuis, S. (2016). Global gain modulation generates time-dependent urgency during perceptual choice in humans. *Nature Communications*, *7*, 13526. https://doi.org/10.1038/ncomms13526

Nakayama, K., Moher, J., & Song, J.-H. (2023). Rethinking Vision and Action [eprint: https://doi.org/10.1146/annurev-psych-021422-043229]. *Annual Review of Psychology*, *74*(1), 59-86. https://doi.org/10.1146/annurev-psych-021422-043229

New, B., Pallier, C., Brysbaert, M., & Ferrand, L. (2004). Lexique 2: A new French lexical database. *Behavior Research Methods, Instruments, & Computers: A Journal of the Psychonomic Society, Inc*, *36*(3), 516-524. https://doi.org/10.3758/bf03195598

O'Connell, R. G., Dockree, P. M., & Kelly, S. P. (2012). A supramodal accumulation-to-bound signal that determines perceptual decisions in humans. *Nature Neuroscience*, *15*(12), 1729-1735. https://doi.org/10.1038/nn.3248

O'Connell, R. G., & Kelly, S. P. (2021). Neurophysiology of Human Perceptual Decision-Making. *Annual Review of Neuroscience*, *44*, 495-516. https://doi.org/10.1146/annurev-neuro-092019-100200

O'Connell, R. G., Shadlen, M. N., Wong-Lin, K., & Kelly, S. P. (2018). Bridging Neural and Computational Viewpoints on Perceptual Decision-Making. *Trends in Neurosciences*, *41*(11), 838-852. https://doi.org/10.1016/j.tins.2018.06.005

Øksendal, B. (2003). *Stochastic Differential Equations*. Springer. https://doi.org/10.1007/978-3-642-14394-6

Palmer, J., Huk, A. C., & Shadlen, M. N. (2005). The effect of stimulus strength on the speed and accuracy of a perceptual decision. *Journal of Vision*, *5*(5), 376-404. https://doi.org/10.1167/5.5.1

Peirce, J., Gray, J. R., Simpson, S., MacAskill, M., Höchenberger, R., Sogo, H., Kastman, E., & Lindelöv, J. K. (2019). PsychoPy2: Experiments in behavior made easy. *Behavior Research Methods*, *51*(1), 195-203. https://doi.org/10.3758/s13428-018-01193-y

Pfurtscheller, G., & Lopes da Silva, F. H. (1999). Event-related EEG/MEG synchronization and desynchronization: Basic principles. *Clinical Neurophysiology: Official Journal*
Logan, G. D., & Cowan, W. B. (1984). On the ability to inhibit thought and action: A theory of an act of control [Place: US Publisher: American Psychological Association]. *Psychological Review*, *91*(3), 295-327. https://doi.org/10.1037/0033-295X.91.3.295

Marr, D. (1982). *Vision: A computational investigation into the human representation and processing of visual information*. W.H. Freeman.

McClelland, J. L. (1979). On the time relations of mental processes: An examination of systems of processes in cascade [Place: US Publisher: American Psychological Association]. *Psychological Review*, *86*(4), 287-330. https://doi.org/10.1037/0033-295X.86.4.287

McClelland, J. L., & Rumelhart, D. E. (1981). An interactive activation model of context effects in letter perception: I. An account of basic findings [Place: US Publisher: American Psychological Association]. *Psychological Review*, *88*, 375-407. https://doi.org/10.1037/0033-295X.88.5.375

Mink, J. W. (1996). The basal ganglia: Focused selection and inhibition of competing motor programs. *Progress in Neurobiology*, *50*(4), 381-425. https://doi.org/10.1016/s0301-0082(96)00042-1

Murphy, P. R., Boonstra, E., & Nieuwenhuis, S. (2016). Global gain modulation generates time-dependent urgency during perceptual choice in humans. *Nature Communications*, *7*, 13526. https://doi.org/10.1038/ncomms13526

Nakayama, K., Moher, J., & Song, J.-H. (2023). Rethinking Vision and Action [eprint: https://doi.org/10.1146/annurev-psych-021422-043229]. *Annual Review of Psychology*, *74*(1), 59-86. https://doi.org/10.1146/annurev-psych-021422-043229

New, B., Pallier, C., Brysbaert, M., & Ferrand, L. (2004). Lexique 2: A new French lexical database. *Behavior Research Methods, Instruments, & Computers: A Journal of the Psychonomic Society, Inc*, *36*(3), 516-524. https://doi.org/10.3758/bf03195598

O'Connell, R. G., Dockree, P. M., & Kelly, S. P. (2012). A supramodal accumulation-to-bound signal that determines perceptual decisions in humans. *Nature Neuroscience*, *15*(12), 1729-1735. https://doi.org/10.1038/nn.3248

O'Connell, R. G., & Kelly, S. P. (2021). Neurophysiology of Human Perceptual Decision-Making. *Annual Review of Neuroscience*, *44*, 495-516. https://doi.org/10.1146/annurev-neuro-092019-100200

O'Connell, R. G., Shadlen, M. N., Wong-Lin, K., & Kelly, S. P. (2018). Bridging Neural and Computational Viewpoints on Perceptual Decision-Making. *Trends in Neurosciences*, *41*(11), 838-852. https://doi.org/10.1016/j.tins.2018.06.005

Øksendal, B. (2003). *Stochastic Differential Equations*. Springer. https://doi.org/10.1007/978-3-642-14394-6

Palmer, J., Huk, A. C., & Shadlen, M. N. (2005). The effect of stimulus strength on the speed and accuracy of a perceptual decision. *Journal of Vision*, *5*(5), 376-404. https://doi.org/10.1167/5.5.1

Peirce, J., Gray, J. R., Simpson, S., MacAskill, M., Höchenberger, R., Sogo, H., Kastman, E., & Lindelöv, J. K. (2019). PsychoPy2: Experiments in behavior made easy. *Behavior Research Methods*, *51*(1), 195-203. https://doi.org/10.3758/s13428-018-01193-y

Pfurtscheller, G., & Lopes da Silva, F. H. (1999). Event-related EEG/MEG synchronization and desynchronization: Basic principles. *Clinical Neurophysiology: Official Journal*
*of the International Federation of Clinical Neurophysiology, 110*(11), 1842-1857.
https://doi.org/10.1016/s1388-2457(99)00141-8

Purcell, B. A., Heitz, R. P., Cohen, J. Y., Schall, J. D., Logan, G. D., & Palmeri, T. J. (2010). Neurally constrained modeling of perceptual decision making [Place: US Publisher: American Psychological Association]. *Psychological Review*, *117*(4), 1113-1143. https://doi.org/10.1037/a0020311

Ratcliff, R., Sheu, C. F., & Gronlund, S. D. (1992). Testing global memory models using ROC curves. *Psychological Review*, *99*(3), 518-535. https://doi.org/10.1037/0033-295x.99.3.518

Ratcliff, R. (1978). A theory of memory retrieval. *Psychol. Rev*, *85*(2), 59–108.

Ratcliff, R., Cherian, A., & Segraves, M. (2003). A comparison of macaque behavior and superior colliculus neuronal activity to predictions from models of two-choice decisions. *Journal of Neurophysiology*, *90*(3), 1392-1407. https://doi.org/10.1152/jn.01049.2002

Ratcliff, R., & Childers, R. (2015). Individual Differences and Fitting Methods for the Two-Choice Diffusion Model of Decision Making. *Decision (Washington, D.C.)*, *2015*. https://doi.org/10.1037/dec0000030

Ratcliff, R., Gomez, P., & McKoon, G. (2004). A Diffusion Model Account of the Lexical Decision Task. *Psychological review*, *111*(1), 159-182. https://doi.org/10.1037/0033-295X.111.1.159

Ratcliff, R., & McKoon, G. (2008). The Diffusion Decision Model: Theory and Data for Two-Choice Decision Tasks. *Neural computation*, *20*(4), 873-922. https://doi.org/10.1162/neco.2008.12-06-420

Ratcliff, R., & McKoon, G. (2018). Modeling numerosity representation with an integrated diffusion model. *Psychological Review*, *125*(2), 183-217. https://doi.org/10.1037/rev0000085

Ratcliff, R., & Rouder, J. N. (1998). Modeling Response Times for Two-Choice Decisions. *Psychological Science*, *9*(5), 347-356. Retrieved September 27, 2019, from https://www.jstor.org/stable/40063319

Ratcliff, R., & Smith, P. L. (2004). A comparison of sequential sampling models for two-choice reaction time. *Psychological Review*, *111*(2), 333-367. https://doi.org/10.1037/0033-295X.111.2.333

Ratcliff, R., Smith, P. L., Brown, S. D., & McKoon, G. (2016). Diffusion Decision Model: Current Issues and History. *Trends in Cognitive Sciences*, *20*(4), 260-281. https://doi.org/10.1016/j.tics.2016.01.007

Ratcliff, R., Thapar, A., & McKoon, G. (2010). Individual differences, aging, and IQ in two-choice tasks. *Cognitive Psychology*, *60*(3), 127-157. https://doi.org/10.1016/j.cogpsych.2009.09.001

Resulaj, A., Kiani, R., Wolpert, D. M., & Shadlen, M. N. (2009). Changes of mind in decision-making. *Nature*, *461*(7261), 263-266. https://doi.org/10.1038/nature08275

Robinson, D. A. (1973). Models of the saccadic eye movement control system. *Kybernetik*, *14*(2), 71-83. https://doi.org/10.1007/BF00288906

Schall, J. D. (2019). Accumulators, Neurons, and Response Time. *Trends in neurosciences*, *42*(12), 848-860. https://doi.org/10.1016/j.tins.2019.10.001
*of the International Federation of Clinical Neurophysiology, 110*(11), 1842-1857.
https://doi.org/10.1016/s1388-2457(99)00141-8

Purcell, B. A., Heitz, R. P., Cohen, J. Y., Schall, J. D., Logan, G. D., & Palmeri, T. J. (2010). Neurally constrained modeling of perceptual decision making [Place: US Publisher: American Psychological Association]. *Psychological Review*, *117*(4), 1113-1143. https://doi.org/10.1037/a0020311

Ratcliff, R., Sheu, C. F., & Gronlund, S. D. (1992). Testing global memory models using ROC curves. *Psychological Review*, *99*(3), 518-535. https://doi.org/10.1037/0033-295x.99.3.518

Ratcliff, R. (1978). A theory of memory retrieval. *Psychol. Rev*, *85*(2), 59–108.

