Modeling the Stop-Signal Task to Understand Response Inhibition

Modeling response inhibition
Bram Zandbelt
bramzandbelt@gmail.com
@bbzandbelt
https://www.bramzandbelt.com
Download at:
http://www.slideshare.net/bramzandbelt/modeling-response-inhibition

Preview
Modeling
response
inhibition
1. Response inhibition - what, why, how
1.1 What is it?
1.2 Why is it relevant?
1.3 How is it studied?
1.4 What are the main findings?
2. Independent race model
2.1 What is the independent race model?
2.2 What are its assumptions?
2.3 How does it account for response inhibition
findings?
2.5 What are its strengths and weaknesses?
3. Sequential sampling models of
response inhibition
3.1 What are sequential sampling models?
3.2 What are their assumptions?
3.3 How do they account for response inhibition
findings?
3.4 What are their strengths and weaknesses?
4. Modeling response inhibition in a
broader context
4.1 Response inhibition is multidimensional
4.2 Multiplicity of modeling approaches
Bram Zandbelt

1.1 What is it?
Sources: Aron (2007) Neuroscientist; see also MacLeod et al. (2003) in Psychology of learning and motivation, B. Ross, Ed., vol. 43, pp. 163–214. Lawrence,
Eleanor, ed. Henderson's dictionary of biology. Pearson education, 2005.
Bram Zandbelt

Ubiquitous in everyday life 
From emergency and sports situations
to more complex behavior
Bram Zandbelt

Implicated in many clinical conditions 
From the obvious (ADHD, OCD, TS) to the less
obvious (schizophrenia, Parkinson’s)
Bram Zandbelt

Williams et al. (1999) Dev Psych
Changes across the lifespan 
Stopping latency develops during childhood
and declines during aging
Bram Zandbelt

Changes across the lifespan 
Stopping latency develops during childhood
and declines during aging
Might have translational value 
Response inhibition training might improve  
self-control (food intake, gambling)
Bram Zandbelt

Various paradigms 
Antisaccade, go/no-go, stop-signal, Stroop
Bram Zandbelt

Sources: Aron (2007) Neuroscientist
Bram Zandbelt

Sources: Thomson Reuters Web of Science
Productive 
~150 publications/year, stop-signal task only
Bram Zandbelt

Sources: Verbruggen et al. (2013) Psych Sci
Interdisciplinary 
Medicine, neuroscience, psychology
Productive 
Bram Zandbelt

st SS
GO STOP
βGO
= 0.005
βSTOP
= 0.111
μGO
= 5.08
σGO
= 26.24
μSTOP
= 5.07
σSTOP
= 26.34
ΔGO
= 51 ΔSTOP
= 51
θGO
= 1000
Sources: http://www.healthcare.philips.com/,
Converging methodologies 
Imaging, lesion, modeling, neurophysiology,
pharmacology, stimulation
Productive 
Bram Zandbelt

Sources: http://www.cognitive-fab.com, Schall lab, Schmidt et al. (2013) Nat Neurosci
Different species 
Humans, monkeys, rats
Productive 
Bram Zandbelt

Sources: Massachusetts General Hospital; ; Goonetilleke et al. (2012) J Neurophysiol; Tabu et al. (2012) Neuroimage; Claffey et al. (2010) Neuropsychologia
Different species 
Humans, monkeys, rats
Various effector systems 
Arm, eye, eye-head, eye-hand, finger, foot,
hand, speech
Productive 
Bram Zandbelt

Stop-signal task demonstration
1.3 How is it studied? - Stop-signal task
Bram Zandbelt

no-signal trial
time
Fixation
Target
Bram Zandbelt

no-signal trial
time
RT
Fixation
Target
Bram Zandbelt

time
Fixation
Target
no-signal trial
stop-signal trial
time
RT
Fixation
Target
Bram Zandbelt

time
SSD
SSD
Fixation
Target
no-signal trial
stop-signal trial
time
RT
Fixation
Target
Bram Zandbelt

signal-
inhibit
time
SSD
SSD
Fixation
Target
no-signal trial
stop-signal trial
time
RT
Fixation
Target
Bram Zandbelt

signal-
inhibit
signal-
respond
time
SSD
SSD RT
Fixation
Target
or
no-signal trial
stop-signal trial
time
RT
Fixation
Target
Bram Zandbelt

signal-
inhibit
signal-
respond
time
SSD
SSD RT
Fixation
Target
or
no-signal trial
stop-signal trial
time
RT
Fixation
Target
Dependent variables 
P(response | stop-signal)
RT on no-signal trials
RT on signal-respond trials
Independent variable 
Stop-signal delay (SSD)
Bram Zandbelt

