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Humans Optimize Decision-Making by Delaying Decision Onset

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Why do humans make errors on seemingly trivial perceptual decisions? It has been shown that such errors occur in part because the decision process (evidence accumulation) is initiated before selective attention has isolated the relevant sensory information from salient distractors. Nevertheless, it is typically assumed that subjects increase accuracy by prolonging the decision process rather than delaying decision onset. To date it has not been tested whether humans can strategically delay decision onset to increase response accuracy. To address this question we measured the time course of selective attention in a motion interference task using a novel variant of the response signal paradigm. Based on these measurements we estimated time-dependent drift rate and showed that subjects should in principle be able trade speed for accuracy very effectively by delaying decision onset. Using the time-dependent estimate of drift rate we show that subjects indeed delay decision onset in addition to raising response threshold when asked to stress accuracy over speed in a free reaction version of the same motion-interference task. These findings show that decision onset is a critical aspect of the decision process that can be adjusted to effectively improve decision accuracy.
represents a simplified schematic of the problems that arise when decisions are made in the presence of salient but irrelevant distractors. The lowest panel represents a quick overview of the relevant processing stages. The time-course of the sensory representation is determined by afferent delays, the time it takes for sensory evidence to develop stimulus-selective responses, and the time it takes selective attention to extract the relevant sensory information from salient distractors. The timing of the decision-making stage is determined by the onset of the integration process and its termination. The duration of the last stage of processing is determined by the efferent delays. For the current purposes, we assume that the afferent delays as well as the delay for stimulus-selective sensory information to reach the decision stage is hard-wired and cannot be changed through cognitive control. However, we test the possibility that the onset of the decision process may be under cognitive control. The middle panel provides a more detailed look at the mix of momentary sensory information available to the decision process as a function of time: the initial phase is dominated by random internal fluctuations or the first pulse of sensory information that is not stimulus selective (grey), the second phase is dominated by physically salient stimuli (orange) and the third phase is dominated by the task-relevant stimuli, regardless of salience (blue). The time of transition from the first to the second phase is determined by afferent delays, the transition from the second to the third phase depends on how quickly selective attention can be allocated to the target. The top panel examines the effects of adjusting decision onset: if the decision process is initiated early, it will integrate information from physically salient stimuli that may or may not be relevant for the current task. If decisions are initiated late, response latencies may be prolonged unnecessarily. doi:10.1371/journal.pone.0089638.g001
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Humans Optimize Decision-Making by Delaying Decision
Onset
Tobias Teichert
1,3
*, Vincent P. Ferrera
1
, Jack Grinband
2
1Department of Neuroscience, Columbia University, New York, New York, United States of America, 2Department of Radiology, Columbia University, New York, New York,
United States of America, 3Department of Psychiatry, University of Pittsburgh, Pittsburgh, Pennsylvania, United States of America
Abstract
Why do humans make errors on seemingly trivial perceptual decisions? It has been shown that such errors occur in part
because the decision process (evidence accumulation) is initiated before selective attention has isolated the relevant
sensory information from salient distractors. Nevertheless, it is typically assumed that subjects increase accuracy by
prolonging the decision process rather than delaying decision onset. To date it has not been tested whether humans can
strategically delay decision onset to increase response accuracy. To address this question we measured the time course of
selective attention in a motion interference task using a novel variant of the response signal paradigm. Based on these
measurements we estimated time-dependent drift rate and showed that subjects should in principle be able trade speed
for accuracy very effectively by delaying decision onset. Using the time-dependent estimate of drift rate we show that
subjects indeed delay decision onset in addition to raising response threshold when asked to stress accuracy over speed in a
free reaction version of the same motion-interference task. These findings show that decision onset is a critical aspect of the
decision process that can be adjusted to effectively improve decision accuracy.
Citation: Teichert T, Ferrera VP, Grinband J (2014) Humans Optimize Decision-Making by Delaying Decision Onset. PLoS ONE 9(3): e89638. doi:10.1371/
journal.pone.0089638
Editor: Joy J. Geng, University of California, Davis, United States of America
Received August 7, 2012; Accepted January 24, 2014; Published March 5, 2014
Copyright: ß2014 Teichert et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: The research was funded by the German Research Foundation (DFG, Te819/1-1 to TT) and the National Institutes of Health (NIH-MH059244 to VPF). The
funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing Interests: The authors have declared that no competing interests exist.
* E-mail: teichert@pitt.edu
Introduction
Humans have the remarkable ability to make fast and accurate
decisions in a seemingly endless number of different tasks [1–3].
However, in some situations it may be unnecessary, undesirable or
even counterproductive to initiate a decision. Despite intense
investigation of virtually every other component of the decision
process, it still not clear whether decision onset is under cognitive
control, or whether decisions are initiated automatically by the
presence of an appropriate sensory stimulus. Here we tested
whether humans will delay the onset of a decision process to
increase response accuracy in a situation when it is beneficial to
ignore the initial pulse of sensory evidence that can be dominated
by salient rather than task-relevant information.
Most decisions are based on a subset of stimuli that appears in
close temporal and/or spatial proximity to other, task-irrelevant
information. Often, the irrelevant stimuli interfere with the
processing of the relevant stimuli especially when the distractors
are physically salient [4–7] and/or are associated with behavioral
responses that are similar to those of the current task [1,2]. Thus,
accurate decision-making critically depends on top-down attention-
al selection that enhances task-relevant and/or suppresses irrelevant
information [8,9]. The engagement of selective attention takes time
[10,11], and it has been suggested that errors occur in part because
the decision process (evidence accumulation) is initiated before
selective attention has isolated task-relevant sensory information
from salient but irrelevant distractors [11]. Nevertheless, it has never
been suggested that subjects might increase accuracy by delaying
the onset of the decision process (the onset mechanism, Figure 1). This
possibility is not precluded by the generally accepted finding that
subjects trade speed for accuracy by increasing the amount of
evidence that will trigger a response (the threshold mechanism) [12–15],
as both mechanisms could be used in parallel.
Many studies of decision-making have presented an isolated
stimulus on a uniform background. The lack of distractors
minimizes the need for selective attention and allows the simplifying
assumption that the rate of evidence accumulation (i.e. drift rate)
stays constant over the time course of the decision. In such
conditions, the onset of the decision process does not affect response
accuracy and cannot be distinguished from factors that influence
non-decision time. Decision onset only has an effect on accuracy if
the quality of the sensory information changes over time, as may
happen when selective attention gradually isolates the relevant
information from among distractors. The more salient the distractor
and the longer it takes to re-allocate attention to the target stimulus,
the more beneficial it will be to delay decision onset.
To test whether subjects are able to delay decision onset, it is
necessary to (1) use a task in which drift rate is known to change
over time and (2) explicitly measure its time-course in order to
predict the effects of decision onset on accuracy. While it is
generally accepted that selective attention leads to changes of drift
rate in Stroop-like response interference tasks [11,16,17], explicit
quantitative measurements of the time course of selective attention
within these tasks have been difficult to acquire. Without these
measurements, it is not possible to quantify the effects of decision
onset and test whether subjects delay decision onset to increase
response accuracy.
PLOS ONE | www.plosone.org 1 March 2014 | Volume 9 | Issue 3 | e89638
In the current set of experiments we present two novel methods:
(1) a motion interference task which requires feature-based
selective attention and has a non-stationary drift rate and (2) the
cyclic deadline paradigm which allows us to estimate the time-
course of selective attention and the resulting changes in drift rate.
This enabled us to answer two main questions regarding the role
of decision onset for optimal decision-making: (1) Is delaying
decision onset an effective way to increase response accuracy? (2)
Do humans delay decision onset when asked to stress decision
accuracy over speed? The answers will shed light on an important
but rarely studied aspect of the decision process, namely its
initiation. In particular, it will show whether decisions are initiated
automatically by the presence of appropriate stimuli, or whether
the time of decision onset can be controlled to meet task
requirements.
Methods
Ethics Statement
All participants provided written signed informed consent after
explanation of study procedures. Experiments and study protocol
were approved by the Institutional Review Boards of Columbia
University and New York State Psychiatric Institute.
Experimental overview
Our goal was to determine whether decision onset is under
cognitive control and used to adjust speed and accuracy. We
developed a motion interference task in which two sets of moving
dots were spatially superimposed. This task requires that feature-
based selective attention identify the direction of motion of the
target dots, while ignoring a set of more salient distractor dots. Our
study was divided into three parts. First, we measured reaction
times (RT) and accuracy when subjects were asked to stress either
speed or accuracy (RT paradigm). Second, using a novel
response signal paradigm (cyclic deadline or CD paradigm, see
below), we measured accuracy as a function of how much time
subjects were allowed to process the stimulus before being forced
to respond. Using a modified diffusion model, data from the CD
paradigm allowed us to estimate the duration of the stimulus
selection process as well as drift rate as function of time from
stimulus onset. Third, using the time-dependent drift rate
estimated from the cyclic deadline paradigm, we modeled RT
and accuracy that was previously observed in the RT paradigm.
Figure 1. represents a simplified schematic of the problems that arise when decisions are made in the presence of salient but
irrelevant distractors. The lowest panel represents a quick overview of the relevant processing stages. The time-course of the sensory
representation is determined by afferent delays, the time it takes for sensory evidence to develop stimulus-selective responses, and the time it takes
selective attention to extract the relevant sensory information from salient distractors. The timing of the decision-making stage is determined by the
onset of the integration process and its termination. The duration of the last stage of processing is determined by the efferent delays. For the current
purposes, we assume that the afferent delays as well as the delay for stimulus-selective sensory information to reach the decision stage is hard-wired
and cannot be changed through cognitive control. However, we test the possibility that the onset of the decision process may be under cognitive
control. The middle panel provides a more detailed look at the mix of momentary sensory information available to the decision process as a function
of time: the initial phase is dominated by random internal fluctuations or the first pulse of sensory information that is not stimulus selective (grey), the
second phase is dominated by physically salient stimuli (orange) and the third phase is dominated by the task-relevant stimuli, regardless of salience
(blue). The time of transition from the first to the second phase is determined by afferent delays, the transition from the second to the third phase
depends on how quickly selective attention can be allocated to the target. The top panel examines the effects of adjusting decision onset: if the
decision process is initiated early, it will integrate information from physically salient stimuli that may or may not be relevant for the current task. If
decisions are initiated late, response latencies may be prolonged unnecessarily.
doi:10.1371/journal.pone.0089638.g001
Optimal Decision-Making and Decision Onset
PLOS ONE | www.plosone.org 2 March 2014 | Volume 9 | Issue 3 | e89638
Our results show that the onset mechanism can be a more effective
way to trade speed for accuracy than the threshold mechanism
and that subjects implement both mechanisms during perceptual
decision-making.
Experimental setup
The experiments were performed on two MacBook Pro
computers, with 13 and 17-inch screens. Individual subjects were
tested consistently in one of the two setups. The task was
programmed and executed with Matlab2009a (www.mathworks.
com) using Psychtoolbox3 (www.psychtoolbox.org). Experiments
were conducted in a dark experimental room. Screen resolution
was set to 1280 by 800 pixels. Viewing distance was 24 inches.
Subjects
A total of 13 subjects performed the RT paradigm. One of the
13 subjects was an author of the study. The other 12 subjects were
naı
¨ve to the purpose of the study. Six of these subjects (1 author
and 5 naı
¨ve subjects) went on to the cyclic deadline paradigm. In
addition, a seventh subject (another one of the authors) performed
the cyclic deadline task without participating in the RT paradigm.
In summary, a total of seven human subjects (1 female, 5 naı
¨ve),
between 22 and 41 years old (mean: 30 years), participated in the
cyclic deadline paradigm. Subjects 1 and 2 corresponded to two of
the authors of the study, subjects 3-7 were naı
¨ve. A smaller
number of subjects was used in the CD paradigm because (1) data
collection in this task is very time-intensive and (2) there was less
variability between subjects, thus reducing the need for a bigger
sample. Results from the CD paradigm may be less variable
because the paradigm minimized the range of available strategies
and their impact on the results.
The motion-interference task
Subjects viewed stimuli that consisted of two spatially superim-
posed streams of moving random dots. One stream was darker,
and the other brighter than the uniform grey background [18].
Prior to stimulus onset, a luminance cue indicated which dot-
stream was to be attended. The subjects indicated the direction of
motion of the target dots with a button press of the left or the right
index finger while ignoring the distractor dots. The distractor dots
moved either in the same direction (congruent condition), the
opposite direction (incongruent condition), or orthogonal to the
target dots (neutral condition). For all trials, the distractor dots had
higher contrast relative to background than the target dots. This
ensured that the distractor motion was more salient than the target
motion [19,20], making selective attention necessary for the
successful performance of the task. The task was presented to the
subjects both in the context of the cyclic deadline paradigm and as
a free reaction time task.
Stimuli. The physical parameters of the dots were set such that
the task could be performed with greater than 99% accuracy in the
absence of distractor dots. Luminance value of the background
was set to the mean luminance of the monitor. The luminance of
the target dots was either 32% above (‘‘white’’ dots) or below
(‘‘black’’ dots) the mean luminance. Distractor dots had luminance
values equal to the maximum (‘‘white’’) or minimum (‘‘black’’)
luminance of the monitor. Motion coherence was set to 1.0 for
both target and distractor dots. Each dot stream consisted of 50
dots. All dots had a lifetime of 30 frames. Dots were presented
within a 128 pixel wide circular aperture. Any dot that moved
outside the aperture was replotted within the aperture at a
randomly selected position. A stationary, constantly illuminated
fixation dot was presented in the center of the aperture.
Free reaction time (RT) paradigm. In the free reaction
time version of the task (RT paradigm), subjects were asked to
perform the motion-interference task either as quickly as possible
(speed instruction) or as accurately as possible (accuracy instruction).
Subjects performed 2 blocks of 162 trials each for the two speed-
accuracy instructions. The order of the speed and accuracy block
was randomized between subjects. It is important to note that in
both conditions, subjects were free to respond at any time after
stimulus onset.
Cyclic deadline (CD) paradigm. In the cyclic deadline
paradigm, trials were presented at regular intervals once every two
seconds (Figure 2, see also [21]). The cyclic nature of the task was
conveyed to the subjects by regular clicks that occurred once every
second. The cue indicating which stimulus to attend coincided
with the first click. The dot stimuli appeared at varying times prior
to the second click and disappeared in time with the second click.
Subjects were required to respond at the time of the second click,
without regard to how long the stimulus had been on the screen.
Viewing duration was manipulated between blocks of 60 trials
lasting from 1 to 30 frames (16.7–500 ms).
Training. Prior to the RT paradigm, subjects performed one
practice run to acquaint them with the task. The cyclic deadline
paradigm was more challenging and required several training
sessions. In the initial training sessions they learned to perform the
task with very long viewing times (500 ms) until reaching a
criterion of more than 95% correct responses for all trial types.
Subsequent training sessions were performed with very short
viewing times (#83 ms) to accustom subjects to respond at the
required deadline even when they could not acquire sufficient
information to perform the task correctly. In this case, subjects
were required to respond randomly with either the left or right
index finger. Training continued until the standard deviation of
the response was ,50 ms. In the final stage of training, subjects
performed the task with viewing times ranging from 16.7 to
500 ms.