Ratcliff, R., Cherian, A., & Segraves, M. (2003). A comparison of macaque behavior and superior colliculus neuronal activity to predictions from models of two-choice decisions. *Journal of Neurophysiology*, *90*(3), 1392-1407. https://doi.org/10.1152/jn.01049.2002

Ratcliff, R., & Childers, R. (2015). Individual Differences and Fitting Methods for the Two-Choice Diffusion Model of Decision Making. *Decision (Washington, D.C.)*, *2015*.
https://doi.org/10.1037/dec0000030

Ratcliff, R., Gomez, P., & McKoon, G. (2004). A Diffusion Model Account of the Lexical Decision Task. *Psychological review*, *111*(1), 159-182. https://doi.org/10.1037/0033-295X.111.1.159

Ratcliff, R., & McKoon, G. (2008). The Diffusion Decision Model: Theory and Data for Two-Choice Decision Tasks. *Neural computation*, *20*(4), 873-922. https://doi.org/10.1162/neco.2008.12-06-420

Ratcliff, R., & McKoon, G. (2018). Modeling numerosity representation with an integrated diffusion model. *Psychological Review*, *125*(2), 183-217. https://doi.org/10.1037/rev0000085

Ratcliff, R., & Rouder, J. N. (1998). Modeling Response Times for Two-Choice Decisions. *Psychological Science*, *9*(5), 347-356. Retrieved September 27, 2019, from https://www.jstor.org/stable/40063319

Ratcliff, R., & Smith, P. L. (2004). A comparison of sequential sampling models for two-choice reaction time. *Psychological Review*, *111*(2), 333-367. https://doi.org/10.1037/0033-295X.111.2.333

Ratcliff, R., Smith, P. L., Brown, S. D., & McKoon, G. (2016). Diffusion Decision Model: Current Issues and History. *Trends in Cognitive Sciences*, *20*(4), 260-281. https://doi.org/10.1016/j.tics.2016.01.007

Ratcliff, R., Thapar, A., & McKoon, G. (2010). Individual differences, aging, and IQ in two-choice tasks. *Cognitive Psychology*, *60*(3), 127-157. https://doi.org/10.1016/j.cogpsych.2009.09.001

Resulaj, A., Kiani, R., Wolpert, D. M., & Shadlen, M. N. (2009). Changes of mind in decision-making. *Nature*, *461*(7261), 263-266. https://doi.org/10.1038/nature08275

Robinson, D. A. (1973). Models of the saccadic eye movement control system. *Kybernetik*, *14*(2), 71-83. https://doi.org/10.1007/BF00288906

Schall, J. D. (2019). Accumulators, Neurons, and Response Time. *Trends in neurosciences*, *42*(12), 848-860. https://doi.org/10.1016/j.tins.2019.10.001
Schall, J. D., & Paré, M. (2021). The unknown but knowable relationship between Pre-saccadic Accumulation of activity and Saccade initiation. *Journal of Computational Neuroscience, 49*(3), 213-228. https://doi.org/10.1007/s10827-021-00784-7

Selen, L. P. J., Shadlen, M. N., & Wolpert, D. M. (2012). Deliberation in the motor system: Reflex gains track evolving evidence leading to a decision. *The Journal of Neuroscience: The Official Journal of the Society for Neuroscience, 32*(7), 2276-2286. https://doi.org/10.1523/JNEUROSCI.5273-11.2012

Servant, M., Logan, G. D., Gajdos, T., & Evans, N. J. (2021). An integrated theory of deciding and acting. *Journal of Experimental Psychology. General*. https://doi.org/10.1037/xge0001063

Servant, M., White, C., Montagnini, A., & Burle, B. (2015). Using Covert Response Activation to Test Latent Assumptions of Formal Decision-Making Models in Humans. *The Journal of Neuroscience: The Official Journal of the Society for Neuroscience, 35*(28), 10371-10385. https://doi.org/10.1523/JNEUROSCI.0078-15.2015

Shadlen, M. N., & Kiani, R. (2013). Decision making as a window on cognition. *Neuron, 80*(3), 791-806. https://doi.org/10.1016/j.neuron.2013.10.047

Shadlen, M. N., & Newsome, W. T. (1994). Noise, neural codes and cortical organization. *Current Opinion in Neurobiology, 4*(4), 569-579. https://doi.org/10.1016/0959-4388(94)90059-0

Shiffrin, R. M., & Steyvers, M. (1997). A model for recognition memory: REM-retrieving effectively from memory [Place: US Publisher: Psychonomic Society]. *Psychonomic Bulletin & Review, 4*(2), 145-166. https://doi.org/10.3758/BF03209391

Smith, P. L., & Lilburn, S. D. (2020). Vision for the blind: Visual psychophysics and blinded inference for decision models. *Psychonomic Bulletin & Review*. https://doi.org/10.3758/s13423-020-01742-7

Smith, P. L., & McKenzie, C. R. L. (2011). Diffusive Information Accumulation by Minimal Recurrent Neural Models of Decision Making. *Neural Computation, 23*(8), 2000-2031. https://doi.org/10.1162/NECO_a_00150

Song, J.-H., & Nakayama, K. (2009). Hidden cognitive states revealed in choice reaching tasks. *Trends in Cognitive Sciences, 13*(8), 360-366. https://doi.org/10.1016/j.tics.2009.04.009

Starns, J. J., & Ratcliff, R. (2014). Validating the unequal-variance assumption in recognition memory using response time distributions instead of ROC functions: A diffusion model analysis. *Journal of Memory and Language, 70*, 36-52. https://doi.org/10.1016/j.jml.2013.09.005

Steinemann, N. A., O'Connell, R. G., & Kelly, S. P. (2018). Decisions are expedited through multiple neural adjustments spanning the sensorimotor hierarchy. *Nature Communications, 9*(1), 3627. https://doi.org/10.1038/s41467-018-06117-0

Sternberg, S. (1969). The discovery of processing stages: Extensions of Donders' method. *Acta Psychologica, 30*, 276-315. https://doi.org/10.1016/0001-6918(69)90055-9

Stone, C., Mattingley, J. B., & Rangelov, D. (2022). On second thoughts: Changes of mind in decision-making. *Trends in Cognitive Sciences, 26*(5), 419-431. https://doi.org/10.1016/j.tics.2022.02.004
Schall, J. D., & Paré, M. (2021). The unknown but knowable relationship between Pre-saccadic Accumulation of activity and Saccade initiation. *Journal of Computational Neuroscience, 49*(3), 213-228. https://doi.org/10.1007/s10827-021-00784-7

Selen, L. P. J., Shadlen, M. N., & Wolpert, D. M. (2012). Deliberation in the motor system: Reflex gains track evolving evidence leading to a decision. *The Journal of Neuroscience: The Official Journal of the Society for Neuroscience, 32*(7), 2276-2286. https://doi.org/10.1523/JNEUROSCI.5273-11.2012

Servant, M., Logan, G. D., Gajdos, T., & Evans, N. J. (2021). An integrated theory of deciding and acting. *Journal of Experimental Psychology. General*. https://doi.org/10.1037/xge0001063

Servant, M., White, C., Montagnini, A., & Burle, B. (2015). Using Covert Response Activation to Test Latent Assumptions of Formal Decision-Making Models in Humans. *The Journal of Neuroscience: The Official Journal of the Society for Neuroscience, 35*(28), 10371-10385. https://doi.org/10.1523/JNEUROSCI.0078-15.2015

Shadlen, M. N., & Kiani, R. (2013). Decision making as a window on cognition. *Neuron, 80*(3), 791-806. https://doi.org/10.1016/j.neuron.2013.10.047

Shadlen, M. N., & Newsome, W. T. (1994). Noise, neural codes and cortical organization. *Current Opinion in Neurobiology, 4*(4), 569-579. https://doi.org/10.1016/0959-4388(94)90059-0

Shiffrin, R. M., & Steyvers, M. (1997). A model for recognition memory: REM-retrieving effectively from memory [Place: US Publisher: Psychonomic Society]. *Psychonomic Bulletin & Review, 4*(2), 145-166. https://doi.org/10.3758/BF03209391

Smith, P. L., & Lilburn, S. D. (2020). Vision for the blind: Visual psychophysics and blinded inference for decision models. *Psychonomic Bulletin & Review*. https://doi.org/10.3758/s13423-020-01742-7

Smith, P. L., & McKenzie, C. R. L. (2011). Diffusive Information Accumulation by Minimal Recurrent Neural Models of Decision Making. *Neural Computation, 23*(8), 2000-2031. https://doi.org/10.1162/NECO_a_00150

Song, J.-H., & Nakayama, K. (2009). Hidden cognitive states revealed in choice reaching tasks. *Trends in Cognitive Sciences, 13*(8), 360-366. https://doi.org/10.1016/j.tics.2009.04.009

Starns, J. J., & Ratcliff, R. (2014). Validating the unequal-variance assumption in recognition memory using response time distributions instead of ROC functions: A diffusion model analysis. *Journal of Memory and Language, 70*, 36-52. https://doi.org/10.1016/j.jml.2013.09.005

Steinemann, N. A., O'Connell, R. G., & Kelly, S. P. (2018). Decisions are expedited through multiple neural adjustments spanning the sensorimotor hierarchy. *Nature Communications, 9*(1), 3627. https://doi.org/10.1038/s41467-018-06117-0

Sternberg, S. (1969). The discovery of processing stages: Extensions of Donders' method. *Acta Psychologica, 30*, 276-315. https://doi.org/10.1016/0001-6918(69)90055-9

Stone, C., Mattingley, J. B., & Rangelov, D. (2022). On second thoughts: Changes of mind in decision-making. *Trends in Cognitive Sciences, 26*(5), 419-431. https://doi.org/10.1016/j.tics.2022.02.004
Storn, R., & Price, K. (1997). Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces. *Journal of Global Optimization*, 11(4), 341–359. https://doi.org/10.1023/A:1008202821328

Sullivan, N., Hutcherson, C., Harris, A., & Rangel, A. (2015). Dietary self-control is related to the speed with which attributes of healthfulness and tastiness are processed. *Psychological Science*, 26(2), 122–134. https://doi.org/10.1177/0956797614559543