1.4 What are the main findings? - Behavior
1. Ability to stop decreases with delay 
Bram Zandbelt

2. Inhibition error RTs are fast … 
Bram Zandbelt

2. Inhibition error RTs are fast … 
… and increase with delay 
Bram Zandbelt

… across effector systems 
e.g. finger, arm, eye
ﬁnger
arm
eye
Remarkable generity of findings
Bram Zandbelt
Sources: Logan & Cowan (1984) Psych Rev; Mirabella et al. (2006) Exp Brain Res; Boucher et al. (2007) Percept Psychophys

auditory
visual
tactile
… across stimulus-modalities 
e.g. visual, auditory, tactile
Bram Zandbelt
Sources: Logan & Cowan (1984) Psych Rev; Cable et al. (2000) Exp Brain Res; Åkerfelt et al. (2006) Exp Brain Res;

monkey
rat
human
… across stimulus-modalities 
e.g. visual, auditory, tactile
… across species 
e.g. rats, monkeys, humans
Bram Zandbelt
Sources: Logan & Cowan (1984) Psych Rev; Hanes & Schall (1995) Vis Res; Eagle et al. (2003) Behav Neurosci

Signatures of stopping in motor system 
Neurophysiology shows that build-up of
response-related activation is interrupted
FEF
PM
M1
SC
Striatum
GP
STN
1.4 What are the main findings? - Brain
Bram Zandbelt

FEF
PM
M1
SC
Striatum
GP
STN
Figure courtesy of J.D. Schall
Sources: Hanes et al. (1998) J Neurophysiol; Paré & Hanes (2003) J Neurosci; Mirabella et al. (2012) J Neurophysiol;
Schmidt et al. (2013) Nat Neurosci; Emeric & Stuphorn (preliminary data)
Bram Zandbelt

Involvement of cognitive systems 
Neuroimaging reveals activation of a large
network of fronto-parietal and basal ganglia
areas when stopping a response
FEF
PM
M1
SC
Striatum
GP
STN
Bram Zandbelt

Sources: Aron & Poldrack (2006) J Neurosci; Li et al. (2006) J Neurosci; Zandbelt & Vink (2010) PLoS ONE
Bram Zandbelt

Involvement of cognitive systems 
Neuroimaging reveals activation of a large
network of fronto-parietal and basal ganglia
areas on stop trials
Disturbance/damage affects stopping 
Perturbance and lesions to cognitive and motor
areas influence ability to stop
FEF
PM
M1
SC
Striatum
GP
STN
Bram Zandbelt

Sources: Aron et al. (2003) Nat Neurosci; Chambers et al. (2006) J Cogn Neurosci; Floden & Stuss (2006) J Cogn Neurosci; Nachev et al. (2007) Neuroimage; Swick
et al. (2008) BMC Neurosci; Chen et al. (2009) Neuroimage; Verbruggen et al. (2010) Proc Natl Acad Sci USA
Bram Zandbelt

Modeling
response
inhibition
1. Response inhibition - what, why, how
1.1 What is it?
1.4 What are the main findings?
2. Independent race model
2.3 How does it account for response inhibition
findings?
3. Sequential sampling models of
response inhibition
3.3 How do they account for response inhibition
findings?
4. Modeling response inhibition in a
broader context
4.1 Response inhibition is multidimensional
4.2 Multiplicity of modeling approaches
Bram Zandbelt