Definitions
In the cyclic deadline task, intended processing time was defined as
the duration that subjects were allowed to process the stimulus
before being required to respond. This value was identical to the
duration of the stimulus on the screen. Actual processing time (PT) was
defined as the time of the response minus the time of stimulus
onset. Thus, PT represents the intended processing time plus trial-
to-trial variability in response time. In the free reaction time
version of the task, we use the term reaction time (RT) when referring
to the same quantity, i.e. the time between stimulus onset and
response. The use of different abbreviations is meant to emphasize
whether response time was under the subject’s (RT) or experi-
menter’s (PT) control. Trials were grouped according to the
direction of the distractor dots relative to the target dots
(congruent, incongruent, and neutral). Trials with processing
times outside a window of 6
.two standard deviations around the
mean processing time for the corresponding condition were
excluded from the analysis.
The biased competition model of decision-making
Overview. We used a simple, physiologically inspired com-
putational model with 6 free parameters to fit the behavioral data
from the cyclic deadline paradigm (Figure 3 and Table 1). After
determining several key variables based on the fits to the cyclic
deadline paradigm, the model was expanded to explain accuracy
and RT distributions in the RT paradigm. The model consisted of
rate-coding units distributed in four layers that could be grouped
into two luminance and two direction-of-motion channels.
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Computational units in the input layer were selective for
luminance contrast and had temporal impulse responses that
converted the boxcar inputs into realistic neural dynamics. The
second layer simulated biased competition between the two
luminance channels. Units in the third layer were grouped into
two motion channels that received inputs from both luminance
channels. Information from the two luminance channels was
combined within each motion channel and passed through a non-
linearity. The fourth layer integrated the difference of the output
of the two motion channels over time. The input to the fourth
layer could be shunted by a gate that restricts the flow of
information to the integrator units (temporal gating). Overall, the
model is conceptually similar to other existing models of
interference tasks [22] with the exception that the time course of
competition between the luminance channels is directly deter-
mined by three explicit model parameters rather than indirectly
through the weights and temporal dynamics of recurrent
connections. Our modeling efforts are most closely related to a
recent model by White and colleagues [16]. The key difference is
the presence of the temporal gate that was not present in the
White model. With few exceptions [23,24], the majority of
decision models do not include a gating parameter. In the
particular case of decision-making under conflict, we are not
aware of any model that uses temporal gating.
Layer 1 – temporal dynamics. The units in layer 1 received
input from the two streams of dot-motion that were modeled as
box-car functions representing the presence or absence of the dots
on the screen. The amplitude of the boxcar was set to the absolute
value of the luminance contrast. Following standard procedure
[25] the visual input was smoothed by convolution with a gamma
kernel. For the gamma kernel we chose a shape parameter of 7
and scale parameter of 6 ms to provide a qualitative approxima-
tion to response properties of sensory neurons in early visual cortex
[26]. These values (as well as all other fixed parameter values
Figure 2. Cyclic Deadline Task. (A) A cue instructed subjects to attend to one of two streams of coherently moving random dots and report its
direction of motion by pressing a button with their left or right index finger. The relevant stream of target dots was either lighter than the
background, in which case the distractor was black, or darker than the background, in which case the distractor was white. The distractor dots could
move either in the same or opposite direction as the target (congruent and incongruent condition). In addition, the distractor could move upwards,
i.e. orthogonal to the axis of motion of the target dots (neutral condition). (B/C) The task was performed in a cyclic manner requiring a response from
the subject once every 2 seconds. The time of the intended response was indicated by an auditory click. Clicks were presented once every second to
convey a stronger sense of rhythm, but responses were only required on every other click, following the cue and stimulus presentation. Stimulus
duration was randomized between blocks of trials.
doi:10.1371/journal.pone.0089638.g002
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Figure 3. Biased competition model. The model combines two basic neural mechanisms: stimulus selection via biased competition between
different luminance channels (layer 2) and the reduction of noise by integrating over time (layer 4) with a total of 6 free parameters: 3 describing
biased competition, 1 describing the non-linear neural contrast response function, 1 scaling parameter, and 1 parameter describing non-decision
related delays. (Layer 1) The input to the system consists of two boxcar functions that indicate the presence of the two moving random dot patterns
with positive (white arrows) and negative luminance contrast (black arrows). In the first stage these inputs are filtered with a gamma-kernel to yield
realistic temporal dynamics for the encoding of visual information by sensory neurons. (Layer 2) Biased competition between mutually inhibitory
luminance channels is implemented as multiplicative weights s(t) for the target luminance and 1 - s(t) for the distractor where 0#s(t)#1. Prior to
stimulus onset, the weights of both luminance channels are equal (i.e. 0.5). To simulate the development of the biased competition in favor of the
target luminance (black-and-white inset in layer 2), the weight of the target stimulus increases from 0.5 to an asymptote. Three parameters determine
the time course of the competition: the time of the transition (t), the speed of the transition (s), and the asymptote (a). (Layer 3) The information from
each luminance channel is routed to both motion channels. A stimulus elicits activity only if it matches the preferred direction of the motion channel
(i.e. leftward or rightward motion). Activity from both luminance channels is summed within each motion channel. To simulate physiological neuronal
responses, the activity is passed through a non-linear, Naka-Rushton contrast response function. (Layer 4) The input to the integration stage is the
difference of the output of the right and leftward motion channel. In addition, neural noise is added in the form of a continuous Gaussian white noise
with a standard deviation of 1 arbitrary unit per second. The percentage of correct responses as a function of time is calculated as the mass of the
integrator above zero. When modeling the free reaction time version of the task, upper and lower response thresholds are included in the model. A
decision is aborted and considered correct/incorrect when the diffusion process reaches the positive/negative bound. In addition, the time of
integration onset t
0
is assumed to be variable and under cognitive control.
doi:10.1371/journal.pone.0089638.g003
Table 1. List of the 10 parameters of the biased competition model of decision-making.
Cyclic deadline
paradigm
Reaction time
paradigm Valid Range Description
Non-decision time, ndt [ms] free free 0–500 Afferent and efferent delays in the system. Difference in non-
decision time between tasks/conditions were assumed to be
caused by differences of efferent delays
Onset of stimulus
selection process
t
[ms]
free fixed from CD paradigm 0–500 Defines when selective attention starts isolating the target
stimulus
Duration of stimulus
selection process
s
[ms]
free fixed/free (in some
versions)
0–500 Defines how long selective attention needs to isolate the target
stimulus
Asymptote of stimulus
selection process
a
free fixed from CD paradigm 0.5–1 Defines how thoroughly selective attention will isolate the target
stimulus
Contrast response
parameter
I
in
free fixed from CD paradigm 0–1 Defines the semi-saturation point of the contrast response function
Shape parameter of contrast
response, q
fixed/free in one
variant
fixed from CD paradigm 0.01–10.0 Defines the shape of the contrast response function. Fixed to 2
unless mentioned otherwise
Signal-to-noise ratio free fixed from cyclic task 0–100 Scalar that scales signal strength to the arbitrarily chosen noise
level of 1 au
2
/sec
Starting point variability,
Var[X(t
0
)]
0 fixed/free (in some
versions)
0–1 The variability of the integrator unit at the time of decision onset
Response threshold
B
NA free 0–10 Threshold for response initiation –
the threshold mechanism
Decision onset
t
0
[ms] NA free 0–500 Onset of integration of sensory evidence –
the onset mechanism
By default, six parameters were used to model the data from the CD paradigm. The top four bold-faced parameters are the core components of the model that define
how drift rate changes as a function of time from stimulus onset. The lower two bold-faced parameters were introduced to model behavior in the RT paradigm. Two
additional parameters (q and Var[X(t
0
)]) were allowed to vary in certain exploratory analyses.
doi:10.1371/journal.pone.0089638.t001
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described below) were never subjected to any optimization
procedure and were selected prior to the actual data analysis.
Layer 2 – biased competition. Layer 2 consisted of units
selective for either positive or negative luminance contrast and
mediated the biased competition between them. To that aim,
activity in units coding the target luminance was multiplied by the
attentional selection term s(t) with 0,s(t),1; activity in units
preferring the distractor luminance were multiplied by 1 - s(t).
Whenever s(t) was equal to 0.5, both luminance channels were
weighted equally. By setting s(t) to 1, the output of layer 2 was
determined exclusively by the target stimulus. This operation was
used to mimic biased competition between the two luminance
channels and can be thought of as a time-dependent weighting of
the two luminance channels. Note that the overall sum of the two
weights always added to 1. This is reminiscent of neurons in early
visual cortex that respond with intermediate firing rates when two
stimuli in their receptive field receive are attended to different
degrees [10].
Of particular importance was the time course of the selection
term s(t). By default s(t) was set to 0.5 at the beginning of a trial,
but it was allowed to increase towards an asymptote 0#a#1over
the time course of each trial. The transition from 0.5 to awas
modeled by a Gaussian distribution function Wthat was scaled by
the term a- 0.5 and offset by 0.5:
s(t)~0:5z(a{0:5)Wt{t
s
 ð1Þ
In equation (1), tindicates the halfway transition point between
no and full stimulus selection, and sdetermines how fast the
transition occurs. The asymptote adetermines how completely the
target stimulus is selected during the biased competition. We are
certain that other functions can also be used to model the temporal
dynamics of the selection process. Most likely, any sigmoidal
function with three parameters (asymptote, mean, and width)
would provide a reasonably good fit. Though we could have
estimated the three parameters of the selection process using the
single cell data of Desimone and colleagues [10], the evidence in
favor of the biased competition approach would be much stronger
if we were able to recover similar selection parameters directly
from our behavioral data. We also experimented with asymmetric
four-parameter sigmoidal functions, but were not convinced that
our data allowed us to fit the fourth parameter with sufficient
reliability.
Layer 3 – motion processing. Layer 3 consisted of two units
selective for left- and rightward motion, respectively. An implicit
third unit selective for upward motion was not explicitly modeled,
as in our simple framework its activity would not affect the
integrator unit in Layer 4 and hence, would not affect the output
of the model. The units in each motion channel received input
from both of the layer 2 luminance channels. The inputs were
filtered with a simplistic direction-selective receptive field: if the
direction of motion of the dots matched the preferred direction of
the unit, its activity was multiplied by 1; otherwise it was multiplied
by 0. The model could easily be expanded to include more realistic
speed-tuning profiles. However, at this point we tried to keep the
model as simple as possible and we do not believe that adding
realistic tuning curves would change the main results and
conclusions. Consequently, each stream of dots elicited activity
in one of the four joint direction and contrast-selective input
pathways to layer 3. The activity of the two luminance channels
was summed within each motion channel. The activity within each
motion channel was then divisively normalized using a Naka-
Rushton function:
Y(t)~½y(t)q
½y(t)qzIin
ð2Þ
The Naka-Rushton function is a standard non-linear term used
to model the cortical gain control in a variety of settings
[25,27,28]. The exponent determines the shape of the non-
linearity, typically taking a value of ,2 [25]. To simplify the model
and reduce the number of free parameters, we fixed qto a value of
2. In one follow-up analysis we fit qto the population data and
recovered a value of 1.31. Using this value rather than q=2, did
not change the main findings regarding decision onset; thus for all
remaining analyses we allowed qto remain fixed. The divisive
inhibition term I
in
was a free parameter of the model. (I
in
)
1/q
controls the midpoint of the saturation and is also referred to as the
semi-saturation point. The smaller I
in
, the earlier the neurons
saturate their firing rate. The output of layer 3 and the effect of I
in
is illustrated in Figure S1.
Layer 4 – integration of evidence. Layer 4 consisted of a
single integrator unit that received input from the two layer 3
units. The inputs from the two layer 3 units had opposite signs.
The sign of the unit selective for the direction of motion of the
target was arbitrarily set to +1 and vice verse. The output of the
layer 4 unit was determined as integration over time of the two
inputs plus a noise term:
X(t)~ð
t
t0
jYT(t){YT
ðÞzn(t)dtð3Þ
In equation (3), the subscripts Tand
TTdenote units with
direction preference equal and opposite to the direction of motion
of the target dots. The noise term n(t) was modeled as a white noise
process with mean 0 and standard deviation of 1 au/sec. jis a
scalar gain term that adjusts the amplitude of the inputs to the
arbitrarily chosen variability of the noise term. jis one of the free
parameters of the model. For a summary of all parameters of the
model see Table 1.
Equation 3 describes a straightforward extension of the standard
drift diffusion model (DDM) to situations with time-dependent
drift rate. The only new component that is not present in the
standard DDM is the variable t
0,
which refers to the time at which
the integrator starts its integration process and can be thought of as
a gate that regulates the flow of information to the integrator
indicating when the decision process is initiated. Alternatively, t
0
can represent the time at which the value of the integrator is reset.
This reset may be related to the dip in firing rate that can be
observed in LIP neurons immediately after the onset of the
relevant sensory information [29]. The effect of the reset was
modeled by setting the state of the integrator at time t
0
equal to a
Gaussian distribution with mean 0 and standard deviation sigma.
In the cyclic deadline paradigm, subjects could anticipate the
onset of the relevant stimuli and were encouraged to make the
most use of the available sensory information thereby allowing us
to assume that they began integrating information at the earliest
possible time. To model data from the cyclic deadline task, the
decision onset (t
0
) was therefore set to the time at which stimulus
selective information first reached the integrator unit. This
assumption is consistent with many diffusion models that do not
have an explicit gate parameter t
0
, but implicitly assume that
Optimal Decision-Making and Decision Onset
PLOS ONE | www.plosone.org 6 March 2014 | Volume 9 | Issue 3 | e89638
integration starts as soon as information is available. Starting-point
variability was set to zero to model the data from the cyclic
deadline paradigm.
To model response accuracy in the cyclic deadline paradigm,
we made two assumptions: (1) the decision variable X(t) is not
bounded by a decision threshold, and (2) subjects have access to
the decision variable even though the integration has not
terminated at a response threshold. This was implemented by
allowing the model to choose the correct response when X(t) was
greater than zero at the time of the forced response, and the
incorrect response when X(t) was less than zero [30,31]. The
percentage of correct responses as a function of time was
calculated from the expected value and variance of Xat time t:
PCor(t)~PX(t)w0
ðÞ
~W{E½X(t)
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
(Var½X(t)
p
!
ð4Þ
where Wis the distribution function of the normal distribution.
The variance of X(t) is given as the variance of the integrated white
noise process plus the variance of X(t) at the time t
0
:
Var X (tjtwt0)½~(t{t0)Var½nzVar X(t0)ðÞ~
(t{t0)zVar X (t0)½ ð5Þ
For the cyclic deadline task Var[X(t
0
)] was set to zero (see above).
The expected value of E[X(t)] was calculated from equation (3)
while setting the noise term n(t) to zero. In summary, response
accuracy in the cyclic deadline task as a function of processing time
was predicted with 6 free parameters. Table 1 provides a summary
of all free variables. Four of the free parameters determine drift
rate as a function of time during the trial. One parameter
determines non-decision time and the last parameters scales
stimulus strength relative to the noise amplitude that was
arbitrarily set to 1 au
2
/sec.