Summerfield, C., & Parpart, P. (2022). Normative Principles for Decision-Making in Natural Environments. *Annual Review of Psychology*, 73, 53–77. https://doi.org/10.1146/annurev-psych-020821-104057

Tillman, G., Osth, A. F., van Ravenzwaaij, D., & Heathcote, A. (2017). A diffusion decision model analysis of evidence variability in the lexical decision task. *Psychonomic Bulletin & Review*, 24(6), 1949–1956. https://doi.org/10.3758/s13423-017-1259-y

Tillman, G., Van Zandt, T., & Logan, G. D. (2020). Sequential sampling models without random between-trial variability: The racing diffusion model of speeded decision making. *Psychonomic Bulletin & Review*, 27(5), 911–936. https://doi.org/10.3758/s13423-020-01719-6

Tosoni, A., Galati, G., Romani, G. L., & Corbetta, M. (2008). Sensory-motor mechanisms in human parietal cortex underlie arbitrary visual decisions [Number: 12 Publisher: Nature Publishing Group]. *Nature Neuroscience*, 11(12), 1446–1453. https://doi.org/10.1038/nn.2221

Trueblood, J. S., Heathcote, A., Evans, N. J., & Holmes, W. R. (2021). Urgency, leakage, and the relative nature of information processing in decision-making [Place: US Publisher: American Psychological Association]. *Psychological Review*, 128(1), 160–186. https://doi.org/10.1037/rev0000255

Twomey, D. M., Kelly, S. P., & O'Connell, R. G. (2016). Abstract and Effector-Selective Decision Signals Exhibit Qualitatively Distinct Dynamics before Delayed Perceptual Reports. *The Journal of Neuroscience: The Official Journal of the Society for Neuroscience*, 36(28), 7346–7352. https://doi.org/10.1523/JNEUROSCI.4162-15.2016

Twomey, D. M., Murphy, P. R., Kelly, S. P., & O'Connell, R. G. (2015). The classic P300 encodes a build-to-threshold decision variable. *The European Journal of Neuroscience*, 42(1), 1636–1643. https://doi.org/10.1111/ejn.12936

Usher, M., & McClelland, J. L. (2001). The time course of perceptual choice: The leaky, competing accumulator model. *Psychological Review*, 108(3), 550–592. https://doi.org/10.1037/0033-295x.108.3.550

Verdonck, S., Loossens, T., & Philiastides, M. G. (2021). The Leaky Integrating Threshold and its impact on evidence accumulation models of choice response time (RT). *Psychological Review*. https://doi.org/10.1037/rev0000258

Vickers, D. (1970). Evidence for an accumulator model of psychophysical discrimination. *Ergonomics*, 13(1), 37–58. https://doi.org/10.1080/00140137008931117

Vigotsky, A. D., Halperin, I., Lehman, G. J., Trajano, G. S., & Vieira, T. M. (2018). Interpreting Signal Amplitudes in Surface Electromyography Studies in Sport and Rehabilitation Sciences [Publisher: Frontiers]. *Frontiers in Physiology*, 8. https://doi.org/10.3389/fphys.2017.00985
Storn, R., & Price, K. (1997). Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces. *Journal of Global Optimization*, 11(4), 341–359. https://doi.org/10.1023/A:1008202821328

Sullivan, N., Hutcherson, C., Harris, A., & Rangel, A. (2015). Dietary self-control is related to the speed with which attributes of healthfulness and tastiness are processed. *Psychological Science*, 26(2), 122–134. https://doi.org/10.1177/0956797614559543

Summerfield, C., & Parpart, P. (2022). Normative Principles for Decision-Making in Natural Environments. *Annual Review of Psychology*, 73, 53–77. https://doi.org/10.1146/annurev-psych-020821-104057

Tillman, G., Osth, A. F., van Ravenzwaaij, D., & Heathcote, A. (2017). A diffusion decision model analysis of evidence variability in the lexical decision task. *Psychonomic Bulletin & Review*, 24(6), 1949–1956. https://doi.org/10.3758/s13423-017-1259-y

Tillman, G., Van Zandt, T., & Logan, G. D. (2020). Sequential sampling models without random between-trial variability: The racing diffusion model of speeded decision making. *Psychonomic Bulletin & Review*, 27(5), 911–936. https://doi.org/10.3758/s13423-020-01719-6

Tosoni, A., Galati, G., Romani, G. L., & Corbetta, M. (2008). Sensory-motor mechanisms in human parietal cortex underlie arbitrary visual decisions [Number: 12 Publisher: Nature Publishing Group]. *Nature Neuroscience*, 11(12), 1446–1453. https://doi.org/10.1038/nn.2221

Trueblood, J. S., Heathcote, A., Evans, N. J., & Holmes, W. R. (2021). Urgency, leakage, and the relative nature of information processing in decision-making [Place: US Publisher: American Psychological Association]. *Psychological Review*, 128(1), 160–186. https://doi.org/10.1037/rev0000255

Twomey, D. M., Kelly, S. P., & O'Connell, R. G. (2016). Abstract and Effector-Selective Decision Signals Exhibit Qualitatively Distinct Dynamics before Delayed Perceptual Reports. *The Journal of Neuroscience: The Official Journal of the Society for Neuroscience*, 36(28), 7346–7352. https://doi.org/10.1523/JNEUROSCI.4162-15.2016

Twomey, D. M., Murphy, P. R., Kelly, S. P., & O'Connell, R. G. (2015). The classic P300 encodes a build-to-threshold decision variable. *The European Journal of Neuroscience*, 42(1), 1636–1643. https://doi.org/10.1111/ejn.12936

Usher, M., & McClelland, J. L. (2001). The time course of perceptual choice: The leaky, competing accumulator model. *Psychological Review*, 108(3), 550–592. https://doi.org/10.1037/0033-295x.108.3.550

Verdonck, S., Loossens, T., & Philiastides, M. G. (2021). The Leaky Integrating Threshold and its impact on evidence accumulation models of choice response time (RT). *Psychological Review*. https://doi.org/10.1037/rev0000258

Vickers, D. (1970). Evidence for an accumulator model of psychophysical discrimination. *Ergonomics*, 13(1), 37–58. https://doi.org/10.1080/00140137008931117

Vigotsky, A. D., Halperin, I., Lehman, G. J., Trajano, G. S., & Vieira, T. M. (2018). Interpreting Signal Amplitudes in Surface Electromyography Studies in Sport and Rehabilitation Sciences [Publisher: Frontiers]. *Frontiers in Physiology*, 8. https://doi.org/10.3389/fphys.2017.00985
Voss, A., Rothermund, K., & Voss, J. (2004). Interpreting the parameters of the diffusion model: An empirical validation. *Memory & Cognition, 32*(7), 1206-1220. https://doi.org/10.3758/BF03196893

Vrieze, S. I. (2012). Model selection and psychological theory: A discussion of the differences between the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) [Place: US Publisher: American Psychological Association]. *Psychological Methods*, *17*(2), 228-243. https://doi.org/10.1037/a0027127

Wagenmakers, E.-J., Steyvers, M., Raaijmakers, J. G. W., Shiffrin, R. M., van Rijn, H., & Zeelenberg, R. (2004). A model for evidence accumulation in the lexical decision task. *Cognitive Psychology, 48*(3), 332-367. https://doi.org/10.1016/j.cogpsych.2003.08.001

Wang, X.-J. (2002). Probabilistic decision making by slow reverberation in cortical circuits. *Neuron*, *36*(5), 955-968. https://doi.org/10.1016/s0896-6273(02)01092-9

Weindel, G., Anders, R., Alario, F.-X., & Burle, B. (2021). Assessing model-based inferences in decision making with single-trial response time decomposition. *Journal of Experimental Psychology. General*. https://doi.org/10.1037/xge0001010

Weiss, A. D. (1965). THE LOCUS OF REACTION TIME CHANGE WITH SET, MOTIVATION, AND AGE. *Journal of Gerontology, 20*, 60-64. https://doi.org/10.1093/geronj/20.1.60

Wiecki, T. V., Sofer, I., & Frank, M. J. (2013). HDDM: Hierarchical Bayesian estimation of the Drift-Diffusion Model in Python. *Frontiers in Neuroinformatics, 7*, 14. https://doi.org/10.3389/fninf.2013.00014

Wixted, J. T. (2007). Dual-process theory and signal-detection theory of recognition memory. *Psychological Review*, *114*(1), 152-176. https://doi.org/10.1037/0033-295X.114.1.152

Wong, K.-F., & Wang, X.-J. (2006). A recurrent network mechanism of time integration in perceptual decisions. *The Journal of Neuroscience: The Official Journal of the Society for Neuroscience*, *26*(4), 1314-1328. https://doi.org/10.1523/JNEUROSCI.3733-05.2006

*(Appendices continue)*
Voss, A., Rothermund, K., & Voss, J. (2004). Interpreting the parameters of the diffusion model: An empirical validation. *Memory & Cognition, 32*(7), 1206-1220. https://doi.org/10.3758/BF03196893

Vrieze, S. I. (2012). Model selection and psychological theory: A discussion of the differences between the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) [Place: US Publisher: American Psychological Association]. *Psychological Methods*, *17*(2), 228-243. https://doi.org/10.1037/a0027127

Wagenmakers, E.-J., Steyvers, M., Raaijmakers, J. G. W., Shiffrin, R. M., van Rijn, H., & Zeelenberg, R. (2004). A model for evidence accumulation in the lexical decision task. *Cognitive Psychology, 48*(3), 332-367. https://doi.org/10.1016/j.cogpsych.2003.08.001

Wang, X.-J. (2002). Probabilistic decision making by slow reverberation in cortical circuits. *Neuron*, *36*(5), 955-968. https://doi.org/10.1016/s0896-6273(02)01092-9

Weindel, G., Anders, R., Alario, F.-X., & Burle, B. (2021). Assessing model-based inferences in decision making with single-trial response time decomposition. *Journal of Experimental Psychology. General*. https://doi.org/10.1037/xge0001010

Weiss, A. D. (1965). THE LOCUS OF REACTION TIME CHANGE WITH SET, MOTIVATION, AND AGE. *Journal of Gerontology, 20*, 60-64. https://doi.org/10.1093/geronj/20.1.60

Wiecki, T. V., Sofer, I., & Frank, M. J. (2013). HDDM: Hierarchical Bayesian estimation of the Drift-Diffusion Model in Python. *Frontiers in Neuroinformatics, 7*, 14. https://doi.org/10.3389/fninf.2013.00014

Wixted, J. T. (2007). Dual-process theory and signal-detection theory of recognition memory. *Psychological Review*, *114*(1), 152-176. https://doi.org/10.1037/0033-295X.114.1.152

Wong, K.-F., & Wang, X.-J. (2006). A recurrent network mechanism of time integration in perceptual decisions. *The Journal of Neuroscience: The Official Journal of the Society for Neuroscience*, *26*(4), 1314-1328. https://doi.org/10.1523/JNEUROSCI.3733-05.2006

*(Appendices continue)*
Appendix A
Empirical Illustrations of Trials Containing at Least One Partial EMG Burst During PMT

<figure><img src="image_10.png" /></figure>

*Note.* Panels (A), (B), (C), and (D) show trials that contain one partial EMG burst in the same EMG channel as the response. Panel (E) shows a trial with a partial EMG burst in the opposite EMG channel as the response. Panel (F) shows a trial with two partial EMG bursts in the same EMG channel as the response. PMT = premotor time; EMG = electromyographic. See the online article for the color version of this figure.