Psychological Review
1984, Vol. 91, No. 3, 295-327
Copyright 1984 by the
American Psychological Association, Inc.
On the Ability to Inhibit Thought and Action:
A Theory of an Act of Control
Gordon D. Logan
University of British Columbia, Vancouver,
British Columbia, Canada
William B. Cowan
National Research Council of Canada, Ottawa,
Ontario, Canada
Many situations require people to stop or change their current thoughts and actions.
We present a theory of the inhibition of thought and action to account for people's
performance in such situations. The theory proposes that a control signal, such as
an external stop signal or an error during performance, starts a stopping process
that races against the processes underlying ongoing thought and action. If the
stopping process wins, thought and action are inhibited; if the ongoing process
wins, thought and action run on to completion. We develop the theory formally
to account for many aspects of performance in situations with explicit stop signals,
and we apply it to several sets of data. We discuss the relation between response
inhibition and other acts of control in motor performance and in cognition, and
we consider how our theory relates to current thinking about attentional control
and automaticity.
Thought and action are important to sur-
vival primarily because they can be controlled;
that is, they can be directed toward the ful-
fillment of a person's goals. Control has been
a central issue in the study of motor behavior
since the turn ofthe century (e.g., Sherrington,
1906; Woodworth, 1899; see Gallistel, 1980,
for a review), and it has been important in
psychology since K. J. W. Craik's seminal pa-
pers in 1947 and 1948. Students of motor be-
havior have not forgotten the importance of
control and have developed sophisticated the-
ories that integrate behavioral and physiolog-
ical data (e.g., Feldman, 1981; Kelso & Holt,
1980; Navas & Stark, 1968; Robinson, 1973;
Young & Stark, 1963). However, psychologists
have strayed from the path somewhat over the
years,
Craik's papers, which described the human
performer as an engineering system, provided
a framework in which to study tracking tasks
and stimulated interest in the (possibly inter-
mittent) nature of the control system in such
tasks. This approach kindled interest in the
psychological refractory period (e.g., Hick,
This research was supported by Grant U0053 from the
Natural Sciences and Engineering Research Council of
Canada to Gordon D. Logan.
Requests forreprints should be sent to Gordon D. Logan,
who is now at the Department of Psychological Sciences,
Purdue University, West Lafayette, Indiana 47907.
1949; Vince, 1948), which led to the formu-
lation of single-channel theory (Davis, 1957;
Welford, 1952). In the hands of Broadbent
(1958) and others, single-channel theory was
extended to deal with many diverse phenom-
ena of attention, and dominated theories of
attention for nearly 20 years. The extended
single-channel theory attracted the interest of
cognitive psychologists who dealt primarily
with tasks other than tracking, and, in their
hands, control became less important than did
other issues such as memory (Norman, 1968),
expectancy (LaBerge, 1973), selectivity (Treis-
man, 1969), and time sharing (Posner &Boies,
1971). Single-channel theory was replaced by
capacity theory (Kahneman, 1973) and mul-
tiple-resource theory (Navon & Gopher, 1979),
and little attention was paid to problems of
control (but see Broadbent, 1977; Reason &
Myceilska, 1982; Shallice, 1972; more gen-
erally, see Gallistel, 1980; Kimble & Perlmuter,
1970; Miller, Galanter, & Pribram, 1960;
Powers, 1978),
Recently, cognitive psychologists have be-
come interested in control once more, in the
guise of research on automaticity and skill(e.g.,
Anderson, 1982; Hasher & Zacks, 1979; Lo-
gan, 1978; Posner, 1978;Shiffrin& Schneider,
1977), but the studies bear little resemblance
to the early fruits of Craik's seminal thinking
and even less resemblance to studies of motor
behavior. Whereasthe earlier studies in Craik's
295
Sources: Logan& Cowan (1984) Psych Rev; see also Logan et al. (2014) Psych Rev
Theory of performance in stop task 
Published in 1984 by Logan and Cowan
Bram Zandbelt

Sources: Verbruggen et al. (2013) Psych Sci
Widely used across various fields 
Bram Zandbelt

Sources: Verbruggen & Logan (2008) Trends Cogn Sci
Widely used across various fields 
Method for estimating stopping latency 
Stopping latency cannot be observed directly,
but can be estimated from the data with help of
the independent race model
Bram Zandbelt

timetarget stop-
signal
signal-
inhibit
GO
STOP
GO
STOP
signal-
respond
RT
RT
SSRT
SSRT
Race between GO and STOP 
Target triggers GO, stop-signal triggers STOP
If GO wins, a response is produced
If STOP wins, a response is inhibited
Bram Zandbelt

Stochastic independence
Context independence
STOP and GO are independent 
Stochastic: random variation is unrelated
Context: trial type does not influence GO RT
Bram Zandbelt

Stopping latency derived from data 
The stop-signal reaction time (SSRT) can be
derived by integrating the no-signal RT
distribution until the point where it equals
P(respond | stop-signal)
STOP and GO are independent 
Stochastic: random variation is unrelated
Context: trial type does not influence GO RT
Bram Zandbelt

2.3 How does it account for the main findings?
Delays bias the race in favor of GO 
So ability to stop decreases with longer delays
Bram Zandbelt

Bram Zandbelt

So ability to stop decreases with longer delays
RTs occur only when RTGO < RTSTOP 
Therefore, inhibition error RTs are fast
Hence, inhibition error RTs increase with delay
Bram Zandbelt

Criterion Description Evaluation of the independent race model
Falsifiability
Do potential observations exist that would
be incompatible with the modell?
Plausibility
Does the theoretical account of the model
make sense of established findings?
Interpretability
Are the components of the model
understandable and linked to known
processes?
Goodness of fit
Does the model fit the observed data
sufficiently well?
Complexity
Is the model’s description of the data
achieved in the simplest possible manner?
Generalizability
Does the model provide a good prediction
of future observations?
Bram Zandbelt