The model was fit to the data either for each subject separately,
or by combining all 7 subjects that performed the cyclic deadline
task. In order to combine subjects, we first fit the model to each
subject individually to estimate non-decision time. Before com-
bining data across subjects, we subtracted individual non-decision
time from processing time and added the mean non-decision time
averaged across all subjects. This allowed us to combine subjects
with different non-decision time.
Three general comments are in order to place these modeling
efforts into context. (1) We make no claim that our model is
superior to existing models when it comes to describing the
temporal dynamics of the stimulus selection/drift rate over time in
the cyclic deadline paradigm. Other models with a similar number
of free parameters will probably provide similarly good fits.
Rather, we use this specific model because its parameterization is
very descriptive on the level of abstraction that is relevant for our
analysis. (2) The key question that we try to answer with this model
is whether or not the temporal gating parameter, i.e., decision
onset, is necessary to model human behavior in the RT paradigm
(see below). (3) The key parameter of interest (decision onset in the
RT paradigm) is independent of the specific model that is used to
estimate drift rate from the cyclic deadline paradigm.
Modeling speed-accuracy tradeoff in the RT paradigm
The model as described above was used to predict the data from
the cyclic deadline paradigm where the termination of the decision
process was under experimental control. This variant of the model
never terminates a decision process by itself and hence could not
be used to predict reaction time distributions. In order to predict
reaction time distributions in the RT paradigm, we added a
mechanism that allowed the model to abort the decision process
(i.e. a decision threshold or bound, B) based on the amount of
differential evidence accumulated by the integrator unit. The
decision was terminated when the decision variable X(t) reached a
positive or a negative bound at 6B.
In a series of simulations, we allowed several parameters of the
model to vary in order to provide a satisfactory fit to the speed and
accuracy condition of the RT paradigm (for an example fit see
Figure S3). All 4 parameters that determine drift rate as a
function of time, as well as the scaling parameter j, were fixed to
the values estimated from the cyclic deadline task. Because not all
of the subjects in the RT paradigm had completed the cyclic
deadline paradigm, we decided to use the parameters from the
combined group-based fit, rather than the individual subject fits.
The use of the group-level parameters is supported by the finding
that all subjects had similar drift rate estimates.
In the RT paradigm, twelve of the subjects showed unimodal
RT distributions. In eight of these subjects it was not necessary to
remove any outliers. In four of these subjects, we removed a small
fraction of trials (,2%) with either untypically short or long RTs.
The remaining subject showed bi-modal RT distributions with a
clearly defined cluster of anticipatory responses that was larger in
the speed (10%) than accuracy condition (4%). These anticipatory
trials were excluded for the fitting of the RT distributions.
Some parameters were either not present in the cyclic deadline
model (decision bound B, and decision onset t
0
), or might take on
different values in the RT paradigm (non-decision time, starting-
point variability, stimulus selection time). The additional param-
eters in the RT paradigm had either one degree of freedom (same
value for both speed and accuracy condition) or two degrees of
freedom (different values for speed and accuracy condition). We
initiated the fitting process using the simplest model possible, in
which only Bound was allowed to vary between the speed and
accuracy condition. This model provided an unsatisfactory fit to
the data (data not shown) and it became clear that it was necessary
to allow non-decision time to vary between the two paradigms.
The resulting fits revealed that non-decision time was significantly
longer in the RT paradigm. This was true for all variants of the
model that we tested. A more detailed interpretation of this finding
can be found in the Discussion.
Model implementation, fitting routines, and model
evaluation
All computations were discretized at a temporal resolution of
2 ms and simulated numerically using in-house software pro-
grammed with the statistical software package R (Version 2.13).
Fitting was performed with the genoud function that combines a
genetic search followed by a standard gradient descent [32]. By
default, we used a limited genetic search to identify a good starting
point for the gradient descent method. The limited genetic search
consisted of 10 generations with 500 individuals in each
population. We used the default settings of the genoud function
regarding the proportion of different operators (Cloning: 65
individuals; Uniform Mutation, Boundary Mutation, Non-Uni-
form Mutation, Polytope Crossover, Simple Crossover, While
Non-Uniform Mutation, Heuristic Crossover: 62 individuals each).
After a burn-in period of 5 generations, a gradient descent was
conducted on the best individual of each generation using a quasi-
Newton method with enforced boundary conditions (L-BFGS-B).
In some instances we used a more extensive optimization
algorithm to test whether the limited search provides the best fit.
Optimal Decision-Making and Decision Onset
PLOS ONE | www.plosone.org 7 March 2014 | Volume 9 | Issue 3 | e89638
The extensive optimization algorithm consisted of 100 generations
of 1000 individuals each with a burn-in period of 50 generations.
In all instances, the results from the full and limited search were
numerically identical. This is evidence that the limited genetic
search was sufficient to find the best possible fits. Hence, we used
the limited search in all remaining fitting procedures.
The goal of the fitting procedure was to minimize a log-
likelihood of the data given a particular set of free parameters. For
each of the 6 RT distributions for correct responses (congruent,
neutral, incongruent in the speed and accuracy condition), we
measured the 10
th
,30
th
,50
th
,70
th
and 90
th
percentiles. We then
determined the probability that the model placed in each of the 6
RT bins, and calculated the log-likelihood of the data given a
specific set of parameters. Due to the limited number of trials in
the error condition it was not feasible to get good RT quantile
estimates for the error RT distributions. Hence, we used the limits
from the correct RT distributions to bin the RT distributions on
error trials of the corresponding distribution. In earlier efforts, we
calculated log-likelihoods using the 2 ms native temporal resolu-
tion of our model. We discontinued the use of 2 ms bins since the
fits were more sensitive to outliers. However, the initial fits that
were done using the 2 ms binning provided the same qualitative
results as the quantile binning procedure.
We used three different approaches to assess model fits: (1)
Wilkes chi-square tests for nested models, (2) Bayesian Information
Criterion (BIC) for non-nested models and (3) paired t-tests to
compare parameter estimates in the speed and accuracy condition.
(1) The Wilkes chi-square test for log-likelihood ratios uses a
test-statistic proportional to the difference between log-likelihood
of two nested models, and compares this value to a Chi-square
distribution with the number of degrees of freedom equal to the
difference between the two models. We used this test on each
subject as well as on the population. To extend the test to the
population, we summed the log-likelihood values and the
differences in the number of degrees of freedom across all subjects.
(2) The BIC enables the comparison of non-nested models with
different degrees of freedom by penalizing the log-likelihood for
the number of free parameters in the model. In our case, most
comparisons of interest involved either nested models, or non-
nested models with identical numbers of free parameters. Hence,
the BIC was of limited use and included only because it is a
commonly used measure. (3) The tests outlined above provide a
measure of whether a specific parameter can help improve the fit
of a model. However, they do not test if the parameter in question
differs systematically across the entire population. To test this, we
used population-based paired t-tests of parameter estimates from
the speed and the accuracy conditions.
Assumptions about non-decision times in the system
The data analysis and the modeling efforts critically depend on
several key assumptions regarding the delays in the system. In the
following we make these assumptions explicit. (1) Non-decision
time comprises afferent and efferent delays. (2) Afferent delays can
further be split into two components: conduction delays that
model the time from stimulus presentation to the first detectable
increase of activity above baseline, and the additional time it takes
before neural activity becomes stimulus selective, distinguishing
the different directions of motion. (3) The afferent delays are not
under cognitive control and will always be constant as long as the
properties of the stimulus (contrast, spatial frequency, etc) do not
change. (4a) The time it takes to select the relevant sensory
information via feature-based selective attention has a physiolog-
ically defined lower limit, and subjects achieve this lower limit in
the cyclic deadline paradigm. (4b) Stimulus selection time is
constant in all paradigms and across speed-accuracy instructions.
With the exception of assumption 4b, all assumptions are
necessary for our interpretation of the data. In one of the follow-
up analyses we relaxed assumption 4b to test if this can provide a
better fit to the data.
Results
Speed-accuracy instructions in the RT paradigm.
In Experiment 1, subjects performed four blocks of the RT
version of the motion-interference task in which they were
required to stress either speed or accuracy. In line with the
instructions, accuracy and RTs were significantly higher in the
accuracy compared to the speed condition (Acc: 9861%; Spd:
9066%, mean6std; one-sided paired t-test, df = 12, t = 25.7,
p,10
211
; Acc: 593687 ms; Spd: 498666 ms; one-sided paired t-
test, df = 12, t = 8.2, p,10
25
). The aim of the current study was to
model both accuracy and the RT distributions in order to
understand the contribution of the threshold and onset mecha-
nisms to the observed speed-accuracy tradeoff. In line with
previous studies [16,17] we used a modified version of the
standard diffusion model that allows systematic variations of drift
rate over the time course of an individual trial. There are two main
differences that distinguish our approach from previous ones. (1)
We added a temporal gating parameter to the modified diffusion
model that prevents the integration of evidence until a particular
predetermined time t
0
. This allows us to test the role of decision
onset in speed-accuracy tradeoff. (2) We set out to explicitly
measure the time course of drift rate using an independent
experiment (see below) rather than fitting the time course post-hoc
to the data from the RT paradigm itself. These independent
measurements of drift rate from the response signal task form the
basis of our modified version of the standard diffusion model that,
if our assumptions and measurements are accurate, should provide
a plausible fit to the data in the RT paradigm. This approach of
using two independent experimental paradigms was recently
pioneered by Ratcliff [33] and, albeit challenging, is arguably the
most informative way to analyze reaction time data. So far,
however, it has not been applied successfully to understand
decision-making under conflict. The following sections describe
the response signal experiment that uses our novel cyclic-deadline
paradigm to measure the time course of drift rate over the course
of an individual trial. After that, we will return to the modeling of
the data from the RT paradigm with the new modified diffusion
model.
Evaluating the cyclic deadline paradigm
In Experiment 2, subjects were required to respond at the
anticipated time of the auditory response cue without regard to
when or what kind of stimulus was presented. The cyclic deadline
(CD) paradigm reliably induced significant differences in process-
ing time (see Methods) between conditions that differed in
duration by as little as 16.7 ms (Figure 4A). To further quantify
how well subjects were able to follow the timing requirements of
the cyclic deadline task we measured (1) variability of processing
times around the mean (random errors), and (2) systematic
deviations of the mean from the intended processing time
(systematic errors). Random error was calculated as the standard
deviation of single trial processing times after subtracting the mean
for each block and stimulus condition. The smaller the standard
deviation, the tighter the processing times are distributed around
the mean. The results of this analysis are summarized in Table 2.
Seven of nine subjects that were trained in the cyclic deadline
paradigm had random errors that met our criterion of 50 ms or
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PLOS ONE | www.plosone.org 8 March 2014 | Volume 9 | Issue 3 | e89638
less. Based on this analysis, two subjects were excluded from
participation in the main cyclic deadline experiment because they
failed to meet the criterion during the training phase.
To quantify systematic errors, mean processing times were
calculated for each block of trials and distractor congruency. For
each subject we modeled mean observed processing time as a
function of block number – a proxy for intended processing time
that was varied in blocks – and congruency. The results indicate
that between 84 and 98% of the variability in mean processing
time was explained by intended processing time, and hence under
experimental control (see Table 3). In six of seven cases, less than
1% of the variability was due to congruency of the stimuli.
Subjects 6 and 7 exhibited the weakest timing performance (see
also Figure S2). However, the quantitative results are comparable
to the other subjects. This can be taken as evidence that moderate
violations from the instructions still provide interpretable results.
We re-ran the main analyses excluding these two subjects. This led
to small quantitative, but no qualitative, differences (see below).
In RT paradigms, accuracy and reaction time typically increase
after error responses [34]. A somewhat more complex pattern is
observed after incongruent trials: accuracy and reaction time
differences between congruent and incongruent trials are reduced
[17]. Changes in reaction time and accuracy can be explained at
least in part as adjustments in cognitive control that change the
threshold for triggering a motor response. The aim of the CD
paradigm was to force subjects to respond at a particular point in
time, rendering their behavior independent of such adjustments.
To test independence, we fit a linear model to the accuracy and
processing times for each subject as functions of intended
processing time and congruency of the current trial, as well as
congruency and accuracy of the previous trial (Table 4 and 5).
Tables 4 summarizes the effects of accuracy and response conflict
in the previous trial on processing time in the current trial. We
observed a significant increase in processing time after error trials
for only one of the seven subjects. On the population level there is
no systematic increase in processing time after error trials (t-test,
df = 6, t = 21.34, p = 0.88).
Similarly, processing times were not significantly affected by
response conflict on the previous trial (t-test, df = 6, t = 20.56,
p = 0.71). Tables 5 summarizes the effects of accuracy and
response conflict in the previous trial on accuracy in the current
trial. We observed a significant increase in accuracy after error
trials for two of seven subjects. In one subject we found a
significant decrease in accuracy. On the population level, we failed
to find a significant increase in accuracy as a function of accuracy
on the previous trial (t-test, t = 0.18, df = 6, p = 0.43). Similarly, we
failed to find a significant increase of accuracy as a function of
response conflict on the previous trial (t-test, t = 0.17, df = 6,
p = 0.44). In summary, neither congruency nor error on the
previous trial had significant effects on accuracy or processing
time, consistent with the idea that the cyclic deadline task
neutralizes serial order effects.
Figure 4. Processing times of all subjects as a function of stimulus duration, i.e. intended processing time in (A). The box and whiskers
indicate mean 6one and two standard deviations, respectively. The brackets over two adjacent stimulus durations indicate significant differences at
p,0.01. An additional asterisk above the bracket indicates a p-value below 0.001. In nearly all cases, a 16.7 ms increase in intended processing time
resulted in a significant difference in observed processing time. (B) Percent correct responses are plotted as a function of mean processing time and
stimulus congruency. Each dot describes a block of trials with a particular intended processing time and congruency (green-congruent; black-neutral;
red-incongruent). The x-value of the dots corresponds to the mean observed processing time and the y-value corresponds to the mean proportion of
correct responses. In the congruent and neutral conditions response accuracy increases monotonically as a function of RT. For the incongruent
condition, in contrast, there is an initial dip with accuracy decreasing significantly below chance. The solid lines correspond to the maximum-
likelihood fit of the data with the biased competition model. The left-hand vertical dotted lines correspond to the total non-decision times in the
system. The right-hand dotted vertical line corresponds to the time at which the stimulus selection process has finished. (C) Time-resolved estimates
of drift rate that give rise to the model predictions in (B). For all three conditions, drift rate converges to the same asymptote. This feature is not hard-
coded into the model, but arises from the fit to the data. It indicates that attention selects the target stimulus in a winner-take-all fashion (a= 1), such
that in the steady state, the identity of the distractor no longer affects drift rate. Drift rate in (C) is determined by four parameters of the biased-
competition model.
doi:10.1371/journal.pone.0089638.g004
Table 2. Timing accuracy in the cyclic deadline task.