*(Appendices continue)*
Appendix A
Empirical Illustrations of Trials Containing at Least One Partial EMG Burst During PMT

<figure><img src="image_11.png" /></figure>

*Note.* Panels (A), (B), (C), and (D) show trials that contain one partial EMG burst in the same EMG channel as the response. Panel (E) shows a trial with a partial EMG burst in the opposite EMG channel as the response. Panel (F) shows a trial with two partial EMG bursts in the same EMG channel as the response. PMT = premotor time; EMG = electromyographic. See the online article for the color version of this figure.

*(Appendices continue)*
## Appendix B
Mathematical details

### Derivation of the Kalman-Bucy Filter at the Motor Preparation Level (Equation 6)

Definitions of the decision variable $x(t)$ and its noisy variant $\tilde{x}(t)$ received by the motor preparation system are provided in the main text by Equations 1 and 5 respectively. In order to have a tractable mathematical representation of the problem, it is better to write it down in terms of differential equations. This is already the case for $x(t)$. However, we cannot differentiate $\tilde{x}(t)$ as it stands, because we cannot differentiate a white noise. We thus introduce a new process $q(t)$, defined as $q(t) = \int_{0}^{t} \tilde{x}(s)ds$. We have:

$$dq(t) = x(t)dt + \xi dV(t), \quad q(0) = x_0, \qquad (B1)$$

where $V(t)$ is a Brownian motion, independent of $W(t)$. Note that processes $q(t)$ and $\tilde{x}(t)$ contain the exact same information.

The Kalman-Bucy filtered motor preparation process $\tilde{y}(t)$ satisfies the following differential equation (Øksendal, 2003):

$$d\tilde{y}(t) = \left( v - \frac{S(t)}{\xi^2} \tilde{y}(t) \right) dt + \frac{S(t)}{\xi^2} dq(t), \quad \tilde{y}(0) = x_0, \qquad (B2)$$

where $S(t) = E[(x(t) - \tilde{y}(t))^2]$, and satisfies the Riccati equation:

$$\frac{dS}{dt} = -\frac{S^2}{\xi^2} + \sigma^2, \quad S(0) = 0. \qquad (B3)$$

The solution to the Riccati equation is:

$$S(t) = \frac{-\xi\sigma + \xi\sigma e^{\frac{2\sigma}{\xi}t}}{1 + e^{\frac{2\sigma}{\xi}t}} \qquad (B4) \\ = \xi\sigma \tanh\left(\frac{\sigma}{\xi}t\right).$$

Substituting $S(t)$ in Equation B2, we obtain:

$$d\tilde{y}(t) = \frac{\sigma}{\xi} \tanh\left(\frac{\sigma}{\xi}t\right) (dq(t) - \tilde{y}(t)dt) + vdt, \quad \tilde{y}(0) = x_0. \qquad (B5)$$

Finally, from the definition of $q(t)$, we have $dq(t) = \tilde{x}(t)dt$, which leads to:

$$d\tilde{y}(t) = \frac{\sigma}{\xi} \tanh\left(\frac{\sigma}{\xi}t\right) (\tilde{x}(t) - \tilde{y}(t))dt + vdt, \quad \tilde{y}(0) = x_0. \qquad (B6)$$

### Relationship Between Equation 3 and 8

In the main text, we noted that Equation 3 and Equation 8 differ with respect to the input to motor preparation. This difference can be further characterized by solving each
## Appendix B
Mathematical details

### Derivation of the Kalman–Bucy Filter at the Motor Preparation Level (Equation 6)

Definitions of the decision variable $x(t)$ and its noisy variant $\tilde{x}(t)$ received by the motor preparation system are provided in the main text by Equations 1 and 5 respectively. In order to have a tractable mathematical representation of the problem, it is better to write it down in terms of differential equations. This is already the case for $x(t)$. However, we cannot differentiate $\tilde{x}(t)$ as it stands, because we cannot differentiate a white noise. We thus introduce a new process $q(t)$, defined as $q(t) = \int_{0}^{t} \tilde{x}(s)ds$. We have:

$$dq(t) = x(t)dt + \xi dV(t), \quad q(0) = x_0, \qquad (B1)$$

where $V(t)$ is a Brownian motion, independent of $W(t)$. Note that processes $q(t)$ and $\tilde{x}(t)$ contain the exact same information.

The Kalman-Bucy filtered motor preparation process $\tilde{y}(t)$ satisfies the following differential equation (Øksendal, 2003):

$$d\tilde{y}(t) = \left( v - \frac{S(t)}{\xi^2} \tilde{y}(t) \right) dt + \frac{S(t)}{\xi^2} dq(t), \quad \tilde{y}(0) = x_0, \qquad (B2)$$

where $S(t) = E[(x(t) - \tilde{y}(t))^2]$, and satisfies the Riccati equation:

$$\frac{dS}{dt} = -\frac{S^2}{\xi^2} + \sigma^2, \quad S(0) = 0. \qquad (B3)$$

The solution to the Riccati equation is:

$$S(t) = \frac{-\xi\sigma + \xi\sigma e^{\frac{2\sigma}{\xi}t}}{1 + e^{\frac{2\sigma}{\xi}t}} \qquad (B4) \\ = \xi\sigma \tanh\left(\frac{\sigma}{\xi}t\right).$$

Substituting $S(t)$ in Equation B2, we obtain:

$$d\tilde{y}(t) = \frac{\sigma}{\xi} \tanh\left(\frac{\sigma}{\xi}t\right) (dq(t) - \tilde{y}(t)dt) + vdt, \quad \tilde{y}(0) = x_0. \qquad (B5)$$

Finally, from the definition of $q(t)$, we have $dq(t) = \tilde{x}(t)dt$, which leads to:

$$d\tilde{y}(t) = \frac{\sigma}{\xi} \tanh\left(\frac{\sigma}{\xi}t\right) (\tilde{x}(t) - \tilde{y}(t))dt + vdt, \quad \tilde{y}(0) = x_0. \qquad (B6)$$

### Relationship Between Equation 3 and 8

In the main text, we noted that Equation 3 and Equation 8 differ with respect to the input to motor preparation. This difference can be further characterized by solving each
equation, and replacing parameter $\lambda'$ by $\lambda$ in Equation 8:

$$ 
\begin{aligned}
y(t) &= \lambda \int_{0}^{t} e^{\lambda(s-t)} x(s) ds \\
\tilde{y}(t) &= \lambda \int_{0}^{t} e^{\lambda(s-t)} \tilde{x}(s) ds.
\end{aligned} 
\qquad (B7) 
$$

Since $\tilde{x}(s)ds = dq(s) = x(s)ds + \xi dV(s)$, we obtain:

$$ 
\begin{aligned}
\tilde{y}(t) &= \lambda \int_{0}^{t} e^{\lambda(s-t)} (x(s)ds + \xi dV(s)) \\
&= \lambda \int_{0}^{t} e^{\lambda(s-t)} x(s)ds + \lambda\xi \int_{0}^{t} e^{\lambda(s-t)} dV(s) \\
&= y(t) + \lambda\xi \int_{0}^{t} e^{\lambda(s-t)} dV(s).
\end{aligned} 
\qquad (B8) 
$$

Using Itô isometry, we see that $\tilde{y}(t)$ is equal to $y(t)$ plus a Gaussian noise with mean 0 and variance $\varphi = \lambda\xi^2 \frac{1-e^{-2\lambda t}}{2}$. This Gaussian noise is independent from $y$ (because $V$ and $W$ are independent). Note that $\varphi < \frac{\lambda\xi^2}{2}$, and $\tilde{y}(t)$ converges towards $y(t)$ as the amplitude of transmission noise $\xi$ approaches 0.

(Appendices continue)
equation, and replacing parameter $\lambda'$ by $\lambda$ in Equation 8:

$$ 
\begin{aligned}
y(t) &= \lambda \int_{0}^{t} e^{\lambda(s-t)} x(s) ds \\
\tilde{y}(t) &= \lambda \int_{0}^{t} e^{\lambda(s-t)} \tilde{x}(s) ds.
\end{aligned} 
\qquad (B7) 
$$

Since $\tilde{x}(s)ds = dq(s) = x(s)ds + \xi dV(s)$, we obtain:

$$ 
\begin{aligned}
\tilde{y}(t) &= \lambda \int_{0}^{t} e^{\lambda(s-t)} (x(s)ds + \xi dV(s)) \\
&= \lambda \int_{0}^{t} e^{\lambda(s-t)} x(s)ds + \lambda\xi \int_{0}^{t} e^{\lambda(s-t)} dV(s) \\
&= y(t) + \lambda\xi \int_{0}^{t} e^{\lambda(s-t)} dV(s).
\end{aligned} 
\qquad (B8) 
$$

Using Itô isometry, we see that $\tilde{y}(t)$ is equal to $y(t)$ plus a Gaussian noise with mean 0 and variance $\varphi = \lambda\xi^2 \frac{1-e^{-2\lambda t}}{2}$. This Gaussian noise is independent from $y$ (because $V$ and $W$ are independent). Note that $\varphi < \frac{\lambda\xi^2}{2}$, and $\tilde{y}(t)$ converges towards $y(t)$ as the amplitude of transmission noise $\xi$ approaches 0.