Falsifiability
Decreasing inhibition function
Signal-respond RTs that are slower than no-signal RTs
Signal-respond RTs that do not increase with delay
Plausibility
Interpretability
processes?
Goodness of fit
sufficiently well?
Complexity
Generalizability
Bram Zandbelt

Falsifiability
Plausibility
Assumption of a race seems plausible
Assumption of independence appears unlikely
It cannot explain deflection of motor-related activity
Interpretability
processes?
Goodness of fit
sufficiently well?
Complexity
Generalizability
Bram Zandbelt

Falsifiability
Plausibility
Interpretability
processes?
SSRT has face validity in psychology and neuroscience
It does not specify subprocesses of GO and STOP
It does not predict trial-to-trial variation in SSRT
Goodness of fit
sufficiently well?
Complexity
Generalizability
Bram Zandbelt

Bram Zandbelt

Bram Zandbelt
Lesions Magnetic stimulation Pharmacology
Clinical disorders Development
Sources: Thakkar et al. (2011) Biol Psychiatry; Van de Laar et al. (2011) Front Psychol; Aron et al. (2003); Chambers et al. (2006) J Cogn Neurosci; Chamberlain et
al. (2006) Science

FEF
PM
M1
SC
Striatum
GP
STN
Figure courtesy of J.D. Schall
Sources: Hanes et al. (1998) J Neurophysiol; Paré & Hanes (2003) J Neurosci; Mirabella et al. (2012) J Neurophysiol;
Schmidt et al. (2013) Nat Neurosci; Emeric & Stuphorn (preliminary data)
Bram Zandbelt

Falsifiability
Plausibility
Interpretability
processes?
Goodness of fit
sufficiently well?
Model’s predictions have held for decades
It underestimates signal-respond RTs for early SSDs
(e.g. Colonius, 2001; Gulberti & Colonius, 2014)
Complexity
Generalizability
Bram Zandbelt

Falsifiability
Plausibility
Interpretability
processes?
Goodness of fit
sufficiently well?
Complexity
It makes few assumptions, and is generic, non-parametric
Generalizability
Bram Zandbelt

Falsifiability
Plausibility
Interpretability
processes?
Goodness of fit
sufficiently well?
Complexity
It makes few assumptions, and is generic, non-parametric
Generalizability
It generalizes across effector systems, stimulus
modalities and species
Bram Zandbelt

Moving left or right?
Prefer Doritos or M&M’s?
Models of decision making 
Choices between alternatives, based on
perceptual evidence or subjective preference
Bram Zandbelt

Choose left
Choose right
+
Explain choice and response time 
Of all response types, relation between error
and correct response times
Bram Zandbelt

Choose left
Choose right
Mechanism: accumulation to threshold 
Accumulation of perceptual evidence or
subjective preference
Bram Zandbelt

Various sequential sampling models …
… and their relationships
Sources: Bogacz et al. (2006) Psych Rev
Constitute a family of models 
Diffusion (feed-forward), leaky competitive
accumulator (mutual inhibition), linear ballistic
accumulator (race)
Bram Zandbelt

Constitute a family of models 
Diffusion (feed-forward), leaky competitive
accumulator (mutual inhibition), linear ballistic
accumulator (race)
Extended to other domains 
Decision making in intertemporal choice, visual
search, response inhibition, among others
Visual search
Response inhibition
Sources: Purcell et al. (2012) J Neurosci; Boucher et al. (2007) Psych Rev
Bram Zandbelt

Evidence accumulation to a threshold 
Evidence favoring each alternative is integrated
over time. A decision is made when sufficient
evidence is accumulated.
Evidence
Choose left / Doritos
Choose right / M&M’s
Bram Zandbelt

t0
v
θ
Evidence
Behavior decomposed into parameters
that map onto cognitive processes 
Non-decision time (t0) - encoding, execution 
Rate (v) - accumulation of evidence/preference 
Threshold (θ) - decision making criterion
Leakage (k) - ‘memory loss’
Lateral inhibition (w) - choice competition
LEFT RIGHT
v, t0v, t0
w
kk
w
Bram Zandbelt

3.2 What are their assumptions?Evidence
LEFT RIGHT
Behavior decomposed into parameters
that map onto cognitive processes 
Non-decision time (t0) - encoding, execution 
Rate (v) - accumulation of evidence/preference 
Threshold (θ) - decision making criterion
Leakage (k) - ‘memory loss’
Lateral inhibition (w) - choice competition
Subject to random fluctuations 
Variation in parameters, within and/or across
trials, determines fluctuations in performance
Response time distribution
Bram Zandbelt