Subj 1 Subj 2 Subj 3 Subj 4 Subj 5 Subj 6 Subj 7
sd (residual PT)
[ms]
27 34 44 41 40 43 48
Timing accuracy in the cyclic deadline task measured as standard deviation of
single trial processing time from the mean processing time in each block and
condition.
doi:10.1371/journal.pone.0089638.t002
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PLOS ONE | www.plosone.org 9 March 2014 | Volume 9 | Issue 3 | e89638
Cyclic deadline paradigm – measuring and modeling
response accuracy
Having established that the subjects perform the timing
requirements of the cyclic deadline paradigm, we analyzed their
choice behavior. Figure 4B shows the proportion of correct
responses as a function of normalized mean processing time and
distractor congruency for all subjects. As expected [11], accuracy
on incongruent trials dropped below chance for medium
processing times. This effect began to reverse at ,330 ms,
suggesting that momentary sensory evidence tipped in favor of the
less salient target stimulus.
To quantitatively relate these findings to the dynamics of
selective attention, we developed a simple computational frame-
work that we refer to as the biased competition model of decision-making
(Figure 3 and Table 1). The model combines two well-
established neural principles: stimulus selection via biased compe-
tition in sensory cortex [10] and decision making as the integration
of noisy sensory information over time [30]. The model assumes
that decisions are based on a time-continuous stochastic process
with a starting point of zero and non-stationary Gaussian
increments. The mean of the increments, i.e. the drift rate, varies
as a function of distractor congruency and the ongoing dynamics
of the attentional selection process. The proportion of correct
responses as a function of processing time and distractor
congruency is predicted by the mass of the stochastic process
above zero [30,31]. Three key parameters of the model determine
how strongly attention selects the target over the distractor as a
function of time from stimulus onset (Figure 3, black-and-white
inset in layer 2). The fourth parameter of the model determines the
saturation point of the non-linear contrast response function
(Figure 3, inset layer 3, Figure S1). In combination with the
stimulus parameters, i.e. contrast and direction of motion of the
target/distractor, these four variables determine the precise time
course of drift rate for a given trial. A fifth parameter scales drift
rate to the amplitude of the white-noise process with an arbitrarily
chosen variance of 1 au
2
/sec. The sixth parameter models all
efferent and afferent non-decision related delays of the system.
Using a maximum-likelihood method we fit 6 free parameters of
the biased competition model (Table 1) to the data either
separately for each subject (Figure S2) or pooled over all subjects
(Figure 4B). The fits not only capture the qualitative properties of
the data, in particular the initial dip in the incongruent condition,
but also provide an excellent quantitative approximation. Our
simulations indicated that attention finalizes the selection of the
target in a winner-take-all fashion approximately 150 ms after the
onset of the decision process (Table 6). This suggests that
systematic errors observed in the incongruent condition are
caused by evidence accumulated during the first 150 ms of the
decision process, allowing the possibility that delaying decision
onset can improve response accuracy. In a follow-up analysis we
re-ran the population fit while excluding subjects 6 and 7 that
exhibited the weakest timing performance. The fits were similar
with the exception of small quantitative differences. In particular,
stimulus selection times were markedly shorter (,120 ms rather
than ,150 ms when all 7 subjects were included). Using the
population fit based on the 5 best subjects rather than all seven
subjects did not change the main conclusions regarding decision
onset in the CD paradigm.
Additional analyses showed that the data from the CD
paradigm can also be explained if perfect integration is replaced
with leaky integration. However, the main conclusions regarding
the duration and selectivity of the stimulus selection process were
not affected. Similarly, it is likely that other network architectures
building on race processes [15] or leaky competing accumulation
[31] may be able to predict the data from the cyclic deadline task.
Hence, it is not our intention to make strong claims that the
proposed model is the only one that can be used to fit the data.
Rather, we conclude that it is one model that can capture the
temporal dynamics of drift rate with sufficient quantitative detail
and a very low number of free parameters that explicitly map onto
core concepts such as the duration of the stimulus selection
process. However, for the purposes of the current study, the scope
of models under consideration was limited to perfect integration of
differential evidence.
Table 3. Determinants of processing time.
Subj 1 Subj 2 Subj 3 Subj 4 Subj 5 Subj 6 Subj 7
Intended PT 97.39 (***) 96.65 (***) 88.53 (***) 91.96 (***) 92.54 (***) 86.38 (***) 84.83 (***)
Congruency 0.07 (ns) 0.29 (**) 0.52 (**) 0.15 (ns) 0.10 (ns) 0.97 (**) 1.10 (**)
Interaction 0.03 (ns) 0.22 (**) 0.15 (ns) 0.14 (ns) 0.09 (ns) 0.28 (**) 0.83 (*)
Percent variance of mean processing times explained by the experimental manipulations (intended processing time, congruency, and their interaction). Asterisks in
brackets indicate the significance levels: (*): p,0.05, (**): p,0.01, (***):p,10
210
.
doi:10.1371/journal.pone.0089638.t003
Table 4. Trial history effects: processing time.
Subj 1 Subj 2 Subj 3 Subj 4 Subj 5 Subj 6 Subj 7
Effect of previous trial error on
processing time [ms]
2.7 (***) 21.5 (ns)23.7 (***) 22.1 (*) 23.5 (***) 210.7 (***) 1.6 (ns)
Effect of previous trial response
conflict on processing time [ms]
20.02 (ns)20.30 (ns)23.51 (***) 0.80 (ns)0.95(ns)24.48
(**
)2.96 (ns)
Top row: Effect of previous trial error on current trial processing time in ms. Positive values indicate slower responses after an error trial, and vice verse. Bottom row:
Effect of previous trial response conflict on current trial processing time. Positive values indicate slower responses after an incongruent compared to a congruent trial.
doi:10.1371/journal.pone.0089638.t004
Optimal Decision-Making and Decision Onset
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RT paradigm – modeling the speed-accuracy tradeoff
To understand whether humans can use the onset and/or
threshold mechanism to trade speed for accuracy when free to
respond at any time, we extended the 6-parameter biased
competition model to include a response threshold in the form
of two absorbing boundaries (+B and –B) and a decision onset (t
0
).
The model terminates a decision as soon as the stochastic process
reaches one of the two boundaries and is considered a correct
response if it reaches the positive boundary. These boundaries
allowed the model to terminate a decision process and generate
RT distributions for correct and error trials that can be used to fit
the observed data. By varying decision onset, the model can
actively choose when to initiate the evidence accumulation
process.
In theory, decision onset could be controlled online, on a trial-
by-trial basis depending on the presence of stimulus and/or
response interference (interference-dependent gating). Alter-
natively, decision onset can be predetermined such that integra-
tion starts at a fixed point in time relative to the onset of the
stimulus. The delay between stimulus onset and integration onset
could be predetermined, for example, based on task requirements
that stress either speed or accuracy (task set-dependent gating).
Task set-dependent gating would operate in the form of a speed-
accuracy tradeoff: delaying decision onset will increase accuracy
(mainly for incongruent trials) while increasing response latencies
for all three trial types. Interference-dependent gating, in contrast, would
delay decision onset only when necessary (incongruent trials) and
would not cause increased reaction times for the other trial types.
However, the implementation of an interference-dependent gating
mechanism would be costly, if at all possible, and add another
layer of complexity to the decision process. The fact that the data
in the cyclic-deadline paradigm could be fit with a model that
assumes identical decision onset regardless of stimulus congruence,
is strong evidence against interference-dependent gating. Based on
the above considerations, we allowed decision onset to vary as a
function of speed-accuracy instruction in the same way as response
threshold.
Task-set dependent temporal gating
In the following we tested whether task-set dependent gating,
i.e., the onset mechanism, can be a more effective way to trade
speed for accuracy. Based on the estimates of time-dependent
drift-rate that was measured in the CD paradigm (Figure 4C), we
simulated mean RT and accuracy as a function of the response
threshold and decision onset. This allowed us to estimate the
benefit of both mechanisms for the very specific task in question.
In the presence of certain task requirements (e.g. ‘‘99% correct
responses’’), it is possible to define the optimal decision strategy as
the strategy that achieves 99% correct responses while minimizing
mean reaction time. Based on this definition, the implementation
of an optimal decision strategy typically involves changes of
decision onset (Figure 5). For example, our model predicts that
an average response accuracy of 99% can be achieved by setting
response threshold to ,1.4. This setting leads to mean reaction
times around 570 ms. However, if we delay decision onset by
,80 ms the model can achieve the same accuracy for average
mean reaction times around 370 ms. Note that decision onset is
always reported relative to the time at which the first stimulus-
selective information is believed to reach the integrator stage.
Overall, the two mechanisms exhibit large and systematic
differences over a wide range of the sampled parameter space
(Figure 5): for a given increase in response latency, delaying
Table 5. Trial history effects: accuracy.
Subj 1 Subj 2 Subj 3 Subj 4 Subj 5 Subj 6 Subj 7
Effect of previous trial error on
accuracy [au]
20.172 (**) 0.034 (**) 0.098 (**) 0.006 (ns)20.020 (ns) 0.055 (ns) 0.031 (ns)
Effect of previous trial response
conflict on accuracy[au]
20.023 (ns)20.034 (ns)0.168 (*) 20.010 (ns)20.095 (ns) 0.079 (ns)20.047 (ns)
Top row: Effect of previous trial error on current trial accuracy. Positive values indicate higher accuracy after an error trial and vice verse. Bottom row: Effect of previous
trial response conflict on current trial accuracy. Positive values indicate higher accuracy after an incongruent compared to a congruent trial.
doi:10.1371/journal.pone.0089638.t005
Table 6. Model fit of the biased competition model to the cyclic deadline task.
Subj 1 Subj 2 Subj 3 Subj 4 Subj 5 Subj 6 Subj 7 Mean of Fits Subj 1-7 combined
Non-decision time [ms] 277 259 272 253 255 239 254 259613 252.5
Contrast response
parameter I
in
0.149 0.156 0.256 0.086 0.094 0.293 0.057 0.15660.089 0.159
Onset of stimulus
selection process [ms]
000434564421625 0
Duration of stimulus
selection process [ms]
113 138 124 62 118 62 76 105630 149
Asymptote of stimulus
selection process
1.0 1.0 1.0 1.0 1.0 1.0 0.97 160.01 1
Signal-to-noise ratio 7.34 7.98 8.13 5.13 5.82 9.93 6.99 7.3361.58 6.57
The first seven columns show the results of the individual subjects. The column entitled ‘‘mean’’ presents the mean 6standard deviation of the values averaged over all
seven subjects. The last column depicts the results on a population level. To that aim, all experimental blocks from subjects 127 were pooled after correcting
processing times for individual differences in non-decision time.
doi:10.1371/journal.pone.0089638.t006
Optimal Decision-Making and Decision Onset
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decision onset leads to larger improvements in accuracy than
raising response threshold.
In the absence of any task requirements, a strategy can be
defined as optimal if it provides the highest rate of information
transfer measured in bits per second. We chose bits per second rather
than other possible metrics such as reward per unit time because the
latter is subjective and depends on current task demands, i.e. how
valuable/costly a correct/wrong response is assumed to be. The
benefit of delaying decision onset becomes particularly obvious
when analyzing speed and accuracy in terms of information
transfer (Figure 5C). High rates of information transfer above 2
bits/sec can only be found for a low response threshold (,0.7) and
late decision onset (.60 ms). Our simulations also show that the
threshold mechanism by itself is not a very effective way to trade
speed for accuracy in the current task. If the decision onset is
always initiated at time 0, information transfer reaches only very
moderate levels of 1.25 even if threshold is increased to around
2.1. The low rate is mainly due to the high costs in terms of RT
that are incurred when increasing response threshold.
Note that this finding is in clear contrast to situations with
constant drift rate. In such situations, the threshold mechanism has
long been shown to be the optimal way to trade speed for
accuracy. However, in conditions with changing drift rate that can
be encountered for example in interference tasks, delaying decision
onset would be a more effective way to trade speed for accuracy.
In the following we tested whether subjects make use of the onset
mechanism, or if their behavior can be explained by a suboptimal
implementation of the threshold mechanism.
To test the role of decision onset and response threshold to the
speed-accuracy tradeoff, we fit a series of models to the data of
each subject. Except for the implementation of task set-dependent
gating, we used standard drift-diffusion models with variable drift
rate that was determined by modeling the data in the CD
paradigm (Figure 4C). To that aim we fixed five of the six
variables to the values obtained from the CD paradigm. Non-
decision time, though estimated in the CD paradigm, was allowed
to be a free parameter for two reasons. First, our simulations
revealed that non-decision times were significantly longer in the
RT compared to the CD paradigm (for a detailed interpretation of
this finding see Discussion). Second, we allowed non-decision time
to vary between speed-accuracy instructions, because it is possible
that motor execution times (efferent delays) differ when subjects
stress either speed or accuracy. Note that all of our models assume
that afferent delays are outside of cognitive control and hence
independent of speed-accuracy instructions. In addition to
threshold, decision onset, and non-decision time, we allowed
stimulus selection time and starting-point variability of the
integrator unit to vary between speed-accuracy instructions to
test alternative accounts of our data.
Threshold and Non-decision time model (TN_22)
The simplest model that we will discuss in detail included 2
parameters: response threshold, and non-decision time with two
degrees of freedom each. As a shorthand we refer to this model as
TN_22. The letters are abbreviations of the two variables
(Threshold and Non-decision time) and the number refer to the
degrees of freedom for each of the two variables. Figure 6A–D
displays the fits of the TN_22 model to the RT distributions and
accuracy in the speed and accuracy version of the RT paradigm.
Because of the limited number of errors, we display the fits to the
error RT distribution only for incongruent trials of the speed block
(though all of the error distributions were used for the fitting
process). One of the 13 subjects had substantially longer RTs and
higher accuracy, an effect that was consistently captured by all
variants of the model as a higher response threshold (Figure 6D).
The quality of the fits for this subject were similar to those of other
subjects. However, the inclusion of this subject increased the radii
of the confidence ellipses (Figure 6A–C) to a point where, due to
overlap, they were no longer visually informative. Hence, for
visualization purposes only, we excluded this subject from the data
Figure 5. Properties of the onset mechanism. In the biased competition model, speed and accuracy can be manipulated in two independent
ways — adjusting response threshold and/or decision onset. The simulations are based on the fit of the biased competition model to the data of the
CD paradigm combined across all 7 subjects (Figure 3). Simulated response accuracy (A), response latency (B) and rate of information transfer (C)
are depicted as functions of response threshold on the x-axis and onset of the decision process on the y-axis. The dotted line at 0 ms in each panel
indicates the average non-decision time across all subjects. Our null-hypothesis states that decision onset is fixed and coincides with this time-point.
Delaying decision onset increases response accuracy and RT. Increasing response threshold has the same effects, but the effect on response accuracy
is weaker while the effect on RT is stronger. P1 denotes the threshold that is necessary to achieve 99% response accuracy if decision onset is fixed at
0 ms. P2 denotes a second set of parameters that leads to the same accuracy of 99% but allows decision onset to deviate from 0. Note that P1 is
associated with mean reaction times around 570 ms. In contrast, P2 achieves the same accuracy with a mean RT of 370 ms. This shows that decision
onset can be a very effective way to trade speed for accuracy.
doi:10.1371/journal.pone.0089638.g005
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that generated the confidence ellipses. Note that the estimated
model parameters for this subject were included in all analyses.