(Appendices continue)
# Appendix C
## Fits of a GCDF Variant That Uses Variable $\tilde{y}(t)$ to Model Motor Preparation

We compared the fit performance of GCDF with a model variant that uses $\tilde{y}(t)$ computed using Equation 7. We refer to this variant as gated cascade diffusion model with a Kalman-Bucy filter at the motor preparation level (GCDK). Based on our mathematical analysis, we expected a comparable fit performance between the two models. GCDK was fit to behavioral and EMG data from the four choice tasks using a methodology identical to that described in the main text. To avoid complications arising from between-trial variability in processing components, we restricted this analysis to raw models. GCDK has one more free parameter than GCDF (the amplitude of transmission noise $\xi$).

Figure C1 displays model comparison statistics (AIC and BIC) for each task. The plot shows a considerable degree of overlap between GCDF and GCDK, diagnostic of a similar performance. The AIC (BIC) favors GCDK over GCDF for 7 (7) subjects for the random dot motion task, 12 (10) subjects for the numerosity judgment task, 14 (14) subjects for the recognition memory task, and 11 (10) subjects for the lexical decision task. Each of these differences fails to reach statistical significance (two-sided binomial test).

Best fitting GCDK parameters averaged across subjects are reported in Table C1. It is worth noting that the prior $\lambda'$ on the ratio between diffusion noise $\sigma$ and transmission noise $\xi$ is significantly smaller than the ratio computed from an ideal observer perspective, resulting in a stronger smoothing of the corrupted decision variable $\tilde{x}$ than actually needed. This phenomenon could be interpreted as a bias toward response accuracy relative to response speed (Verdonck et al., 2021). This analysis must be taken with caution, as we suspect trade-offs between GCDK parameters (suggested by the very short residual latency $Te$ added to predicted PMT in Experiment 1, or the very small prior $\lambda'$ in Experiment 3). A comprehensive assessment of these trade-offs is beyond the scope of the present work.
Appendix C

Fits of a GCDF Variant That Uses Variable $\tilde{y}(t)$ to Model Motor Preparation

We compared the fit performance of GCDF with a model variant that uses $\tilde{y}(t)$ computed using Equation 7. We refer to this variant as gated cascade diffusion model with a Kalman-Bucy filter at the motor preparation level (GCDK). Based on our mathematical analysis, we expected a comparable fit performance between the two models. GCDK was fit to behavioral and EMG data from the four choice tasks using a methodology identical to that described in the main text. To avoid complications arising from between-trial variability in processing components, we restricted this analysis to raw models. GCDK has one more free parameter than GCDF (the amplitude of transmission noise $\xi$).

Figure C1 displays model comparison statistics (AIC and BIC) for each task. The plot shows a considerable degree of overlap between GCDF and GCDK, diagnostic of a similar performance. The AIC (BIC) favors GCDK over GCDF for 7 (7) subjects for the random dot motion task, 12 (10) subjects for the numerosity judgment task, 14 (14) subjects for the recognition memory task, and 11 (10) subjects for the lexical decision task. Each of these differences fails to reach statistical significance (two-sided binomial test).

Best fitting GCDK parameters averaged across subjects are reported in Table C1. It is worth noting that the prior $\lambda'$ on the ratio between diffusion noise $\sigma$ and transmission noise $\xi$ is significantly smaller than the ratio computed from an ideal observer perspective, resulting in a stronger smoothing of the corrupted decision variable $\tilde{x}$ than actually needed. This phenomenon could be interpreted as a bias toward response accuracy relative to response speed (Verdonck et al., 2021). This analysis must be taken with caution, as we suspect trade-offs between GCDK parameters (suggested by the very short residual latency $Te$ added to predicted PMT in Experiment 1, or the very small prior $\lambda'$ in Experiment 3). A comprehensive assessment of these trade-offs is beyond the scope of the present work.
<caption>Figure C1</caption>

Model Selection Statistics for Experiments 1–4, Including GCDK and Focusing on Raw Models

<figure><img src="image_11.png" /></figure>

*Note.* Panels (A)–(D) correspond to Experiments 1–4. AIC = Akaike information criterion; BIC = Bayesian information criterion; GCD = gated cascade diffusion model; GCDF = gated cascade diffusion model with a filtering mechanism at the motor preparation level; GCDK = gated cascade diffusion model with a Kalman-Bucy filter at the motor preparation level. See the online article for the color version of this figure.
<caption>Figure C1</caption>

*Model Selection Statistics for Experiments 1–4, Including GCDK and Focusing on Raw Models*

<figure><img src="image_12.png" /></figure>

*Note.* Panels (A)–(D) correspond to Experiments 1–4. AIC = Akaike information criterion; BIC = Bayesian information criterion; GCD = gated cascade diffusion model; GCDF = gated cascade diffusion model with a filtering mechanism at the motor preparation level; GCDK = gated cascade diffusion model with a Kalman-Bucy filter at the motor preparation level. See the online article for the color version of this figure.
<table><caption>Table C1</caption><caption>Parameters From the Raw Models (GCD, GCDF, and GCDK) Averaged Across Subjects for Experiments 1-4</caption><thead><tr><th>Exp</th><th>Model</th><th>v<sub>1</sub></th><th>v<sub>2</sub></th><th>v<sub>3</sub></th><th>v<sub>4</sub></th><th>v<sub>5</sub></th><th>k</th><th>dc</th><th>λ</th><th>χ</th><th>ξ</th><th>g</th><th>r</th><th>Te<sub>1</sub></th><th>Te<sub>2</sub></th><th>Te<sub>3</sub></th><th>Te<sub>4</sub></th><th>Te<sub>5</sub></th><th>Tr</th><th>x<sub>0</sub></th></tr></thead><tbody><tr><td>1</td><td>GCD</td><td></td><td></td><td></td><td></td><td>1.147</td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.085</td><td>0.045</td><td>0.271</td><td></td><td></td><td></td><td>0.079</td><td></td></tr><tr><td>1</td><td>GCDF</td><td></td><td></td><td></td><td></td><td>0.694</td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.055</td><td>0.024</td><td>0.193</td><td></td><td></td><td></td><td>0.066</td><td></td></tr><tr><td>1</td><td>GCDK</td><td></td><td></td><td></td><td></td><td>0.620</td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.045</td><td>0.019</td><td>0.084</td><td></td><td></td><td></td><td>0.050</td><td></td></tr><tr><td>2</td><td>GCD</td><td>0.020</td><td></td><td></td><td></td><td></td><td></td><td></td><td>-0.026</td><td></td><td></td><td></td><td>0.058</td><td>0.049</td><td>0.293</td><td></td><td></td><td></td><td>0.089</td><td>0.004</td></tr><tr><td>2</td><td>GCDF</td><td>0.015</td><td></td><td></td><td></td><td></td><td></td><td></td><td>-0.016</td><td>35.937</td><td></td><td></td><td>0.039</td><td>0.032</td><td>0.267</td><td></td><td></td><td></td><td>0.084</td><td>0.002</td></tr><tr><td>2</td><td>GCDK</td><td>0.013</td><td></td><td></td><td></td><td></td><td></td><td></td><td>-0.014</td><td></td><td></td><td></td><td>0.031</td><td>0.028</td><td>0.204</td><td></td><td></td><td></td><td>0.074</td><td>0.002</td></tr><tr><td>3</td><td>GCD</td><td>0.363</td><td>0.588</td><td>0.628</td><td>-0.594</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.259</td><td>0.070</td><td>0.188</td><td></td><td></td><td></td><td>0.067</td><td>-0.001</td></tr><tr><td>3</td><td>GCDF</td><td>0.083</td><td>0.155</td><td>0.223</td><td>-0.216</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.043</td><td>0.029</td><td>0.367</td><td></td><td></td><td></td><td>0.080</td><td>0.001</td></tr><tr><td>3</td><td>GCDK</td><td>0.042</td><td>0.105</td><td>0.154</td><td>-0.148</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.011</td><td>0.012</td><td>0.225</td><td></td><td></td><td></td><td>0.046</td><td>0.001</td></tr><tr><td>4</td><td>GCD</td><td>0.438</td><td>0.472</td><td>0.534</td><td>0.583</td><td>-0.445</td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.225</td><td>0.066</td><td>0.171</td><td>0.167</td><td>0.166</td><td>0.159</td><td>0.180</td><td>0.073</td><td>-0.006</td></tr><tr><td>4</td><td>GCDF</td><td>0.111</td><td>0.176</td><td>0.233</td><td>0.282</td><td>-0.180</td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.043</td><td>0.034</td><td>0.337</td><td>0.330</td><td>0.323</td><td>0.305</td><td>0.369</td><td>0.084</td><td>-0.006</td></tr><tr><td>4</td><td>GCDK</td><td>0.102</td><td>0.169</td><td>0.209</td><td>0.246</td><td>-0.167</td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.034</td><td>0.028</td><td>0.266</td><td>0.265</td><td>0.250</td><td>0.230</td><td>0.311</td><td>0.072</td><td>-0.005</td></tr></tbody></table>