3.3 How do they account for response inhibition findings?
Extend the model with STOP unit 
STOP unit races independently or interactively
with the GO unit
Sources: Boucher et al. (2007) Psych Rev
Independent race
Interactive race
Bram Zandbelt

Independent race
Interactive race
with the GO unit
Bram Zandbelt

with the GO unit
Models explain behavior equally well 
Other data necessary to resolve model mimicry
Bram Zandbelt

Sources: Schall (2009) Encylop Neurosci
with the GO unit
FEF
Interactive race explains neural data 
Independent race model cannot explain
deflection seen in FEF/SC movement neurons
Bram Zandbelt

with the GO unit
Sources: Hanes et al. (1998) J Neurophysiol
Bram Zandbelt

with the GO unit
Bram Zandbelt

GO STOPGO STOP
Δt
with the GO unit
STOP interacts late and potently 
Weak interaction causes slowing of response
times on signal-respond trials
Bram Zandbelt

Sources: Logan et al. (2015) Psych Rev
with the GO unit
STOP interacts late and potently 
Weak interaction causes slowing of response
times on signal-respond trials
Lateral inhibition is just one possibility 
Blocking input to the GO unit is another
Bram Zandbelt

Criterion Description Evaluation of the interactive race model
Falsifiability
Neurophysiological assumptions are falsifiable, for
behavioral assumptions this is less clear (e.g. Jones &
Dzhafarov 2014 Psych Rev)
Plausibility
Interpretability
processes?
Goodness of fit
sufficiently well?
Complexity
Generalizability
Bram Zandbelt

Falsifiability
Plausibility
Late, potent interaction explains seeming independence
Assumes STOP unit is off when model starts
processing (but see Logan et al. 2015)
Interpretability
processes?
Goodness of fit
sufficiently well?
Complexity
Generalizability
Bram Zandbelt

Falsifiability
Plausibility
Interpretability
processes?
Parameters map onto plausible cognitive processes
Model predicts variability in SSRT
Goodness of fit
sufficiently well?
Complexity
Generalizability
Bram Zandbelt

Falsifiability
Plausibility
Interpretability
processes?
Goodness of fit
sufficiently well?
Model fits both behavior and monkey neurophysiology
Complexity
Generalizability
Bram Zandbelt

Falsifiability
Plausibility
Interpretability
processes?
Goodness of fit
sufficiently well?
Complexity
Explaining behavior and neurophysiology, the model is
relatively simple
Generalizability
Bram Zandbelt

Falsifiability
Plausibility
Interpretability
processes?
Goodness of fit
sufficiently well?
Complexity
Explaining behavior and neurophysiology, the model is
relatively simple
Generalizability
Generalizes to data from monkeys performing different
tasks in different labs and also to human data
(e.g. Lo et al. 2009; Ramakrishnan et al. 2012)
Bram Zandbelt

4.1 - Response inhibition is multidimensional
all-or-none
(any response)
spur-of-the-moment
(without preparation)
all-or-none
(any secondary signal)
Bram Zandbelt

Bram Zandbelt

stopping some actions,
while continuing others
restraining actions
in preparation for stopping
stopping to some stimuli,
while ignoring others
non-selective, reactive stopping
Bram Zandbelt

4.2 - Multiplicity of modeling approaches
Neural network
Wilson & Cowan (1972)
Rumelhart (1986)
Stochastic
accumulator
Usher & McClelland (2001)
Brown & Heathcote (2008)
Bayes optimal
decision-making
Non-process/
descriptive
LATER-like
Carpenter & Williams (1995)
simple
stopping
selectivity
choice
simple
changing
executive
control
RT
SSRT
Logan & Cowan (1984)
Camalier et al. (2007)
Zandbelt et al. (in prep.) Wiecki & Frank (2013)
Shenoy & Yu (2011)
Liddle et al. (2009)
Leotti & Wager (2010)
Ide et al. (2014)Pouget et al. (2011)
Ramakrishnan et al. (2012)
Boucher et al. (2007)
Salinas & Stanford (2013)
Marcos et al. (2013)
Yang et al. (2013)
Lo et al. (2009)
Mattia et al. (2013)
Schmidt et al. (2013)
Logan et al. (2014)
Zandbelt et al. (in prep)
Middlebrooks et al. (in prep)
Ramakrishnan et al. (2010)
GO STOP
Hanes & Carpenter (1999);
Kornylo et al. (2003);
Corneil & Elsley (2005);
Walton & Gandhi (2006);
Goonetilleke et al. (2012)
GO2 RT
GO1 RT
SSRT
Logan et al. (2014)
GO STOP
Bram Zandbelt