Overall, the TN_22 model provides a good approximation to
the data. We dropped individual degrees of freedom from the
model to test if all four parameters are necessary (drop-one
routine). The resulting sub-models are TN_21 and TN_12. Using
a test for nested models, we show that removing one degree of
freedom from threshold significantly decreases the accuracy of the
fit (Population-based Wilkes Chi-square test for log-likelihood of
nested models, df = 13, X
2
= 184,p,10
210
). Using the same test
on the single subject level, 9 out of 13 subject showed a significant
effect at p,0.01. Similarly, we show that the second degree of
freedom for non-decision time is necessary (df = 13, X
2
= 246,
p,10
210
, individual subjects: p,0.01 for 9/13).
Figure 6D shows the parameter estimates for threshold and
non-decision time as a function of speed-accuracy instruction. As
expected, response threshold was significantly higher for the
accuracy condition (acc: 0.9460.51 ms, spd: 0.6960.41 ms;
paired t-test, df = 12, t = 5.72, p,10
24
). In addition, non-decision
times were longer in the accuracy condition (acc: 366641 ms, spd:
323637 ms; paired t-test, df = 12, t = 4.33, p,10
23
). The increase
of non-decision time is not necessarily expected. Ideally, non-
decision time represents fixed delays in the system. However, it is
possible that efferent non-decision times are somewhat longer in
the accuracy condition if subjects were to respond more cautiously,
and hence, with less vigor. Qualitatively, the observed effect can
certainly be interpreted in this way, but the effect size (,41 ms)
seems large given the short distance that needs to be covered in
order to press a button.
Despite the reasonable fit to the data, there was one systematic
modeling error. The model predicted higher than observed
accuracy in the speed-condition, and lower than observed
accuracy in the accuracy condition. This effect is particularly
visible for the neutral and incongruent stimuli (Figure 6B&C).
Taken together, these results show that subjects were able to
improve accuracy more effectively, i.e., by investing less extra RT,
than the TN_22 model predicted. This implies that subjects can
make use of an additional mechanism that allows them to trade
speed for accuracy more effectively than predicted by only
increasing the response threshold. We focused on three plausible
Figure 6. Fit of the threshold and non-decision time (TN_22) model to the data from the RT paradigm in (A–D). The first three panels
represent RT distributions as a function of accuracy from the congruent, neutral and incongruent condition. Note that the x-axis covers different
ranges in the incongruent panel in order to include the error trials. The empirical results are represented as 95% confidence ellipses around 5
different RT quantiles as a function of accuracy (green/red: correct/error trials speed instruction, blue: correct trials accuracy instruction). The model fit
for the same quantiles is represented as the axes of the 95% confidence intervals. The rightmost panel displays the model parameters (green:
accuracy instruction; red: speed instruction). Data-points from each subject are connected by a line. Results of a paired t-test are indicated above the
data (bracket: ns; one star: p,0.05; two stars: p,0.01; three starts: p,0.001). The current model used 4 parameters (bound and non-decision time
two parameters each) to fit the data. Note that the model fails to capture some key properties of the data. (E–H) Fit of the threshold, decision-onset
and non-decision time (TON_222) model to the data from the RT paradigm. Conventions as in panels A–D. Note that the model provides a much
better fit to the data. Speed-accuracy tradeoff is mediated through response threshold and decision onset. There are no systematic differences of
non-decision time between the two conditions.
doi:10.1371/journal.pone.0089638.g006
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mechanisms that could explain this unaccounted increase in
accuracy: the onset mechanism as discussed above, and two
alternatives: a novel mechanism based on the noise-floor of the
integrator unit and a previously proposed mechanism that focuses
on stimulus selection time [17].
Threshold, Onset and Non-decision time model
(TON_222)
The TON_222 model adds two degrees of freedom to the
TN_22 model by allowing decision onset to vary as a function of
speed-accuracy instruction. The resulting model has 6 degrees of
freedom and provides a significantly better fit to the data
(Figure 6E–H; Population-based Wilkes Chi-square test for log-
likelihood of nested models, df = 26, X
2
= 490, p,10
210
). For 12
out of 13 individual subjects the Wilkes Chi-squared test for log-
likelihood in nested models is significant at a level of 0.01 or lower.
As with the TN_22 model, we used the ‘‘leave-one-out’’ method to
test if all 6 degrees of freedom are necessary. The accuracy of the
fit was significantly reduced by dropping a degree of freedom from
threshold (Wilkes Chi-square, df = 13, X
2
= 295,p,10
210
, indi-
vidual subjects: p,0.01 for 12/13), decision onset (df = 13,
X
2
= 212, p,10
210
, individual subjects: p,0.01 for 9/13), as well
as non-decision time (df = 13, X
2
=83,p,10
210
, individual
subjects: p,0.01 for 4/13).
We then tested whether speed-accuracy instructions have a
systematic effect on decision-onset across all subjects by comparing
the parameter estimates of decision onset in the speed and
accuracy conditions. We found a significant delay of decision onset
in the accuracy condition (acc: 30629 ms, spd: 227641 ms;
paired t-test, df = 12, t = 5.4, p,10
23
). Due to the right-skewed
nature of the distribution (one outlier, see Figure 6H), median
decision onset values may be more representative of true decision
onset (acc: 39 ms; spd: 214 ms). Note that zero represents the
time point at which stimulus selective information first reaches the
integrator unit. Thus, when t
0
,0, decision onset occurs before any
stimulus selective information is present i.e. the integrator
processes noise until t
0
= 0. In line with the TN_22 model we
find a significantly higher response threshold in the accuracy
condition (acc: 0.9460.47 ms, spd: 0.6360.37 ms; paired t-test,
df = 12, t = 7.7, p,10
25
). In contrast to the TN_22 model, the
TON_222 model did not detect a significant increase of non-
decision time in the accuracy condition (acc: 347634 ms, spd:
342628 ms; paired t-test, df = 12, t = 0.5, p = 0.6).
Threshold, Onset, Non-decision time and Starting-point
variability model (TONS_222X)
We further tested if it is necessary to include one (TONS_2221)
or two (TONS_2222) additional degrees of freedom by allowing
the starting-point variability of the integrator unit, Var[X(t
0
)],tobe
a free parameter. Presumably, starting point variability determines
the noise level of the integrator prior to stimulus onset. Hence,
there is no a priori reason to believe that this should be affected by
speed-accuracy instructions. However, it is possible that the noise
level is unequal to zero (in contrast to what was assumed in all
previous models). In addition, it is possible that attention is needed
to maintain a low noise level in the integrator unit, and that speed-
accuracy tradeoff is mediated in part by reducing this noise level.
This assumption is particularly relevant, since decision onset may
operate in a similar fashion: if decision onset is initiated too early
(before stimulus-selective information hits the integrator), this
would increase the noise level at the time at which stimulus-
selective information reaches the integrator and deteriorates
performance.
The simulation results showed that the TONS_2221 model
(Figure 7) provided a significant improvement over the
TON_222 model (Wilkes Chi-square, df = 13, X
2
= 41, p,10
24
,
individual subjects: p,0.01 for 4/13). Further, the TONS_2222
model did not significantly improve the TONS_2221 model by
adding another degree of freedom to starting-point variability
(Wilkes Chi-square, df = 13, X
2
= 10 p = 67, individual subjects:
p,0.01 for 1/13). At the same time, decision onset was still
significantly different in the two speed-accuracy conditions
(TONS_2221; acc: 42616 ms, spd: 28630 ms; paired t-test,
df = 12, t = 5.6, p,10
23
; TONS_2222; acc: 43615 ms, spd:
26631 ms; paired t-test, df = 12, t = 5.3, p,10
23
). This indicates
that the effect of decision onset is not mediated indirectly by
affecting the noise level of the integrator at the time stimulus-
selective attention reaches the integrator. Rather decision onset
mediates its effect by reducing the impact of information from the
salient but task-irrelevant distractor. In addition, it shows that
subjects do not reduce the integrator noise level as a mechanism to
increase accuracy.
The main difference between the parameters of the TON_222
and TONS_2221 model is decision onset in the speed condition.
The TON_222 model produces an earlier decision onset, most
likely due to the fact that an earlier decision onset is used to
emulate starting-point variability in some subjects. After allowing
an additional parameter for starting-point variability, decision
onset became more homogenous across the population with values
that were within a physiologically plausible range for all subjects.
Unless mentioned otherwise, the TONS_2221 model is our
preferred model and the basis for reporting parameter estimates of
decision onset in the Discussion.
Threshold, Non-decision time and Starting-point
variability model (TNS_222)
The previous analyses show that integrator noise is not
necessary to model speed-accuracy tradeoff. However, the model
used to test this assumption included decision onset. Hence, it is
possible that the presence of decision onset prevented us from
detecting an effect of integrator noise. To fully confirm the idea
that integrator noise is not sufficient to explain speed-accuracy
tradeoff, we constructed a model that drops decision onset
completely and replaces it with staring-point variability
(TNS_222, Figure 8 E–H). As expected, the TNS_222 model
allows a speed-accuracy tradeoff by increasing starting-point
variability in the speed condition (acc: 0.027616 ms, spd:
0.126630 ms; paired t-test, df = 12, t = 24.43, p,10
23
). Al-
though the TNS_222 model provides a significant improvement
over the TN_22 model (Wilkes Chi-square test, df = 26, X
2
= 188,
p,10
210
, individual subjects: p,0.01 for 5/13 subjects), it
provides a less accurate fit than the TON_222 model (BIC
TNS_222: 51,672; BIC TON_222: 51,067).
Threshold, Attentional selection speed, and Non-decision
time model (TAN_222)
Yeung and colleagues have presented an alternative account for
speed-accuracy tradeoff in interference tasks [17]. The alternative
account states that subjects increase top-down cognitive control in
the accuracy condition. Higher cognitive control speeds up the
stimulus selection process. Conversely, this leads to the counter-
intuitive proposal that subjects increase response speed by
deliberately slowing down the stimulus selection process. However,
both accounts, the attentional selection speed and the decision
onset account, improve accuracy in a very similar manner, namely
by reducing the duration for which information from the salient
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distractor is affecting the decision process. The aim of the current
simulation was to test whether one of the two accounts provides a
numerically better fit to the data.
We emulated Yeung’s model by allowing stimulus selection
speed to vary between the two speed-accuracy instructions. The
resulting model is referred to as the TAN_222 model. The
selection speed model was designed to be as similar as possible to
the TON_222 model. In particular, it contained the same number
of free parameters (6). Four of those six parameters are shared
between the two models: 2 degrees of freedom for non-decision
time and 2 degrees of freedom for the response threshold. The
remaining two degrees of freedom for decision onset were replaced
with two degrees of freedom for stimulus selection speed.
Figure 8A–D shows the fits of the stimulus selection model to
the data. Based on visual inspection, the model provides a
reasonably good fit to the data. Because the two models are not
nested, we could not use the standard Wilkes Chi-square test.
Hence, we calculated an alternative metric, the Bayesian
Figure 7. Fit of the threshold, onset, starting-point variability and non-decision time (TONS_2221) model to the data from the RT
paradigm in (A–D).
doi:10.1371/journal.pone.0089638.g007
Figure 8. Fit of the threshold, selection-speed and non-decision time (TAN_222) model to the data from the RT paradigm in (A–D).
(E–H) Fit of the threshold, non-decision time and starting-point variability model (TNS_222).
doi:10.1371/journal.pone.0089638.g008
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Information Criterion (BIC). Given that the two models have the
same number of degrees of freedom, a comparison of the BIC
values is very similar to the comparison of the underlying log-
likelihood values. Based on the BIC comparison, the decision onset
model provides a numerically better fit to the data (TAN_222:
51,350; TON_222: 51,067). It is also important to note that the
TAN_222 model achieves the fit using very fast attentional
selection times in the accuracy condition (acc: 84629 ms, spd:
158646 ms; paired t-test, df = 12, t = 24.8, p,10
23
), a value
substantially lower than that measured in the CD paradigm. Given
that subjects had more training with the task by the time they
perform the CD paradigm, it is surprising that they should be less
effective at selecting the relevant target stimulus. Furthermore, the
attentional selection speed account makes a second counterintu-
itive prediction – that selection speed should be faster in the
condition with slower reaction times.
‘‘From-Scratch’’ models
One of the main strengths of our approach is that we leverage
the CD paradigm to predict RT and accuracy in the RT
paradigm. In this way, our estimate of the input to the decision
unit (time-dependent drift rate, Figure 4C), is independent of our
estimate of how the decision unit chooses to use this information
(response threshold and decision onset). However, if for some
reason, the CD paradigm provides erroneous estimates of drift
rate, this could lead to erroneous conclusions from the RT
paradigm. We thus tested whether the main effect of decision onset
is dependent on the parameter estimates from the CD paradigm or
whether the main effect could be replicated by allowing previously
fixed parameters to be free parameters in the model. To that aim,
we took the TON_221 model and allowed 5 parameters that were
previously fixed to the values estimated from the CD paradigm to
vary. In addition to the 5 degrees of freedom in the TON_221
model, the new model had another 5 degrees of freedom. We refer
to this model as the CD_TON_221. To test if it is necessary to
keep decision-onset in the model, we compared the
CD_TON_221 model to a sub-model that did not include
decision onset. This model is an equivalent extension of the
TN_21 model, and will be referred to as CD_TN_21.
The two new models allow us to answer two main questions: (1)
can we confirm the role of decision onset for speed-accuracy
tradeoff in this alternative analysis that does not depend on the CD
paradigm, and (2) can we confirm the parameters that were
estimated from the CD paradigm using the RT paradigm? To
answer the first question, we compared the quality of the fits in the
CD_TN_21 model with the fit of the CD_TON_221 model. Our
results show that including the two degrees of freedom for decision
onset provides a significant improvement to the fit (Wilkes Chi-
square, df = 26, X
2
= 456, p,10
210
, individual subjects: p,0.01
for 9/13). At the same time, decision onset was still significantly
different in the two speed-accuracy conditions (decision onset in
CD_TON_221; acc: 29622 ms, spd: 231630 ms; paired t-test,
df = 12, t = 5.2, p,10
23
). The same effect was present if we
included an additional degree of freedom for non-decision time
(Figure 9, decision onset in CD_TON_222; acc: 25623 ms, spd:
236630 ms; paired t-test, df = 12, t = 5.2, p,10
23
). These
analyses show that our main finding regarding decision onset is
not specific to the drift-rates estimated from the CD paradigm.