Note. Experiment 3 (recognition memory): subscripts 1-4 for parameter v correspond to conditions old words studied one time, old words studied two times, old words studied four times, and new words, respectively. Experiment 4 (lexical knowledge): subscripts 1-5 for parameters v and Te correspond to conditions very-low frequency words, low frequency words, medium frequency words, high frequency words, and pseudowords, respectively. GCD = gated cascade diffusion model; GCDF = gated cascade diffusion model with a filtering mechanism at the motor preparation level; GCDK = gated cascade diffusion model with a Kalman-Bucy filter at the motor preparation level.
<table><caption>Table C1</caption><caption>Parameters From the Raw Models (GCD, GCDF, and GCDK) Averaged Across Subjects for Experiments 1-4</caption><thead><tr><th>Exp</th><th>Model</th><th>v<sub>1</sub></th><th>v<sub>2</sub></th><th>v<sub>3</sub></th><th>v<sub>4</sub></th><th>v<sub>5</sub></th><th>k</th><th>dc</th><th>λ</th><th>χ</th><th>ξ</th><th>g</th><th>r</th><th>Te<sub>1</sub></th><th>Te<sub>2</sub></th><th>Te<sub>3</sub></th><th>Te<sub>4</sub></th><th>Te<sub>5</sub></th><th>Tr</th><th>x<sub>0</sub></th></tr></thead><tbody><tr><td>1</td><td>GCD</td><td></td><td></td><td></td><td></td><td>1.147</td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.085</td><td>0.045</td><td>0.271</td><td></td><td></td><td></td><td>0.079</td><td></td></tr><tr><td>1</td><td>GCDF</td><td></td><td></td><td></td><td></td><td>0.694</td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.055</td><td>0.024</td><td>0.193</td><td></td><td></td><td></td><td>0.066</td><td></td></tr><tr><td>1</td><td>GCDK</td><td></td><td></td><td></td><td></td><td>0.620</td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.045</td><td>0.019</td><td>0.084</td><td></td><td></td><td></td><td>0.050</td><td></td></tr><tr><td>2</td><td>GCD</td><td>0.020</td><td></td><td></td><td></td><td></td><td></td><td></td><td>-0.026</td><td></td><td></td><td></td><td>0.058</td><td>0.049</td><td>0.293</td><td></td><td></td><td></td><td>0.089</td><td>0.004</td></tr><tr><td>2</td><td>GCDF</td><td>0.015</td><td></td><td></td><td></td><td></td><td></td><td></td><td>-0.016</td><td>35.937</td><td></td><td></td><td>0.039</td><td>0.032</td><td>0.267</td><td></td><td></td><td></td><td>0.084</td><td>0.002</td></tr><tr><td>2</td><td>GCDK</td><td>0.013</td><td></td><td></td><td></td><td></td><td></td><td></td><td>-0.014</td><td></td><td></td><td></td><td>0.031</td><td>0.028</td><td>0.204</td><td></td><td></td><td></td><td>0.074</td><td>0.002</td></tr><tr><td>3</td><td>GCD</td><td>0.363</td><td>0.588</td><td>0.628</td><td>-0.594</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.259</td><td>0.070</td><td>0.188</td><td></td><td></td><td></td><td>0.067</td><td>-0.001</td></tr><tr><td>3</td><td>GCDF</td><td>0.083</td><td>0.155</td><td>0.223</td><td>-0.216</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.043</td><td>0.029</td><td>0.367</td><td></td><td></td><td></td><td>0.080</td><td>0.001</td></tr><tr><td>3</td><td>GCDK</td><td>0.042</td><td>0.105</td><td>0.154</td><td>-0.148</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.011</td><td>0.012</td><td>0.225</td><td></td><td></td><td></td><td>0.046</td><td>0.001</td></tr><tr><td>4</td><td>GCD</td><td>0.438</td><td>0.472</td><td>0.534</td><td>0.583</td><td>-0.445</td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.225</td><td>0.066</td><td>0.171</td><td>0.167</td><td>0.166</td><td>0.159</td><td>0.180</td><td>0.073</td><td>-0.006</td></tr><tr><td>4</td><td>GCDF</td><td>0.111</td><td>0.176</td><td>0.233</td><td>0.282</td><td>-0.180</td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.043</td><td>0.034</td><td>0.337</td><td>0.330</td><td>0.323</td><td>0.305</td><td>0.369</td><td>0.084</td><td>-0.006</td></tr><tr><td>4</td><td>GCDK</td><td>0.102</td><td>0.169</td><td>0.209</td><td>0.246</td><td>-0.167</td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.034</td><td>0.028</td><td>0.266</td><td>0.265</td><td>0.250</td><td>0.230</td><td>0.311</td><td>0.072</td><td>-0.005</td></tr></tbody></table>

Note. Experiment 3 (recognition memory): subscripts 1-4 for parameter v correspond to conditions old words studied one time, old words studied two times, old words studied four times, and new words, respectively. Experiment 4 (lexical knowledge): subscripts 1-5 for parameters v and Te correspond to conditions very-low frequency words, low frequency words, medium frequency words, high frequency words, and pseudowords, respectively. GCD = gated cascade diffusion model; GCDF = gated cascade diffusion model with a filtering mechanism at the motor preparation level; GCDK = gated cascade diffusion model with a Kalman-Bucy filter at the motor preparation level.
*(Appendices continue)*
*(Appendices continue)*
## Appendix D
### Additional Predictions From GCDF

#### Figure D1

*Additional Predictions From GCDF With Varying Levels of Leak $\lambda$ and Drift Rate $v$*

<figure><img src="image_12.png" /></figure>

*Note.* Apart from the leak parameter, simulations used the best fitting GCD parameters averaged across subjects reported by Servant et al. (2021) and 100,000 simulated trials per condition. (A) Predicted mean PMT and mean MT in correct trials. (B) Predicted between-trial correlation between PMT and MT in correct trials. (C) Predicted PMT quantile–MT quantile plot in correct trials. GCD = gated cascade diffusion model; GCDF = gated cascade diffusion model with a filtering mechanism at the motor preparation level; PMT = premotor time; MT = motor time. See the online article for the color version of this figure.
Appendix D

Additional Predictions From GCDF

Figure D1

*Additional Predictions From GCDF With Varying Levels of Leak $\lambda$ and Drift Rate $v$*

<figure><img src="image_13.png" /></figure>

*Note.* Apart from the leak parameter, simulations used the best fitting GCD parameters averaged across subjects reported by Servant et al. (2021) and 100,000 simulated trials per condition. (A) Predicted mean PMT and mean MT in correct trials. (B) Predicted between-trial correlation between PMT and MT in correct trials. (C) Predicted PMT quantile–MT quantile plot in correct trials. GCD = gated cascade diffusion model; GCDF = gated cascade diffusion model with a filtering mechanism at the motor preparation level; PMT = premotor time; MT = motor time. See the online article for the color version of this figure.
Figure D2

*Additional Predictions From GCDF With Varying Levels of Leak λ and Drift Rate v, and With Between-Trial Variability in Drift Rate (Normally Distributed With Mean v and Standard Deviation sv)*

<figure><img src="image_13.png" /></figure>

*Note.* Apart from the leak parameter, simulations used the best fitting GCD parameters averaged across subjects reported by Servant et al. (2021) and 100,000 simulated trials per condition. Parameter *sv* was fixed at .2. (A) Predicted mean PMT and mean MT in correct trials. (B) Predicted between-trial correlation between PMT and MT in correct trials. (C) Predicted PMT quantile–MT quantile plot in correct trials. GCD = gated cascade diffusion model; GCDF = gated cascade diffusion model with a filtering mechanism at the motor preparation level; PMT = premotor time; MT = motor time. See the online article for the color version of this figure.

*(Appendices continue)*
Figure D2

*Additional Predictions From GCDF With Varying Levels of Leak λ and Drift Rate v, and With Between-Trial Variability in Drift Rate (Normally Distributed With Mean v and Standard Deviation sv)*

<figure><img src="image_14.png" /></figure>

*Note.* Apart from the leak parameter, simulations used the best fitting GCD parameters averaged across subjects reported by Servant et al. (2021) and 100,000 simulated trials per condition. Parameter *sv* was fixed at .2. (A) Predicted mean PMT and mean MT in correct trials. (B) Predicted between-trial correlation between PMT and MT in correct trials. (C) Predicted PMT quantile–MT quantile plot in correct trials. GCD = gated cascade diffusion model; GCDF = gated cascade diffusion model with a filtering mechanism at the motor preparation level; PMT = premotor time; MT = motor time. See the online article for the color version of this figure.

*(Appendices continue)*
# Appendix E
## Methods for Experiments 2-4

### Experiment 2

#### Participants

Manipulations of numerosity produce smaller modulations of mean RT compared to motion coherence manipulations. Consequently, we increased the sample size from 18 to 24 subjects in order to maintain a reasonable amount of statistical power while keeping electrophysiological and modeling work in manageable proportions.

Twenty-four students (five men; mean age: 20.6) from the University of Franche-Comté took part in the experiment in exchange for course credits or as volunteers. All subjects met the following criteria: being 18-30 years old, being right-handed, having a normal or corrected vision, and having no history of motor, psychiatric, or neurological disorder. Subjects were not aware of the purpose of the experiment and provided written consent to participate. This study was approved by the ethical committee for research of the university (Agreement No. CERUBFC-2022-01-18-002). It was not preregistered.

#### Apparatus

The experiment took place in a dimly lit room. Subjects sat on a comfortable chair at a distance of 75 cm from a 34.7 × 19.5 cm² liquid crystal display monitor (resolution: 1920 × 1080; frame rate: 60 Hz). The experiment was programmed in Python, using functions from the PsychoPy library (Peirce et al., 2019). Response buttons were identical to those used in Experiment 1. Subjects' hands were faced palm-down, resting on a supportive cushion placed on their laps in order to minimize tonic muscular activity and maximize comfort.

#### Stimuli

For each trial, between 31 and 70 black dots were displayed on a gray background screen in random positions within a 10 x 10 virtual grid. Each dot was 0.24° in diameter. The horizontal and vertical separation between two adjacent dots (from center to center) was 1.15°.

#### Procedure

Participants were instructed to press the left button with their left thumb if they judged the number of dots displayed was less than or equal to 50, and the right button with their right thumb if they judged it was greater. Left responses to 31-50 dots and right responses to 51-70 dots were counted as correct. Participants were told not to count the dots but instead provide a global and rapid estimation of their number. Dots remained on the screen until the participant responded. An RT deadline was set to 4 s. If participants failed to respond by then, the message "Too late! Please respond faster." was displayed for 1.5 s. The intertrial interval was 1.5 s. Participants first completed a practice block of 40 trials, containing each of the 40 numerosity conditions presented in a random order. A feedback on performance ("correct response" or "incorrect response") was displayed for
# Appendix E
## Methods for Experiments 2-4

### Experiment 2

#### Participants

Manipulations of numerosity produce smaller modulations of mean RT compared to motion coherence manipulations. Consequently, we increased the sample size from 18 to 24 subjects in order to maintain a reasonable amount of statistical power while keeping electrophysiological and modeling work in manageable proportions.

Twenty-four students (five men; mean age: 20.6) from the University of Franche-Comté took part in the experiment in exchange for course credits or as volunteers. All subjects met the following criteria: being 18-30 years old, being right-handed, having a normal or corrected vision, and having no history of motor, psychiatric, or neurological disorder. Subjects were not aware of the purpose of the experiment and provided written consent to participate. This study was approved by the ethical committee for research of the university (Agreement No. CERUBFC-2022-01-18-002). It was not preregistered.