Further reading
Boucher, L., Palmeri, T. J., Logan, G. D., & Schall, J. D.
(2007). Inhibitory control in mind and brain: an
interactive race model of countermanding saccades.
Psychological Review, 114(2), 376.
Verbruggen, F., & Logan, G. D. (2008). Response
inhibition in the stop-signal paradigm. Trends in
Cognitive Sciences, 12(11), 418–424
Logan, G. D., Yamaguchi, M., Schall, J. D., & Palmeri,
T. J. (2015). Inhibitory control in mind and brain 2.0:
Blocked-input models of saccadic countermanding.
Psychological Review, 122(2), 115–147
Inhibitory Control in Mind and Brain: An Interactive Race Model of
Countermanding Saccades
Leanne Boucher, Thomas J. Palmeri, Gordon D. Logan, and Jeffrey D. Schall
Vanderbilt University
The stop-signal task has been used to study normal cognitive control and clinical dysfunction. Its utility
is derived from a race model that accounts for performance and provides an estimate of the time it takes
to stop a movement. This model posits a race between go and stop processes with stochastically
independent finish times. However, neurophysiological studies demonstrate that the neural correlates of
the go and stop processes produce movements through a network of interacting neurons. The juxtapo-
sition of the computational model with the neural data exposes a paradox—how can a network of
interacting units produce behavior that appears to be the outcome of an independent race? The authors
report how a simple, competitive network can solve this paradox and provide an account of what is
measured by stop-signal reaction time.
Keywords: stop-signal task, cognitive control, frontal eye field, cognitive modeling, stochastic decision
models
The task of cognitive neuroscience is to bring behavioral and
physiological data together to explain how mental computations
are implemented in the brain. This task is difficult when behavioral
and physiological data appear to contradict each other. In these
situations, a new theory is required to resolve the contradiction.
This article reports results from an endeavor to resolve a paradox
in the behavioral and physiological analyses of the stop-signal
task. For over 20 years, behavioral data have been modeled suc-
cessfully in terms of a race between two independent processes
that respond to the stop signal and the go signal (Logan & Cowan,
1984). However, the neural systems that control movements com-
prise layers of inhibitory interactions between neurons that imple-
ment movement inhibition and movement initiation (reviewed by
Munoz & Schall, 2003). These two facts present a paradox: How
can interacting neurons produce behavior that appears to be the
outcome of independent processes? We present a new theory of
performance in the stop-signal task—the interactive race model—
which assumes that the stop and go processes are independent for
most of their latent periods. After this latent period, a second stage
occurs in which the stop process interacts strongly and briefly to
interrupt the go process. The theory resolves the paradox and
unifies behavioral and physiological perspectives on stop-signal
task performance. More generally, our work illustrates a novel
approach to bringing neurophysiological data to bear on quantita-
tive computational model testing.
The Stop-Signal Task
The stop-signal task investigates the control of thought and
action by probing subjects’ ability to withhold a planned move-
ment in response to an infrequent countermanding signal (see
Figure 1a; e.g., Lappin & Eriksen, 1966; Logan, 1994; Logan &
Cowan, 1984). Subjects are instructed to make a response as
quickly as possible to a go signal (no-stop-signal trial). On a
minority of trials, a stop signal is presented and subjects have to
inhibit the previously planned response (stop-signal trial). Sub-
jects’ ability to inhibit the response is probabilistic due to vari-
ability in reaction times (RTs) of the stop and go processes and
depends on the interval between the go-signal and stop-signal
presentation, referred to as the stop-signal delay (SSD). A trial is
labeled signal inhibit (or cancelled) if the subject inhibits the
response that would have been produced otherwise. A trial is
labeled as signal respond (or noncancelled) if the subject is unable
to inhibit the response. Typically, as SSD increases, subjects’
ability to inhibit the response decreases, so the probability of
signal-respond trials increases. Plotting the probability of respond-
ing given a stop signal against SSD is described as the inhibition
function and is illustrated in Figure 1. In addition to the inhibition
function, other dependent measures include RTs on trials with no
stop signal and RTs on trials in which a response was made despite
the stop signal (i.e., the signal-respond trials).
Leanne Boucher, Thomas J. Palmeri, Gordon D. Logan, and Jeffrey D.
Schall, Department of Psychology, Vanderbilt University.
This work was supported by Robin and Richard Patton through the E.
Bronson Ingram Chair in Neuroscience; National Science Foundation
Grants BCS0218507 and BCS0446806; and National Institutes of Health
Grants F32-EY016679, RO1-MH55806, RO1-EY13358, P30-EY08126,