In the next step we tested whether including the additional
degrees of freedom for the CD parameters improved the fit. To
that aim we compared the fit of the two CD_TON models with
the fit of the two TON models. In both cases, we found a
significant improvement of fit accuracy if the 5 additional CD
parameters were included (TON_221 vs CD_TON_221:Wilkes
Chi-square, df = 65, X
2
= 255, p,10
210
, individual subjects:
p,0.01 for 6/13; TON_222 vs CD_TON_222:Wilkes Chi-
square, df = 65, X
2
= 256, p,10
210
, individual subjects: p,0.01
for 7/13). We then compared the parameters estimated from the
CD_TON_222 fit with the parameters estimated from the CD
paradigm (Figure 9D). In particular, we were interested if the
increased improvement of fit was achieved by systematic or
random deviations from the parameters estimated from the CD
paradigm. For two parameters, we found systematic changes: the
onset and duration of the stimulus selection process (selection
onset: one-sample t-test, df = 12, t = 2.8, p,0.05; duration of
selection process: df = 12, t = 24.8, p,10
23
). Based on the
CD_TON_222 model, the stimulus selection process was estimat-
ed to begin ,10 ms later, and be 40 ms shorter than estimated
from the CD paradigm. Overall, the stimulus selection process was
estimated to end approximately 120 ms after the first pulse of
stimulus-selective information hit the integrator unit. Interestingly,
this is the same number that was recovered from the CD paradigm
if subjects 6 and 7 that exhibited the weakest timing performance
were dropped from the sample. It is particularly important to note
that even with the shorter attentional selection times of the
CD_TON model, it was still necessary to allow decision onset to
be a function of speed-accuracy instruction.
Optimality of human decision strategies
Based on our simulations, we concluded that the high rates of
information transfer (.2 bit/sec) can be achieved by low response
thresholds (,0.7) and late decision onset (.60 ms). The results of
our simulations allowed us to test whether subjects picked optimal
or close to optimal decision parameters. Figure 10B plots
threshold and onset estimates from the TONS_2221 model on top
of the map of information transfer. With the exception of one
instance, none of the subjects reached high values .2 bit/sec. The
majority of subjects increased the rate of information transfer in
the accuracy condition. However, all subjects could have
improved performance by using more optimal decision strategies:
delaying decision onset and lowering response threshold. These
adjustments could have been implemented without sacrificing the
desired level of response latency or accuracy.
To estimate the contributions of the different mechanisms, we
used the TONS_2221 model to predict changes in mean RT and
accuracy if subjects had increased either decision threshold or
delayed decision onset. The observed value was then normalized
to the total value that was predicted based on the estimated
adjustment of both response threshold and decision onset. Note
that these analyses are approximations only and implicitly
assumed a perfect fit of the model to the data. On average, the
increase of decision threshold alone explained 73616%
(mean6std) of the increase in RT and 56617% of the increase
in accuracy. Decision onset alone explained 31618% of the
increase in RT and 75623% of the increase in accuracy. Overall,
decision onset was a much more effective way of trading speed for
accuracy.
Discussion
The current study examined the role of decision onset for
optimal decision-making when selective feature-based attention is
needed to reduce interference from salient but irrelevant
distractors. Our study provides the first explicit measurements of
how strongly feature-based selective attention biases the flow of
sensory information on a millisecond time-scale over the time-
course of a decision. Our results suggest that it takes ,120 to
150 ms before the less salient but task-relevant target stimulus
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Figure 9. Fits of one of the ‘‘From-Scratch’’ models (CD_TON_222) to the data from the RT paradigm. Allowing the parameters of the CD
model to vary provided a significant improvement to the fits. Three of the CD parameters were not significantly different from the values recovered
from the CD paradigm. Two parameters (stimulus selection speed and stimulus selection onset) did show significant differences. Nevertheless,
decision onset was needed to explain the speed-accuracy tradeoff.
doi:10.1371/journal.pone.0089638.g009
Figure 10. Parameter estimates for decision onset and response threshold. (A) Time dependent drift rate as estimated from the CD
paradigm. The arrows indicate decision onset in the speed and accuracy condition as estimated from the TONS_2221 model. (B) Rate of information
transfer as a function of response threshold on the x-axis and onset of the decision process on the y-axis. Overlaid are the parameter estimates for
decision onset and response threshold from the TONS_2221 model. The lower left point on each line represents the parameters in the speed
condition, the upper right point represents the parameters in the accuracy condition. All subjects delayed decision onset and increased response
threshold in the accuracy condition. However, none of the subjects performed optimally. Information transfer in both conditions could have
improved by further delaying the onset of the decision and lowering response threshold.
doi:10.1371/journal.pone.0089638.g010
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exclusively determines the input to the decision process. Based on
the time-course of selective attention, we predicted that subjects
could trade speed for accuracy by delaying decision onset, and that
the onset mechanism could be more effective than the established
threshold mechanism. The third part of our study shows that
human subjects indeed use the onset mechanism to trade speed for
accuracy: they automatically delay decision onset until selective
attention can begin to isolate the relevant target when they are
required to stress response accuracy over speed. The estimated
delay of decision onset is substantial (50632 ms), significant
(p,10
24
), and highly consistent across all subjects. On average,
the observed 50 ms delay of decision onset alone would have
accounted for an estimated 75% of the observed improvement in
response accuracy while incurring only 31% of the cost in the form
of longer response latencies.
Alternative accounts: Attentional selection speed
It has been suggested that subjects stress accuracy by increasing
cognitive control in order to minimize distractor interference,
thereby accelerating the stimulus selection process [17]. In our
case, this account would require that subjects were capable of
accelerating the stimulus selection process beyond what was
explicitly measured in the cyclic deadline task. This is unlikely
because subjects were well-trained and motivated to perform
optimally in all task conditions, especially the cyclic deadline
version. If one were to assume that subjects were not performing
optimally on the cyclic deadline task, such that greater cognitive
control could and would have accelerated the selection process,
then stimulus selection should be faster on trials following errors
and incongruent stimuli, conditions believed to trigger cognitive
control [17]. The lack of such an effect (Table 4 and 5) provides
strong support for the argument that the speed of stimulus
selection measured in the cyclic deadline task indeed forms a lower
limit for the accuracy condition.
Alternatively, it is possible that the CD paradigm overestimated
the time it takes to select the relevant stimulus. Two observations
suggest that some overestimation could exist: (1) if the two subjects
with the weakest overall timing performance (subjects 6 and 7,
Tables 2 and 3) are excluded from the sample, stimulus selection
times based on data collapsed across the remaining 5 subjects are
reduced from ,150 to ,120 ms; (2) if the stimulus selection
parameters are fit directly to the data from the RT paradigm,
stimulus selection times are estimated to be ,110 ms. In both
cases, the termination of the stimulus selection process was
estimated to occur 120 ms after stimulus onset. This is still
significantly later than the 85 ms that are necessary to explain
speed-accuracy tradeoff according to the attentional selection
speed account (TAN_222 model).
A second argument against the attentional selection speed
account is its somewhat un-intuitive main assumption: greater
cognitive control and faster attentional selection result in slower
responses in the accuracy condition, and less cognitive control and
slower attentional selection result in faster responses in the speed
condition. First, it is unclear why subjects would choose to invest
less effort and cognitive control for the speed condition. After all,
subjects are never instructed to use less effort in the speed
condition; they are merely asked to stress a different aspect of the
task. The speed-condition provides a very engaging experimental
setting that should not go along with reduced effort. Second, faster
attentional selection would be equally if not more helpful for the
speed condition.
Overall, we believe that the onset mechanism provides a more
intuitive account of the data: accuracy is increased by delaying the
onset of the decision process to a more beneficial point in time;
speed is emphasized by advancing decision onset to a less
beneficial point in time. The subjects’ motivation to do the best
possible job in both conditions is reflected by the fact that the
amount of cognitive control, and hence attentional selection speed,
is assumed to be the same in both conditions. Because both
mechanisms can mimic each other and provide similar overall
effects in terms of accuracy and mean RT, it is important to note
that fits achieved with the onset mechanisms (TON_222 model)
are significantly better than the fits from the attentional selection
speed account (TAN_222 model). Taken together, these consid-
erations provide strong support for the delayed onset mechanism.
Neural correlates of delayed decision onset
Our findings suggest that decisions are not necessarily initiated
automatically by the presence of appropriate stimuli, but can be
adjusted within limits to current task demands. The observed
effects can only be explained by a neural mechanism that can
delay the onset of the decision process without interfering with the
allocation of selective attention. Note that this cannot be achieved
by blocking out sensory input, for example, by closing one’s eyes.
In the absence of sensory input, selective attention cannot be
allocated and the benefit of delaying decision onset is lost. To date
we are not aware of a compelling neural correlate of delayed
decision onset. Extra-cranial measurements of the onset of the
lateralized readiness potential (LRP) are inconclusive because it is
not clear whether LRP onset is more closely related to the onset of
the decision process [11] or its termination [35]. Regardless of
these problems of interpretation, different studies have either
found effects of speed-accuracy tradeoff on LRP onset [35] or not
[36,37].
There is some evidence in favor of a gating mechanism from
intracranial single-unit recordings [24,38] in the frontal eye-fields
(FEF). Based on the assumption that FEF motor neurons reflect the
accumulation of sensory evidence that is represented in visual FEF
neurons, these authors conclude that models with explicit gating of
sensory evidence provide the best account of behavioral and
neural data. Though the findings indicate the presence of a gating
mechanism that delays the onset of the response selection process,
the actual gating was not believed to occur in the temporal
domain. Rather, the authors support a model with two nested
firing rate thresholds, one that gates the flow of information from
FEF sensory neurons to FEF motor neurons and a second
threshold for response initiation.
A similar gating mechanism that operates in the firing rate
domain might also play a role in our dot-interference task.
However, there are strong arguments that favor temporal gating in
our task. First, increasing the gating threshold for both motion
channels would delay the integration of evidence for both
channels, but this delay would not be equal for the two channels
because the target contrast in our task was lower than the
distractor contrast. Thus, it would take the target motion channel
longer to cross threshold, thus increasing the impact of the
distractor and partially reversing the desired effect. Secondly, in
Purcell’s case [24], the gating operates on the activity of visual FEF
neurons that are believed to represent top-down mediated
salience. These salience signals require significant preprocessing
and have slow temporal dynamics that are reminiscent of neural
integrators. In our case, however, the gating would be expected to
operate on the activity of motion-selective neurons (e.g., in MT)
that have much faster temporal dynamics and lack the slow
increases of firing rate over time. Instead, MT neurons typically
respond with a burst of activity to motion onset before they begin
to become direction selective at a lower sustained firing rate.
Because of this strong unselective burst of activity, firing rate
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PLOS ONE | www.plosone.org 18 March 2014 | Volume 9 | Issue 3 | e89638
dependent gating would affect decision onset only within a rather
small range. Even more problematic, the predicted decision onset
would always happen during the initial burst, i.e. before MT
activity actually becomes selective for the direction of motion. The
key finding of our study, however, states that subjects delay
decision onset up to an average of 50 ms after the sensory evidence
becomes selective for direction of motion (Figure 10). Despite
these differences, we believe that there may be a way to partially
reconcile activity-dependent and temporal gating as outlined
below.
Our data indicate that decision onset can be affected by the
instructions to the subject to stress either speed or accuracy.
However, this is not necessarily the only determinant. In the
context of the RT paradigm we find a potentially informative
slight misfit of our model that may hint at an additional
determinant of decision onset: RTs in the neutral condition are
systematically longer than predicted by the model. In principle,
this may be due to additional non-decision time that is specific to
the neutral condition. However, the longer RTs also go along with
higher than predicted accuracy, indicating that they might be due
to a higher decision threshold or delayed decision onset (both
mechanisms lead to longer reaction times and higher accuracy).
But why would decision onset be delayed for the neutral relative to
the congruent and incongruent condition? Here we speculate that
decision onset may be modulated by the amount and/or salience
of potentially task-relevant information. Potentially task-relevant
information are dots moving either left- or rightwards. Dots
moving up- or downwards are a priori irrelevant to the task. In the
neutral condition, the distractors move upwards, thus reducing the
amount of potentially task-relevant information. If our hypothesis
is correct, this should delay decision onset, and increase RTs as
well as accuracy in the neutral condition only. In summary, we
speculate that that decision onset has at least two determinants:
internal factors (speed-accuracy setting) and sensory drive in the
shape of potentially relevant sensory information. This interpre-
tation partially blurs the border between strict activity-based
gating on the one hand (see above and [24]) and strict temporal
gating on the other. Alternative explanations for the slight misfit in
the neutral condition are possible, and at this point we have not
conducted additional experiments to confirm our hypothesis.
Subthalamic Nucleus and decision onset
In a number of groundbreaking recent studies, Frank and
colleagues have dissected the role of the sub-thalamic nucleus
(STN) for value-based decision making [39]. Their work has
generated a neural network model of decision-making that is based
on basal-ganglia anatomy and physiology (the BG model). In a
recent paper, Ratcliff & Frank [40] set out to modify a numerically
tractable diffusion model to capture the main properties of the
more complex BG model. They argue that higher activity in the
STN node of the BG model can be captured as an increase in
decision threshold. The temporal dynamics of STN activity can be
captured by exponentially collapsing response thresholds. Further,
the authors suggest that STN activity can be so high as to prevent
any responses from occurring and argue that this effect can be
captured as an increase in non-decision time. To a certain extent
our model shares common ideas with this body of work. In the
following, we outline some of the most important differences.
(1) The model by Ratcliff & Frank contains one parameter, non-
decision time, that represents both, the time of decision onset and
conduction delays in the system. Our model, in contrast, splits this
value into two independent parameters: decision onset and non-
decision time. This distinction is not only possible, but also
necessary, because in our paradigm drift-rate is non-stationary and
varies systematically over the time-course of a single trial. As a
result, we are able to distinguish whether subjects wait before
initiating the decision process (delayed decision onset), or whether
they wait to execute the response once they have made up their
mind (longer non-decision time). Though Ratcliff and Frank
present theoretical arguments that the former is the case, they
provide no experimental evidence for the assumption that subjects
delay decision onset, rather than increasing non-decision time.
The two scenarios can only be distinguished experimentally when
drift rate varies systematically over the time-course of a trial as is
the case in our paradigm.
(2) Ratcliff and Frank propose that STN activity has two effects:
an increase of the bound and an increase of non-decision time/
decision onset. While the former is beneficial and helps subjects
prolong the decision process in order to make more accurate
choices, the delayed decision onset serves its purpose only if the
quality of the sensory information improves over time. In our case,
the delayed decision onset dramatically improves accuracy
because it allows the decision to start at a point in time when
the sensory information is more selective for the target stimulus.
Hence, our study is the first demonstration that delaying decision
onset can serve a purpose and improve response accuracy.
(3) In the Frank & Ratcliff model, STN activity, and hence
decision onset, is determined by the amount of sensory conflict in
the stimulus – that is, decision onset is not necessarily controlled by
the subject. In our study, the stimuli are identical and the
difference in decision onset must be mediated by the instructions.
Hence, our study is the first demonstration that humans can
actively manipulate decision onset to improve decision accuracy.
Note, however, that subjects were not aware of how they were
improving accuracy. Hence, most likely, decision onset is out of
conscious control.
(4) Conversely, we do not allow our model to adjust decision
onset as a function of sensory conflict. The main argument for this
choice comes from the data of the CD paradigm that can be fit
very nicely with a model that assumes identical decision onsets that
are independent of conflict. However, the current study did not
explicitly test whether the model would benefit from letting
decision onset vary as a function of congruency. Hence, it is
possible that future analyses may reveal such an effect.