#### Apparatus

The experiment took place in a dimly lit room. Subjects sat on a comfortable chair at a distance of 75 cm from a 34.7 × 19.5 cm² liquid crystal display monitor (resolution: 1920 × 1080; frame rate: 60 Hz). The experiment was programmed in Python, using functions from the PsychoPy library (Peirce et al., 2019). Response buttons were identical to those used in Experiment 1. Subjects' hands were faced palm-down, resting on a supportive cushion placed on their laps in order to minimize tonic muscular activity and maximize comfort.

#### Stimuli

For each trial, between 31 and 70 black dots were displayed on a gray background screen in random positions within a 10 x 10 virtual grid. Each dot was 0.24° in diameter. The horizontal and vertical separation between two adjacent dots (from center to center) was 1.15°.

#### Procedure

Participants were instructed to press the left button with their left thumb if they judged the number of dots displayed was less than or equal to 50, and the right button with their right thumb if they judged it was greater. Left responses to 31-50 dots and right responses to 51-70 dots were counted as correct. Participants were told not to count the dots but instead provide a global and rapid estimation of their number. Dots remained on the screen until the participant responded. An RT deadline was set to 4 s. If participants failed to respond by then, the message “Too late! Please respond faster.” was displayed for 1.5 s. The intertrial interval was 1.5 s. Participants first completed a practice block of 40 trials, containing each of the 40 numerosity conditions presented in a random order. A feedback on performance ("correct response" or "incorrect response") was displayed for
1.5 s after each response. Practice trials were not considered in the analyses. Subjects then completed 30 blocks of 40 trials with a similar structure, except that no feedback was provided after each response. Blocks were separated by self-paced breaks. The experiment lasted about an hour.

## EMG Recordings and Signal Processing

The procedure used for EMG recordings and signal processing was similar to Experiment 1, except that EMG signals were epoched -0.5 s to 4 s relative to stimulus onset. Trials with a high level of noise were discarded from analyses (2.7% of trials on average; range 0%-11.7%).

## Models and Fit Procedure

The data were grouped into eight conditions represented by the mean number of dots N of each bin (33, 38, 43, 48, 53, 58, 63, 68). Following Ratcliff and McKoon (2018), we assumed that the drift rate v of GCD and GCDF is a linear function of N and the criterion (50):

$$v = dc + v_1(N - 50). \qquad (E1)$$

Parameter $v_1$ accounts for interindividual differences in discrimination performance. Parameter $dc$ (drift criterion) accounts for interindividual differences in the representation of the criterion. Without this parameter (i.e., assuming $dc = 0$), the representation of the criterion would correspond exactly to 50 dots for every subject, which is not realistic. Between-trial variability in drift rate is assumed to be normally distributed with mean v and standard deviation sv defined as follows:

$$sv = \eta_0 + \sigma_1 \sqrt{N^2 + 50^2}. \qquad (E2)$$

All parameters were fixed across numerosity conditions. We treated the starting point $x_0$ of the evidence accumulation process as a free parameter, resulting in seven (12) free parameters for the raw (full) GCD and eight (14) free parameters for the raw (full) GCDF.<fnref n="8" /> All parameters (except $dc$ and $x_0$) were constrained to be $\ge 0$. Between-trial variability parameters $sx_0$, $sTe$, $sTr$, and $s\lambda$ were constrained to not exceed 180% of $g$, $Te$, $Tr$, and $\lambda$, respectively. Parameter $sx_0$ was further constrained to not exceed $2*(g - |x_0|)$. Model selection statistics (AIC and BIC) were computed using Equations 11 and 12. By a two-sided binomial test, if 18 out of 24 subjects support one model over the other, then the result is significant.

## Experiment 3

### Participants

Twenty-four students (six men; mean age: 19.78) from the University of Franche-Comté took part in the experiment in exchange for course credits or as volunteers. All participants met the same inclusion criteria as for Experiment 2. Subjects were not aware of the

<footnote n="8">⁸Ratcliff and McKoon (2018) also evaluated a model variant in which subjects solve the task by comparing the number of dots to the number of blank spaces, and found similar fits. We found similar fits for this GCD and GCDF variant.</footnote>
1.5 s after each response. Practice trials were not considered in the analyses. Subjects then completed 30 blocks of 40 trials with a similar structure, except that no feedback was provided after each response. Blocks were separated by self-paced breaks. The experiment lasted about an hour.

## EMG Recordings and Signal Processing

The procedure used for EMG recordings and signal processing was similar to Experiment 1, except that EMG signals were epoched -0.5 s to 4 s relative to stimulus onset. Trials with a high level of noise were discarded from analyses (2.7% of trials on average; range 0%-11.7%).

## Models and Fit Procedure

The data were grouped into eight conditions represented by the mean number of dots N of each bin (33, 38, 43, 48, 53, 58, 63, 68). Following Ratcliff and McKoon (2018), we assumed that the drift rate v of GCD and GCDF is a linear function of N and the criterion (50):

$$v = dc + v_1(N - 50). \qquad (E1)$$

Parameter $v_1$ accounts for interindividual differences in discrimination performance. Parameter $dc$ (drift criterion) accounts for interindividual differences in the representation of the criterion. Without this parameter (i.e., assuming $dc = 0$), the representation of the criterion would correspond exactly to 50 dots for every subject, which is not realistic. Between-trial variability in drift rate is assumed to be normally distributed with mean v and standard deviation sv defined as follows:

$$sv = \eta_0 + \sigma_1 \sqrt{N^2 + 50^2}. \qquad (E2)$$

All parameters were fixed across numerosity conditions. We treated the starting point $x_0$ of the evidence accumulation process as a free parameter, resulting in seven (12) free parameters for the raw (full) GCD and eight (14) free parameters for the raw (full) GCDF.<fnref n="8" /> All parameters (except $dc$ and $x_0$) were constrained to be ≥ 0. Between-trial variability parameters $sx_0$, $sTe$, $sTr$, and $s\lambda$ were constrained to not exceed 180% of $g$, $Te$, $Tr$, and $\lambda$, respectively. Parameter $sx_0$ was further constrained to not exceed $2*(g - |x_0|)$. Model selection statistics (AIC and BIC) were computed using Equations 11 and 12. By a two-sided binomial test, if 18 out of 24 subjects support one model over the other, then the result is significant.

## Experiment 3

### Participants

Twenty-four students (six men; mean age: 19.78) from the University of Franche-Comté took part in the experiment in exchange for course credits or as volunteers. All participants met the same inclusion criteria as for Experiment 2. Subjects were not aware of the

<footnote n="8">⁸Ratcliff and McKoon (2018) also evaluated a model variant in which subjects solve the task by comparing the number of dots to the number of blank spaces, and found similar fits. We found similar fits for this GCD and GCDF variant.</footnote>
purpose of the experiment and provided written consent to participate. This study was approved by the ethical committee for research of the university (Agreement No. CERUBFC-2022-01-18-002). It was not preregistered.

## Apparatus

The apparatus was identical to Experiment 2.

## Stimuli

We selected a set of 1,058 French words (number of letters ranging from five to eight; *M* = 6.50; *SD* = 1.12) from the Lexique database (New et al., 2004). Word frequency ranged from one to six occurrences per million (*M* = 2.96, *SD* = 1.14). Words were presented in black against a gray background (font: Consolas) at the center of the screen. The height of the letters was 0.76°.

## Procedure

The experiment consisted of 23 blocks (one training block with a feedback on accuracy after each trial and 22 experimental blocks without feedback), separated by self-paced breaks. Each block consisted of a study phase and a test phase. During the study, participants were instructed to learn 25 words. The first two words served as fillers to control for primacy effects, and the last two words served as fillers to control for recency effects. Among the 21 remaining words, seven were studied one time, seven were studied two times, and seven were studied four times. Words were presented in a random order, at a pace of 1 s. The test phase occurred right after the study phase and consisted of 42 words (21 old words and 21 new words, presented in a random order). Participants were instructed to press the left or the right button with their left or right thumb depending on whether the word was old or new (stimulus-response mapping balanced across participants). Each test word remained on screen until the participant responded, or until a 4 s RT deadline. If participants failed to respond by then, the message “Too late! Please respond faster.” was displayed for 1.5 s. The intertrial interval was 1.5 s. Words presented in a block never appeared in another block (participants were made aware of this during task instructions). In addition, the assignment of words to blocks and conditions was randomly determined. The experiment lasted about an hour and a half.

## EMG Recordings and Signal Processing

The procedure used for EMG recordings and signal processing was similar to Experiment 2. Trials with a high level of noise were discarded from analyses (12.4% of trials on average; range 1.6%-25%).

## Models and Fit Procedure

Drift rate *v* and between-trial variability in drift rate *sv* were the only parameters free to vary between conditions. Similar to Experiment 2, we treated the starting point *x*₀ of the decision-making process as a free parameter, resulting in nine (16) parameters for the raw (full) GCD, and 10 (18) parameters for the raw (full) GCDF. All parameters (except drift rates and *x*₀) were constrained to be ≥ 0. Between-trial variability parameters *sx*₀,
purpose of the experiment and provided written consent to participate. This study was approved by the ethical committee for research of the university (Agreement No. CERUBFC-2022-01-18-002). It was not preregistered.

## Apparatus

The apparatus was identical to Experiment 2.

## Stimuli

We selected a set of 1,058 French words (number of letters ranging from five to eight; *M* = 6.50; *SD* = 1.12) from the Lexique database (New et al., 2004). Word frequency ranged from one to six occurrences per million (*M* = 2.96, *SD* = 1.14). Words were presented in black against a gray background (font: Consolas) at the center of the screen. The height of the letters was 0.76°.

## Procedure

The experiment consisted of 23 blocks (one training block with a feedback on accuracy after each trial and 22 experimental blocks without feedback), separated by self-paced breaks. Each block consisted of a study phase and a test phase. During the study, participants were instructed to learn 25 words. The first two words served as fillers to control for primacy effects, and the last two words served as fillers to control for recency effects. Among the 21 remaining words, seven were studied one time, seven were studied two times, and seven were studied four times. Words were presented in a random order, at a pace of 1 s. The test phase occurred right after the study phase and consisted of 42 words (21 old words and 21 new words, presented in a random order). Participants were instructed to press the left or the right button with their left or right thumb depending on whether the word was old or new (stimulus-response mapping balanced across participants). Each test word remained on screen until the participant responded, or until a 4 s RT deadline. If participants failed to respond by then, the message “Too late! Please respond faster.” was displayed for 1.5 s. The intertrial interval was 1.5 s. Words presented in a block never appeared in another block (participants were made aware of this during task instructions). In addition, the assignment of words to blocks and conditions was randomly determined. The experiment lasted about an hour and a half.