and P30-HD015052. We thank M. Pare´ for sharing data; J. Brown, C.
Camalier, M. Leslie, R. Krauzlis, M. Pare´, L. Pearson, E. Priddy, V.
Stuphorn, and K. Thompson for comments; D. Shima for computer pro-
gramming assistance; K. Reis for figures; and the Vanderbilt Advanced
Center for Computing for Research and Education for access to the
high-performance computing cluster (http://www.accre.vanderbilt.edu/
research).
Correspondence concerning this article should be addressed to Leanne
Boucher, Thomas J. Palmeri, Gordon D. Logan, or Jeffrey D. Schall,
Department of Psychology, Vanderbilt University, Nashville, TN 37221.
E-mail: leanne.boucher@vanderbilt.edu, thomas.j.palmeri@
vanderbilt.edu, gordon.logan@vanderbilt.edu or jeffrey.d.schall@
vanderbilt.edu
Psychological Review Copyright 2007 by the American Psychological Association
2007, Vol. 114, No. 2, 376–397 0033-295X/07/$12.00 DOI: 10.1037/0033-295X.114.2.376
376
Response inhibition in the stop-signal
paradigm
Frederick Verbruggen1,2
and Gordon D. Logan1
1
Department of Psychology, Vanderbilt University, Nashville, TN 37203, USA
2
Department of Experimental Psychology, Ghent University, B-9000 Ghent, Belgium
Response inhibition is a hallmark of executive control.
The concept refers to the suppression of actions that are
no longer required or that are inappropriate, which
supports flexible and goal-directed behavior in ever-
changing environments. The stop-signal paradigm is
most suitable for the study of response inhibition in a
laboratory setting. The paradigm has become increas-
ingly popular in cognitive psychology, cognitive neuro-
science and psychopathology. We review recent findings
in the stop-signal literature with the specific aim of
demonstrating how each of these different fields con-
tributes to a better understanding of the processes
involved in inhibiting a response and monitoring stop-
ping performance, and more generally, discovering how
behavior is controlled.
People can readily stop talking, walking, typing and so on,
in response to changes in internal states or changes in the
environment. This ability to inhibit inappropriate or irre-
levant responses is a hallmark of executive control. The
role of inhibition in many experimental paradigms is
debated, but most researchers agree that some kind of
inhibition is involved in deliberately stopping a motor
response. Here, we focus on the stop-signal paradigm
[1], which has proven to be a useful tool for the study of
response inhibition in cognitive psychology, cognitive
neuroscience and psychopathology. We review recent
developments in the stop-signal paradigm in these differ-
ent fields. The focus is primarily on the inhibition of
manual responses. Studies of oculomotor inhibition are
discussed in Box 1.
Successful stopping: inhibition and performance
monitoring
In the stop-signal paradigm, subjects perform a go task
such as reporting the identity of a stimulus. Occasionally,
the go stimulus is followed by a stop signal, which instructs
subjects to withhold the response (Figure 1). Stopping a
response requires a fast control mechanism that prevents
the execution of the motor response [1]. This process
interacts with slower control mechanisms that monitor
and adjust performance [2].
The race between going and stopping
Performance in the stop-signal paradigm is modeled as a
race between a ‘go process’, which is triggered by the
presentation of the go stimulus, and a ‘stop process’, which
is triggered by the presentation of the stop signal. When
the stop process finishes before the go process, the response
is inhibited; when the go processes finishes before the stop
process, the response is emitted. The latency of the stop
process (stop-signal reaction time [SSRT]) is covert and
must be estimated from a stochastic model, such as the
independent race model [3] (Box 2). SSRT has proven to be
an important measure of the cognitive control processes
that are involved in stopping. Cognitive neuroscientists
use SSRT as a criterion to determine whether neural
processes participate directly in response inhibition (Box
1). Psychopathologists use SSRT to study inhibitory defi-
cits in different patient groups (see later). Developmental
scientists found that SSRT is elevated in younger children
and older adults, compared with young adults. In addition,
a comparison of SSRT and go reaction time (RT) showed
that going and stopping develop and decline independently
[4–6].
Monitoring and adjusting go and stop performance
Successful performance in the stop-signal paradigm also
involves monitoring go and stop performance and adjust-
ing response strategies to find an optimal balance between
the conflicting demands of the go task (‘respond as quickly
as possible’) and the stop task (‘stop the response’). Several
studies indicate that subjects change response strategies
proactively when they expect stop signals to occur, trading
speed in the go task for success in the stop task [2,7]. Many
studies indicate that subjects also change response strat-
egies reactively after stop-signal trials [8–11]. Some show
that go RT increases after unsuccessful inhibition, remi-
niscent of the post-error slowing observed in choice reac-