Overall, we believe that our paper shares similarities with the
work by Ratcliff & Frank. We would not be surprised if some of
the differences outlined above could be attributed to differences in
the tasks. In addition, we believe that the collapsing bound
suggested by Ratcliff & Frank may increase the quality of the fits in
our case, by reducing the over-dispersion that is observed for the
RT quantiles in the neutral and incongruent condition.
Challenges for the onset mechanism
A general challenge to the onset mechanism has been presented
by Larsen & Bogacz [23]. They argue that an additional
mechanism that determines decision onset would be computa-
tionally challenging and energy inefficient by adding an additional
layer of complexity to the decision process. Here we have outlined
that adjusting decision onset as a function of task demand (task set-
dependent gating) is computationally no more demanding than
adjusting response thresholds to task demands. The added
complexity can be justified by the potential benefits of delaying
decision onset that can far exceed those of response threshold
adjustments. The benefit of delaying decision onset depends on the
specific task in question. In artificial settings, when no distractors
are present and momentary evidence is approximately constant
over time, the potential benefit would certainly be smaller. In
situations when targets and distractors are far enough apart, overt
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PLOS ONE | www.plosone.org 19 March 2014 | Volume 9 | Issue 3 | e89638
attention, i.e. a gaze-shift to the relevant location, may partially
take over the role that covert allocation of attention plays in the
current task [41]. However, in many realistic situations where
relevant information is presented amidst very salient distractors,
the effect of decision onset can be substantial.
Sub-optimality of observed decision strategies
Our simulations highlight that our subjects set decision onset
and response threshold at suboptimal levels — all subjects could
have further decreased response latency without any loss in
accuracy (Figure 10). To maximize the rate of information
transfer, subjects would have needed to delay decision onset even
further while lowering response threshold. This result raises the
question: why did they not adopt a more optimal decision
strategy? We will argue below that subjects use suboptimal
strategies because they did not have enough time to find the
optimal strategy. In the context of the threshold model,
requirements of speed and accuracy are mutually exclusive and
subjects can trade one for the other by changing threshold; that is,
for any desired level of accuracy, there exists exactly one response
threshold. The resulting response latencies are, thus, ‘‘optimal’’.
Decision onset expands this one-dimensional view: the optimal
strategy is best described as a two-dimensional vector that specifies
response threshold and decision onset. Within this expanded
framework, any desired level of accuracy or response latency can
be achieved by an infinite number of threshold/onset combina-
tions (iso-accuracy/iso-latency lines in Figure 5A&B). All settings
will differ with respect to the rate of information transfer that they
provide (Figure 5C) and the true challenge is not only to meet a
required level of response accuracy/latency, but to do so while
optimizing information transfer. Moreover, in this framework it
may be imprecise to view the adjustment of speed and accuracy as
atradeoff rather than a two-dimensional optimization problem. This
optimization problem is challenging given the stochastic nature of
the dependent variables. For example, it will require hundreds of
trials to reliably differentiate a decision strategy providing 99%
accuracy from one providing 99.5%. A gradient-decent-like search
for the optimal decision strategy would require tens of thousands
of trials before converging on the optimal strategy. Hence, it is not
surprising that the subjects in our task did not find the optimal
strategy. It is possible, however, that subjects may learn to
implement optimal decision strategies through additional training
in combination with specific instructions that encourage them to
delay decision onset and reduce response threshold.
Comparison to other joint response signal/RT studies
Our study uses a powerful approach that includes two distinct
experimental paradigms: a response signal paradigm and a RT paradigm
with different requirements regarding speed and accuracy. This
dual approach was pioneered by Ratcliff to study decision-making
in a numerosity categorization task [33]. Here we applied the same
general approach to study decision-making in the presence of
salient distractors that cause stimulus and/or response conflict.
Due to the different requirements of this type of decision, we
adapted the methodology [33] in a number of ways, for example,
by using the cyclic deadline paradigm instead of the standard
response signal paradigm.
Early studies using a response signal paradigm assumed that
information continues to accumulate until the response signal is
given [30,31]. Ratcliff [33], however, found that it was necessary
to assume the presence of implicit response thresholds in the
response signal paradigm in order to accurately predict data from the
RT paradigm. Our study provides a somewhat different finding: the
assumption of implicit response thresholds in the response signal
paradigm (the CD paradigm) actually prevents accurate modeling of
the data in the CD paradigm itself. The problem is that for very long
processing times, subjects almost always respond accurately, even
in the incongruent condition. This implies that the decision
process never terminates at the threshold for the incorrect
response. There are three ways to deal with this issue when
modeling the data from the CD paradigm: (1) no response
thresholds are present, (2) response thresholds are present but set
to such extreme values that the incorrect threshold is never
reached or (3) the response thresholds are not absorbing but
reflecting, i.e. the integration of evidence continues even after the
threshold has been reached. In the current paper we assume
option (1) because it was conceptually, as well as computationally,
the simplest alternative and provided a very good quantitative fit
to the data in both paradigms. We believe that the apparent
discrepancy with Ratcliff’s earlier finding can be attributed to
differences in the tasks (numerosity categorization vs. Stroop-like
interference task).
Perfect versus leaky integration
All modeling efforts reported here are based on the assumption
of perfect integration. Perfect integration has been shown to be a
good assumption in many different tasks and conditions. However,
it is possible that a short integration time constant might be more
beneficial in a task in which drift rate changes systematically over
the time-course of a trial. In preliminary analyses we found that
data from the CD paradigm can be explained quite well using
perfect as well as leaky integration (data not shown). While it is
possible that the RT paradigm may be able to distinguish between
perfect and leaky integration, establishing this distinction was
beyond the scope of the current paper. It is, however, worth
mentioning that the only other model that predicts entire RT
distributions in a similar interference task, also uses perfect
integration [16].
Comparison of non-decision times in CD and RT task
One surprising yet very consistent finding were the longer non-
decision times in the RT paradigm (346628 ms) compared to the
CD paradigm (259613 ms). In principle, it is possible that the
novel CD paradigm did not provide accurate estimates of non-
decision time. However, the non-decision times measured with the
CD paradigm are in the expected range based on simple visual
RTs [42] that were confirmed in an exploratory experiment using
one example subject (data not shown). Overall, we argue that the
non-decision times estimated from the CD paradigm seem to be a
much more realistic estimate of the fixed delays in the system. This
implies that (1) either non-decision times are not estimated
correctly from the RT paradigm, or (2) non-decision times are
actually longer in the RT paradigm. Option 1 is possible, in
principle, but not very constructive because we cannot propose an
alternative model that can explain the data using shorter non-
decision times.
This leads to option 2. Here we consider 3 possibilities for why
non-decision times could actually be longer in the RT paradigm:
training effects, attention, and true paradigm-related differences.
The simplest explanation of the lower non-decision times in the
CD paradigm is additional training. By the time subjects
performed the CD paradigm, they had performed several hundred
trials in the RT paradigm, as well as a substantial amount of
training in the CD paradigm itself. All of this additional exposure
may have led to a more effective link between a stimulus/decision
and the corresponding response. However, given the intuitive
mapping between stimulus and response, we believe that the
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PLOS ONE | www.plosone.org 20 March 2014 | Volume 9 | Issue 3 | e89638
difference in non-decision time between the two tasks is larger than
what would be expected from training effects.
It is also possible that these differences in non-decision time
could be due to attentional effects. It is a well-known fact that
attention can dramatically affect reaction times [42], in particular
if a stimulus is presented unexpectedly. Hence, it could be argued
that non-decision times are shorter in the CD paradigm because it
provides a more engaging environment that makes it easier for
subjects to focus attention on upcoming stimuli. In fact, based on
our own observations and informal reports by the subjects, the CD
paradigm was more fun and less tiring. However, it is also
important to note that we took care to equalize temporal
predictability of the stimulus: in both paradigms, subjects could
anticipate stimulus onset. Hence, setting aside the ‘fun-factor’ of the
rhythmic responses, there is no reason why subjects should not
have been able to allocate the same amount of attention towards
the time of stimulus onset in both paradigms.
Finally, it is possible that the two paradigms have inherently
different non-decision times. Non-decision time in the RT
paradigm may be longer because of additional post-decision
overhead that is not present if subjects are pushed to their limit in
the CD paradigm. It is unclear what this overhead would
accomplish and why subjects would be willing to incur extra costs
that do not prolong the decision process itself and hence do not
contribute towards improving response accuracy. We speculate
that the additional time might be used to initiate post-decision
meta-analyses of the previous decision. Conversely, non-decision
times might be shorter in the CD paradigm, because it allows
subjects to influence their final motor response into a later stage of
processing. If this were the case, we might expect to see more trials
in which subjects accidentally press both buttons. Our data did not
allow us to quantitatively test this assumption, but from our own
subjective experience, this was not the case. If at all, double presses
seemed to be more common in the RT paradigm. Regardless of
what causes the longer non-decision times in the RT paradigm,
our findings suggest that a cyclic response mode may be quite
beneficial (by reducing non-decision times) in situations where
subjects need to make many successive and potentially boring
decisions.
Conclusions
The current study provides support for the idea that subjects
can strategically adjust decision onset to trade speed for accuracy
in a Stroop-like interference task. The finding that decision onset
can be adjusted to task demands has important implications for the
development of training methods to help individuals make fast
high-stake decisions in complex environments with salient
distractors. Current strategies to improve accuracy suggest subjects
should increase cognitive control in order to speed up the selection
of the relevant target [17,22]. While extensive training may
produce some speeding of the selection process, there is certainly a
physiological limit on how much the dynamics can be accelerated.
Manipulating decision onset provides an independent mechanism
to improve accuracy once that limit is reached by finding the
optimal balance between decision onset and response threshold.
Hence, our finding that decision onset can be controlled may spur
the development of new training programs to delay decision onset,
which could be particularly helpful for individuals or clinical
populations that have a slow stimulus selection process or who
make fast high-stakes decisions in complex realistic environments.
Supporting Information
Figure S1 The effect of biased competition on the
activity of a single motion channel. (A) Based on the
temporal progression of the biased competition in Layer 2, activity
of a motion channel can be grouped into two periods: the bottom-
up period in which activity reflects physical salience, the top-down
period in which activity reflects task-relevance. Note that in the
temporal dynamics of the biased competition process were chosen
for illustration purposes only and do not reflect the results of the
fits to the actual data. Activity is plotted for six different stimulus
configurations depending on the presence and direction of motion
of the target and distractor dots (see Legend for color code).
Conditions where either target and/or the distractor were not
present serve as a reference, but never occurred in the actual
experiment. Note that in the bottom-up period, the distractor
alone (black line) elicits stronger activity than when it is present in
combination with the target (green line). This reflects the finding
that cells will respond with an average firing rate if two stimuli are
presented in its receptive field simultaneously. Note that in the top-
down phase, the green and cyan lines converge towards the grey
line, while the orange line converges towards the red line. This
means that the motion channel responds as if the distractor were
less salient or even absent if the biased competition operates in a
winner-take-all fashion. (B) The relative response strength of the
individual conditions depends on the setting of the divisive
inhibition term I
in
in equation (2) that models the non-linear
contrast response function of the motion channel. All values
represent activity in the bottom-up period. In the top-down
period, responses converge to the grey, and red line, respectively,
as indicated in (A).
(TIFF)
Figure S2 Data and model fits in the cyclic deadline task for all
seven subjects separately. Conventions as in Figure 4.
(TIFF)
Figure S3 RT fits for one example subject and example
model (TON_222). Predicted (green/red lines) and measured
(black lines) RT distributions for one example subject in the RT
paradigm. In different sessions, the subject was instructed to
emphasize either speed (top row) or accuracy (bottom row). The
central portions of the plot depict the density of the simulated
decision variable as it develops over the time course of a trial
(yellow: high density, red: low density, log-scale). The black line
overlays accumulated mean drift rate as estimated from the cyclic
deadline task. The insets above and below the central portion
indicate the RT distribution for correct and error trials,
respectively. The green and red lines indicate the fit of the 6-
parameter TON_222 model to the data. For each condition,
accuracy and RT distributions were fit with three free parameters:
decision onset, t
0,
response threshold, 6B, and non-decision time.
All other parameters were set to the values estimated from the
cyclic deadline version of the task.
(TIFF)
Author Contributions
Conceived and designed the experiments: TT JG. Performed the
experiments: TT JG. Analyzed the data: TT. Contributed reagents/
materials/analysis tools: TT. Wrote the paper: TT JG VPF. Developed the
dots-interference task: JG Developed the cyclic deadline paradigm: TT.
Optimal Decision-Making and Decision Onset
PLOS ONE | www.plosone.org 21 March 2014 | Volume 9 | Issue 3 | e89638
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Optimal Decision-Making and Decision Onset
PLOS ONE | www.plosone.org 22 March 2014 | Volume 9 | Issue 3 | e89638
... According to this viewpoint, the brain needs PLOS time to aggregate enough evidence favoring one alternative over the other before reaching the critical amount of evidence that allows for making the decision. This is a time-costly process, however taking time helps in isolating the relevant sensory information from the noise and therefore to optimize the response [4]. ...
... In DDEs, it is convenient to perform this stimulation by adding a pulse σ to one of the populations. Thus, we set the value of the firing rate in population 2 to r 2 (t) = 0. 4 According to our extensive simulation of this model, presence of (1) values of delay above the critical point, for which the system crosses onto the unstable side; (2) a weak stimulus σ, are necessary for the stability switches to occur. ...
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It is known that cortical networks operate on the edge of instability, in which oscillations can appear. However, the influence of this dynamic regime on performance in decision making, is not well understood. In this work, we propose a population model of decision making based on a winner-take-all mechanism. Using this model, we demonstrate that local slow inhibition within the competing neuronal populations can lead to Hopf bifurcation. At the edge of instability, the system exhibits ambiguity in the decision making, which can account for the perceptual switches observed in human experiments. We further validate this model with fMRI datasets from an experiment on semantic priming in perception of ambivalent (male versus female) faces. We demonstrate that the model can correctly predict the drop in the variance of the BOLD within the Superior Parietal Area and Inferior Parietal Area while watching ambiguous visual stimuli.
... However, as a trial progressed, the mutual location probability showed tracking and avoidance behaviour in the medium and long condition trials. The idea that humans increasingly rely on sensory information as a trial progresses aligns with past research that showed humans delay their decision onset when there is noisy sensory evidence during initial stimulus presentation 32 . During collaborative tasks, utilizing early sensory evidence of a partner is important for achieving a common goal 17,18,[33][34][35] . ...
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We often acquire sensory information from another person’s actions to make decisions on how to move, such as when walking through a crowded hallway. Past interactive decision-making research has focused on cognitive tasks that did not allow for sensory information exchange between humans prior to a decision. Here, we test the idea that humans accumulate sensory evidence of another person’s intended action to decide their own movement. In a competitive sensorimotor task, we show that humans exploit time to accumulate sensory evidence of another’s intended action and utilize this information to decide how to move. We captured this continuous interactive decision-making behaviour with a drift-diffusion model. Surprisingly, aligned with a ‘paralysis-by-analysis’ phenomenon, we found that humans often waited too long to accumulate sensory evidence and failed to make a decision. Understanding how humans engage in interactive and online decision-making has broad implications that spans sociology, athletics, interactive technology, and economics.