## EMG Recordings and Signal Processing

The procedure used for EMG recordings and signal processing was similar to Experiment 2. Trials with a high level of noise were discarded from analyses (12.4% of trials on average; range 1.6%-25%).

## Models and Fit Procedure

Drift rate *v* and between-trial variability in drift rate *sv* were the only parameters free to vary between conditions. Similar to Experiment 2, we treated the starting point *x*₀ of the decision-making process as a free parameter, resulting in nine (16) parameters for the raw (full) GCD, and 10 (18) parameters for the raw (full) GCDF. All parameters (except drift rates and *x*₀) were constrained to be ≥ 0. Between-trial variability parameters *sx*₀,
$sTe$, $sTr$, and $s\lambda$ were constrained to not exceed 180% of $g$, $Te$, $Tr$, and $\lambda$, respectively. Parameter $sx_0$ was further constrained to not exceed $2 * (g - |x_0|)$.

# Experiment 4

## Participants

Twenty-four students (four men; mean age: 21.00) from the University of Franche-Comté took part in the experiment in exchange for course credits or as volunteers. All participants met the same criteria as for Experiments 2 and 3. Subjects were not aware of the purpose of the experiment and provided written consent to participate. This study was approved by the ethical committee for research of the university (Agreement No. CERUBFC-2022-01-18-002). It was not preregistered.

## Apparatus

The apparatus was identical to Experiments 2 and 3.

## Stimuli

Four lists of French words (5-12 letters) of differing frequencies (high frequency: range 10-2,736 occurrences per million; medium frequency: range 2-5; low frequency: range 0.5-1; very-low frequency: range 0.01-0.1) were created using the Lexique database (New et al., 2004). To obtain the stimuli used in the present experiment, the lists underwent the following steps. First, all plural and feminine agreements were removed. Second, low and very-low frequency words were screened by two students, and any words they did not know were eliminated. Third, a pool of 408 words was pseudorandomly selected from each list, with the constraint of obtaining a homogeneous number of letters across pools. For each pool, 204 words were randomly selected to become pseudowords (i.e., pronounceable nonwords), created with the multilingual pseudoword generator Wuggy (Keuleers and Brysbaert, 2010). Pseudowords were screened by two other students to ensure that they were pronounceable and did not correspond to an existing word. This procedure resulted in four lists, each list comprising 204 words (four for practice and 200 for the experiment) and 204 pseudowords (four for practice and 200 for the experiment). The four students recruited for screening stimuli did not participate in the experiment. Statistics relative to frequency and number of letters for the final sample of words used in the experiment are provided in Table E1. Words were presented in black against a gray background (font: Consolas) at the center of the screen. The height of the letters was 0.76°.

## Procedure

Participants were instructed to press the left or the right button with their left or right thumb depending on whether the stimulus was a French word or not (stimulus-response mapping balanced across participants). Participants first performed a practice block of 32 trials (four words in each frequency level and 16 pseudowords) during which feedback on accuracy after each trial was provided and worked through 10 blocks of 160 trials (20 words in each frequency level and 80 pseudowords) with no feedback on accuracy. Blocks were separated by self-paced breaks. Each stimulus appeared once in the experiment.
$sTe$, $sTr$, and $s\lambda$ were constrained to not exceed 180% of $g$, $Te$, $Tr$, and $\lambda$, respectively. Parameter $sx_0$ was further constrained to not exceed $2 * (g - |x_0|)$.

# Experiment 4

## Participants

Twenty-four students (four men; mean age: 21.00) from the University of Franche-Comté took part in the experiment in exchange for course credits or as volunteers. All participants met the same criteria as for Experiments 2 and 3. Subjects were not aware of the purpose of the experiment and provided written consent to participate. This study was approved by the ethical committee for research of the university (Agreement No. CERUBFC-2022-01-18-002). It was not preregistered.

## Apparatus

The apparatus was identical to Experiments 2 and 3.

## Stimuli

Four lists of French words (5-12 letters) of differing frequencies (high frequency: range 10-2,736 occurrences per million; medium frequency: range 2-5; low frequency: range 0.5-1; very-low frequency: range 0.01-0.1) were created using the Lexique database (New et al., 2004). To obtain the stimuli used in the present experiment, the lists underwent the following steps. First, all plural and feminine agreements were removed. Second, low and very-low frequency words were screened by two students, and any words they did not know were eliminated. Third, a pool of 408 words was pseudorandomly selected from each list, with the constraint of obtaining a homogeneous number of letters across pools. For each pool, 204 words were randomly selected to become pseudowords (i.e., pronounceable nonwords), created with the multilingual pseudoword generator Wuggy (Keuleers and Brysbaert, 2010). Pseudowords were screened by two other students to ensure that they were pronounceable and did not correspond to an existing word. This procedure resulted in four lists, each list comprising 204 words (four for practice and 200 for the experiment) and 204 pseudowords (four for practice and 200 for the experiment). The four students recruited for screening stimuli did not participate in the experiment. Statistics relative to frequency and number of letters for the final sample of words used in the experiment are provided in Table E1. Words were presented in black against a gray background (font: Consolas) at the center of the screen. The height of the letters was 0.76°.

## Procedure

Participants were instructed to press the left or the right button with their left or right thumb depending on whether the stimulus was a French word or not (stimulus-response mapping balanced across participants). Participants first performed a practice block of 32 trials (four words in each frequency level and 16 pseudowords) during which feedback on accuracy after each trial was provided and worked through 10 blocks of 160 trials (20 words in each frequency level and 80 pseudowords) with no feedback on accuracy. Blocks were separated by self-paced breaks. Each stimulus appeared once in the experiment.
Participants were thus exposed to the same word and pseudoword stimuli. Stimuli were randomly assigned to blocks and presented in a random order within blocks. Each trial started with the presentation of the stimulus until the participant responded, or until a 4 s RT deadline. If participants failed to respond by then, the message “Too late! Please respond faster.” was displayed for 1.5 s. The intertrial interval was 1.5 s. Overall, the experiment lasted about an hour.

## EMG Recordings and Signal Processing

The procedure used for EMG recordings and signal processing was similar to Experiments 2 and 3. Trials with a high level of noise were discarded from analyses (10.4% of trials on average; range 0.06%-27.3%).

## Models and Fit Procedure

Drift rate ($v$), between-trial variability in drift rate ($sv$), and mean residual time added to predicted PMT ($Te$) were the only parameters free to vary between conditions. We treated the starting point $x_0$ of the evidence accumulation process as a free parameter, resulting in 14 (22) parameters for the raw (full) GCD and 15 (24) parameters for the raw (full) GCDF. All parameters (except drift rates and $x_0$) were constrained to be $\ge 0$. Between-trial variability parameters $sx_0$, $sTe$, $sTr$, and $s\lambda$ were constrained to not exceed 180% of $g$, $Te$, $Tr$, and $\lambda$, respectively. Parameter $sx_0$ was further constrained to not exceed $2 * (g - |x_0|)$.

<caption>**Table E1**</caption>

*Statistics Relative to Frequency and Number of Letters for the Sample of Words Used in Experiment 4*

<table><thead><tr><th rowspan="2">Word frequency condition</th><th colspan="2">Occurrences per million</th><th colspan="2">Letters</th></tr><tr><th>M</th><th>SD</th><th>M</th><th>SD</th></tr></thead><tbody><tr><td>High frequency words</td><td>77.26</td><td>142.37</td><td>7.05</td><td>1.70</td></tr><tr><td>Medium frequency words</td><td>3.32</td><td>0.89</td><td>7.03</td><td>1.66</td></tr><tr><td>Low frequency words</td><td>0.72</td><td>0.15</td><td>7.05</td><td>1.70</td></tr><tr><td>Very low frequency words</td><td>0.04</td><td>0.03</td><td>7.05</td><td>1.69</td></tr></tbody></table>
Participants were thus exposed to the same word and pseudoword stimuli. Stimuli were randomly assigned to blocks and presented in a random order within blocks. Each trial started with the presentation of the stimulus until the participant responded, or until a 4 s RT deadline. If participants failed to respond by then, the message “Too late! Please respond faster.” was displayed for 1.5 s. The intertrial interval was 1.5 s. Overall, the experiment lasted about an hour.

## EMG Recordings and Signal Processing

The procedure used for EMG recordings and signal processing was similar to Experiments 2 and 3. Trials with a high level of noise were discarded from analyses (10.4% of trials on average; range 0.06%-27.3%).

## Models and Fit Procedure

Drift rate ($v$), between-trial variability in drift rate ($sv$), and mean residual time added to predicted PMT ($Te$) were the only parameters free to vary between conditions. We treated the starting point $x_0$ of the evidence accumulation process as a free parameter, resulting in 14 (22) parameters for the raw (full) GCD and 15 (24) parameters for the raw (full) GCDF. All parameters (except drift rates and $x_0$) were constrained to be $\ge 0$. Between-trial variability parameters $sx_0$, $sTe$, $sTr$, and $s\lambda$ were constrained to not exceed 180% of $g$, $Te$, $Tr$, and $\lambda$, respectively. Parameter $sx_0$ was further constrained to not exceed $2 * (g - |x_0|)$.

<caption>Table E1</caption>

*Statistics Relative to Frequency and Number of Letters for the Sample of Words Used in Experiment 4*

<table><thead><tr><th rowspan="2">Word frequency condition</th><th colspan="2">Occurrences per million</th><th colspan="2">Letters</th></tr><tr><th>M</th><th>SD</th><th>M</th><th>SD</th></tr></thead><tbody><tr><td>High frequency words</td><td>77.26</td><td>142.37</td><td>7.05</td><td>1.70</td></tr><tr><td>Medium frequency words</td><td>3.32</td><td>0.89</td><td>7.03</td><td>1.66</td></tr><tr><td>Low frequency words</td><td>0.72</td><td>0.15</td><td>7.05</td><td>1.70</td></tr><tr><td>Very low frequency words</td><td>0.04</td><td>0.03</td><td>7.05</td><td>1.69</td></tr></tbody></table>