tion tasks. Others show that go RT increases after
successful stopping, which is inconsistent with error-cor-
rection but indicates a shift in priority to the stop task after
a stop signal. Recent studies show that stimulus repetition
might be a crucial variable: responding after successful
stopping is typically slower when the stimulus from the
stop trial is repeated, as if the stimulus was associated
with stopping, and retrieval of that association impaired go
performance [8]. This stimulus-specific slowing can persist
over many intervening trials [10] and might support the
development of automatic inhibition [12].
Interim conclusions
Cognitive psychologists have identified the computational
mechanisms underlying performance in the stop-signal
paradigm, identifying a fast-acting stop process that pro-
Review
Corresponding author: Verbruggen, F. (frederick.verbruggen@ugent.be).
418 1364-6613/$ – see front matter ß 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.tics.2008.07.005 Available online 15 September 2008
Inhibitory Control in Mind and Brain 2.0: Blocked-Input Models of
Saccadic Countermanding
Gordon D. Logan
Motonori Yamaguchi
Vanderbilt University and Edge Hill University
Jeffrey D. Schall and Thomas J. Palmeri
The interactive race model of saccadic countermanding assumes that response inhibition results from an
interaction between a go unit, identified with gaze-shifting neurons, and a stop unit, identified with
gaze-holding neurons, in which activation of the stop unit inhibits the growth of activation in the go unit
to prevent it from reaching threshold. The interactive race model accounts for behavioral data and
predicts physiological data in monkeys performing the stop-signal task. We propose an alternative model
that assumes that response inhibition results from blocking the input to the go unit. We show that the
blocked-input model accounts for behavioral data as accurately as the original interactive race model and
predicts aspects of the physiological data more accurately. We extend the models to address the
steady-state fixation period before the go stimulus is presented and find that the blocked-input model fits
better than the interactive race model. We consider a model in which fixation activity is boosted when
a stop signal occurs and find that it fits as well as the blocked input model but predicts very high
steady-state fixation activity after the response is inhibited. We discuss the alternative linking proposi-
tions that connect computational models to neural mechanisms, the lessons to be learned from model
mimicry, and generalization from countermanding saccades to countermanding other kinds of responses.
Keywords: inhibition, cognitive control, executive control, stop signal
The ability to inhibit thought and action is an important com-
ponent of cognitive control. It improves over childhood and de-
clines in old age. It is strong in healthy adults and weak in people
with psychiatric and neurological disorders. It varies between
individuals with different personalities and cognitive abilities. It is
often studied in the stop-signal paradigm, in which people are
asked to inhibit a response they are about to execute (for reviews,
see Logan, 1994; Verbruggen & Logan, 2008). The inhibitory
process in the stop-signal paradigm is not directly observable, so it
must be assessed by applying a mathematical model to the data.
For 25 years stop-signal behavior was explained in terms of Logan
and Cowan’s (1984) independent race model, which assumes that
stop-signal performance depends on the outcome of a race between
a go process that produces an overt response and a stop process
that inhibits it. The independent race model provides estimates of
the latency of the unobservable response to the stop signal (stop-
signal response time or SSRT), which is the primary measure of
inhibitory control in stop-signal studies of development, aging,
psychopathology, and neuropathology (also see Logan, Van Zandt,
Verbruggen, & Wagenmakers, 2014). The independent race model
addresses whether and when a response is inhibited but does not
tiscopyrightedbytheAmericanPsychologicalAssociationoroneofitsalliedpublishers.
endedsolelyforthepersonaluseoftheindividualuserandisnottobedisseminatedbroadly.
Psychological Review © 2015 American Psychological Association
2015, Vol. 122, No. 2, 000 0033-295X/15/$12.00 http://dx.doi.org/10.1037/a0038893

Except where otherwise noted, this work is licensed under
http://creativecommons.org/licenses/by/4.0/
Feel free to distribute, remix, tweak, and build upon these slides.
Please attribute Bram Zandbelt with a link to
http://www.slideshare.net/bramzandbelt/modeling-response-inhibition

Modeling the Stop-Signal Task to Understand Response Inhibition

Recommended

Recommended

More Related Content

What's hot

What's hot (6)

Viewers also liked

Viewers also liked (18)

Similar to Modeling the Stop-Signal Task to Understand Response Inhibition

Similar to Modeling the Stop-Signal Task to Understand Response Inhibition (14)

Recently uploaded

Recently uploaded (20)

Modeling the Stop-Signal Task to Understand Response Inhibition