... For non-regular events resulting from a stochastic process, decision-making can be biased towards timings when target events become more probable (Tsunoda and Kakei 2008;Oswal, Ogden, and Carpenter 2007;Janssen and Shadlen 2005), indicating that temporal expectation can be factored in perceptual decision-making. Consistent with this idea, temporal dynamics of sensory evidence accumulation during decision-making can change depending on the temporal contingencies of the ongoing task through adaptation of the onset (Teichert, Ferrera, and Grinband 2014) or the duration of the integration process (Ossmy et al. 2013;Piet, Hady, and Brody 2017;Mcwalter and Mcdermott 2018). Understanding how decision-making taps into temporal expectation to optimize behavior is of high importance to complement this picture. ...
Preprint
Estimating temporal regularities in incoming sensory inputs supports optimal decisions in noisy environments. In particular, inferred temporal structure can ease the detection of likely target events. Here we postulated that timely urgency signals can adapt subjects' decision-making to the ongoing task temporal structure, possibly through neuromodulatory tone. To test this hypothesis, we used an auditory change detection task in which targets followed a block-based temporal contingency, unbeknownst to participants. False alarm occurrences were driven by the distribution of target timings, indicating that participants adapted their behavior to the ongoing temporal structure. Task-evoked pupillary responses were larger for blocks with earliest target timings, and correlated with individual subjects' behavioral adaptation. Individual pupil responses matched an urgency signal extracted from a decision model fitted to behavior. This work demonstrates that internal temporal expectation can be tracked through pupillary dynamics, suggesting a role of neuromodulatory systems in context-dependent modulation of decision variable dynamics.
... 6. El tiempo, considerando el lapso que el ejecutivo toma para el inicio y finalización del proceso de la toma de decisiones (Teichert, Ferrera, & Grinband, 2014) (Hwang, 1994). El inicio implica el diagnóstico del problema, búsqueda y análisis de alternativas de solución, para finalizar con la selección de la alternativa más conveniente (Kepner & Tregoe, 1981). ...
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La toma de decisiones estratégicas es fundamental en las empresas para mantener sus ventajas competitivas y así asegurar su permanencia en el futuro. El propósito del presente trabajo fue identificar los factores del error humano en la toma de decisiones estratégicas en los niveles directivos de la industria siderúrgica mexicana que inciden en los sesgos de dicho proceso. Dentro de los factores, se determinaron entre otros la emocionalidad, la complejidad cognitiva, el tiempo y el contexto. Durante la primera fase de esta investigación se llevó a cabo un estudio exploratorio cualitativo a 11 ejecutivos de primer nivel dentro de la industria acerera, el análisis de esta información pone en evidencia que el error humano está presente en la toma de decisiones estratégicas.Palabras clave: error humano, niveles directivos y toma de decisiones estratégicas. Abstract.The strategic decision-making process is a keystone for companies to maintain their competitive advantage and prevail in the future. The purpose of this work was to identify the human error factors in the strategic decision-making process that influence bias at executive levels of the Mexican steel industry. Within the factors were, among others, emotionality, cognitive complexity, decision timing, and context. During the first phase of this research, a qualitative exploratory study was performed on 11 top executives from the steelmaking industry, the analysis of this information reveals that human error is present in strategic decision-making process.Key words: human error, strategic decision-making, top management.
... In the case of signals that require time-averaging to be properly estimated, subjects need to decide when it is beneficial to start the process of evidence accumulation. It has been reported that human observers delay their decision onset when asked to emphasize speed over accuracy (Teichert et al. [2014]), suggesting that the decision process is not necessarily initiated as soon as the evidence is available. ...
Thesis
Navigating a busy street while talking on the phone is trivial for a majority of the population. However, how the brain extracts the relevant information from the ever-changing and cluttered acoustic environment to produce the appropriate behavior remains poorly understood. The proposed thesis investigates neural basis of the extraction of relevant information in complex, continuous streams for goal-directed behavior using a combination technique linking electrophysiology to psychophysics. Humans and ferrets performed a similar change detection task that consisted of reporting changes in the underlying statistics of a toned cloud. The brain electrical activity was recorded (scalp level for humans and cell level for ferrets) while subjects engaged in the task. Overall, we find area-specific cortical responses: change-related responses are generalized along the cortical pathway. In addition, task engagement strongly modulates the frontal cortex where decision-related responses are found.
... The second findings are linked to the choice of 5 seconds latency within LED signals which was practical to reduce uncertainty impact due to accidental or recurrent anticipating reactions. This is also in good concordance with earlier observations of Teichert, Ferrera, 45 which showed that subjects increase accuracy by prolonging the decision process. The comparison of the B-percept shotgun results showed that the percentage of R 2 explains only 20.50% of predicted training-related gains in reaction time. ...
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Only a few research works have studied the risks involving young athletes in shooting activities such as noise and risk of projectile impact. Besides, limited studies have explored the environmental concerns caused by remaining projectile fragments scattered into the environment. In recent years, there has been an increasing interest in integrating computing, modeling, and IoT‐based applications and used connected add‐ons (e.g., steams Virtual Reality VR, virtual guns, and game controllers) in sports activities displayed in virtual reality gaming environments. The aim of this paper is, first, to present a multi‐aspect Zigbee‐based protocol system used to assess and to improve reaction time and score prediction abilities of Shotgun sports practitioners indoor and outdoor. Second, B‐percept would be presented as a training solution to reduce environmental scattered wastes of used Clays. After 8 weeks of training, there was significant improvement (p < .001) of participants' reaction time by using the B‐percept simulator. In addition, improvement in real clay shotgun results (p < .0002) but it was difficult to correctly predict more than 60% of correct scores after the test. The results of this study encourage continuing to improve the B‐percept to use wireless moving targets for training purposes.
... Outcomes of interest were judgment accuracy, flags approach knowledge, and attitudes and beliefs toward pain (while controlling for judgment speed and empathy). Research indicates that complex judgments require reflection [26], even though the "reflection" needed to make an accurate judgment may require only less than a second more than its intuitive counterpart [27]. As shorter judgment response times suggest less reflection involved in the judgment-making process, judgment speed was also analyzed in the current study. ...
Article
Background: Chronic lower back pain (CLBP) is a major health care burden and often results in workplace absenteeism. It is a priority for appropriate management of CLBP to get individuals back to work as early as possible. Interventions informed by the flags approach, which integrates cognitive and behavioral approaches via identification of biopsychosocial barriers to recovery, have resulted in reduced pain-related work absences and increased return to work for individuals with CLBP. However, research indicates that physicians' adherence to biopsychosocial guidelines is low. Objective: The current study examined the effects of a flags approach-based educational intervention on clinical judgments of medical students and general practitioner (GP) trainees regarding the risk of future disability of CLBP patients. Design: Randomized controlled trial (trial registration number: ISRCTN53670726). Setting: University classroom. Subjects: Medical students and GP trainees. Methods: Using 40 fictional CLBP cases, differences in clinical judgment accuracy, weighting, and speed (experimental N = 32) were examined pre- and postintervention, as were flags approach knowledge, pain attitudes and beliefs, and empathy, in comparison with a no-intervention control group (control N = 31). Results: Results revealed positive effects of the educational intervention on flags approach knowledge, pain-related attitudes and beliefs, and judgment weighting of psychologically based cues; results are discussed in light of existing theory and research. Conclusions: Short flags approach-based educational video interventions on clinical judgment-making regarding the risk of future disability of CLBP patients may provide opportunities to gain biopsychosocial knowledge, overcome associated attitude barriers, and facilitate development of clinical judgment-making more aligned with psychological cues.
... It is noteworthy that non-decision time was markedly longer-and the drift rate slower-in the uncued-incompatible compared to the uncuedcompatible tasks, resembling the switch cost in task-switching paradigms [75][76][77] . Longer non-decision time most likely reflected a delayed decision onset 78 , which humans can use as a strategy to trade accuracy over speed as previously shown with motioninterference tasks 79 . The increase of non-decision time induced by tSMS in the uncued-incompatible task may thus reflect this strategy of delaying decision onset to degrade consolidated/ automatic associations for resolving the stimulus-response conflict, thereby allowing evidence to be more efficiently accumulated for launching a well-prepared and more accurate action plan. ...
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Focal application of a strong static magnetic field over the human scalp induces measurable local changes in brain function. Whether it also induces distant effects across the brain and how these local and distant effects collectively affect motor behavior remains unclear. Here we applied transcranial static magnetic field stimulation (tSMS) over the supplementary motor area (SMA) in healthy subjects. At a behavioral level, tSMS increased the time to initiate movement while decreasing errors in choice reaction-time tasks. At a functional level, tSMS increased SMA resting-state fMRI activity and bilateral functional connectivity between the SMA and both the paracentral lobule and the lateral frontotemporal cortex, including the inferior frontal gyrus. These results suggest that tSMS over the SMA can induce behavioral aftereffects associated with modulation of both local and distant functionally-connected cortical circuits involved in the control of speed-accuracy tradeoffs, thus offering a promising protocol for cognitive and clinical research. Pineda-Pardo et al. show that focal application of a strong permanent magnet over the supplementary motor area shifts the speed-accuracy tradeoff towards accuracy by modulating both cortical circuits and distant cortical networks. This study suggests the utility of transcranial static magnetic field stimulation for cognitive research.
Article
Everyday life's perceptual decision-making is informed by experience. In particular, temporal expectation can ease the detection of relevant events in noisy sensory streams. Here, we investigated if humans can extract hidden temporal cues from the occurrences of probabilistic targets and utilize them to inform target detection in a complex acoustic stream. To understand what neural mechanisms implement temporal expectation influence on decision-making, we used pupillometry as a proxy for underlying neuromodulatory activity. We found that participants' detection strategy was influenced by the hidden temporal context and correlated with sound-evoked pupil dilation. A model of urgency fitted on false alarms predicted detection reaction time. Altogether, these findings suggest that temporal expectation informs decision-making and could be implemented through neuromodulatory-mediated urgency signals.
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We live in a world that changes on many timescales. To learn and make decisions appropriately, the human brain has evolved to integrate various types of information, such as sensory evidence and reward feedback, on multiple timescales. This is reflected in cortical hierarchies of timescales consisting of heterogeneous neuronal activities and expression of genes related to neurotransmitters critical for learning. We review the recent findings on how timescales of sensory and reward integration are affected by the temporal properties of sensory and reward signals in the environment. Despite existing evidence linking behavioral and neuronal timescales, future studies must examine how neural computations at multiple timescales are adjusted and combined to influence behavior flexibly.
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Traditional views of automaticity are in need of revision. For example, automaticity often has been treated as an all-or-none phenomenon, and traditional theories have held that automatic processes are independent of attention. Yet recent empirical data suggest that automatic processes are continuous, and furthermore are subject to attentional control. A model of attention is presented to address these issues. Within a parallel distributed processing framework, it is proposed that the attributes of automaticity depend on the strength of a processing pathway and that strength increases with training. With the Stroop effect as an example, automatic processes are shown to be continuous and to emerge gradually with practice. Specifically, a computational model of the Stroop task simulates the time course of processing as well as the effects of learning. This was accomplished by combining the cascade mechanism described by McClelland (1979) with the backpropagation learning algorithm (Rumelhart, Hinton, & Williams, 1986). The model can simulate performance in the standard Stroop task, as well as aspects of performance in variants of this task that manipulate stimulus-onset asynchrony, response set, and degree of practice. The model presented is contrasted against other models, and its relation to many of the central issues in the literature on attention, automaticity, and interference is discussed.
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A neglected question regarding cognitive control is how control processes might detect situations calling for their involvement. The authors propose here that the demand for control may be evaluated in part by monitoring for conflicts in information processing. This hypothesis is supported by data concerning the anterior cingulate cortex, a brain area involved in cognitive control, which also appears to respond to the occurrence of conflict. The present article reports two computational modeling studies, serving to articulate the conflict monitoring hypothesis and examine its implications. The first study tests the sufficiency of the hypothesis to account for brain activation data, applying a measure of conflict to existing models of tasks shown to engage the anterior cingulate. The second study implements a feedback loop connecting conflict monitoring to cognitive control, using this to simulate a number of important behavioral phenomena.
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When people make errors during continuous tasks they temporarily pause and then slow down. One line of explanation has been that they monitor feedback to detect errors, that they may make incidental responses when errors occur (e.g. they may swear) and that they may pause to analyse their errors. In all these cases they may be assumed to act as single channel information processing systems of limited capacity, and to be unable to recognise any new signal until these processes have been completed. Analysis of response after errors shows that this cannot be the case. Responses after errors are inaccurate, but are not slow when they require the subject to make the response which he should have made on the previous trial (i.e. to make an error correction response). Subjects thus must recognise new signals as soon as they occur. The present results require a new model of error detection and correction, and a model for response programming and priming.
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Develops a theory of memory retrieval and shows that it applies over a range of experimental paradigms. Access to memory traces is viewed in terms of a resonance metaphor. The probe item evokes the search set on the basis of probe–memory item relatedness, just as a ringing tuning fork evokes sympathetic vibrations in other tuning forks. Evidence is accumulated in parallel from each probe–memory item comparison, and each comparison is modeled by a continuous random walk process. In item recognition, the decision process is self-terminating on matching comparisons and exhaustive on nonmatching comparisons. The mathematical model produces predictions about accuracy, mean reaction time, error latency, and reaction time distributions that are in good accord with data from 2 experiments conducted with 6 undergraduates. The theory is applied to 4 item recognition paradigms (Sternberg, prememorized list, study–test, and continuous) and to speed–accuracy paradigms; results are found to provide a basis for comparison of these paradigms. It is noted that neural network models can be interfaced to the retrieval theory with little difficulty and that semantic memory models may benefit from such a retrieval scheme. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
Article
( This reprinted article originally appeared in the Journal of Experimental Psychology, 1935, Vol 18, 643–662. The following abstract of the original article appeared in PA, Vol 10:1863.) In this study pairs of conflicting stimuli, both being inherent aspects of the same symbols, were presented simultaneously (a name of one color printed in the ink of another color—a word stimulus and a color stimulus). The difference in time for reading the words printed in colors and the same words printed in black is the measure of the interference of color stimuli on reading words. The difference in the time for naming the colors in which the words are printed and the same colors printed in squares is the measure of the interference of conflicting word stimuli on naming colors. The interference of conflicting color stimuli on the time for reading 100 words (each word naming a color unlike the ink-color of its print) caused an increase of 2.3 sec or 5.6% over the normal time for reading the same words printed in black. This increase is not reliable, but the interference of conflicting word stimuli on the time for naming 100 colors (each color being the print of a word which names another color) caused an increase of 47.0 sec or 74.3% of the normal time for naming colors printed in squares.… (PsycINFO Database Record (c) 2012 APA, all rights reserved)