The optimality of sensory processing during the speed-accuracy tradeoff.
ABSTRACT When people make decisions quickly, accuracy suffers. Traditionally, speed-accuracy tradeoffs (SATs) have been almost exclusively ascribed to changes in the amount of sensory evidence required to support a response ("response caution") and the neural correlates associated with the later stages of decision making (e.g., motor response generation and execution). Here, we investigated whether performance decrements under speed pressure also reflect suboptimal information processing in early sensory areas such as primary visual cortex (V1). Human subjects performed an orientation discrimination task while emphasizing either response speed or accuracy. A model of choice behavior revealed that the rate of sensory evidence accumulation was selectively modulated when subjects emphasized accuracy, but not speed, suggesting that changes in sensory processing also influence the SAT. We then used fMRI and a forward encoding model to derive orientation-selective tuning functions based on activation patterns in V1. When accuracy was emphasized, the extent to which orientation-selective tuning profiles exhibited a theoretically optimal gain pattern predicted both response accuracy and the rate of sensory evidence accumulation. However, these relationships were not observed when subjects emphasized speed. Collectively, our findings suggest that, in addition to lowered response thresholds, the performance decrements observed during speeded decision making may result from a failure to optimally process sensory signals.
- SourceAvailable from: Joachim Vandekerckhove[show abstract] [hide abstract]
ABSTRACT: The Ratcliff diffusion model has proved to be a useful tool in reaction time analysis. However, its use has been limited by the practical difficulty of estimating the parameters. We present a software tool, the Diffusion Model Analysis Toolbox (DMAT), intended to make the Ratcliff diffusion model for reaction time and accuracy data more accessible to experimental psychologists. The tool takes the form of a MATLAB toolbox and can be freely downloaded from ppw.kuleuven.be/okp/dmatoolbox. Using the program does not require a background in mathematics, nor any advanced programming experience (but familiarity with MATLAB is useful). We demonstrate the basic use of DMAT with two examples.Behavior Research Methods 03/2008; 40(1):61-72. · 2.12 Impact Factor
- [show abstract] [hide abstract]
ABSTRACT: Top-down visual attention improves perception of selected stimuli and that improvement is reflected in the neural activity at many stages throughout the visual system. Recent studies of top-down attention have elaborated on the signatures of its effects within visual cortex and have begun identifying its causal basis. Evidence from these studies suggests that the correlates of spatial attention exhibited by neurons within the visual system originate from a distributed network of structures involved in the programming of saccadic eye movements. We summarize this evidence and discuss its relationship to the neural mechanisms of spatial working memory.Current opinion in neurobiology 03/2010; 20(2):183-90. · 7.21 Impact Factor
- [show abstract] [hide abstract]
ABSTRACT: Here we address two recent commentaries on our finding of an anticipatory trial-related signal that could not be predicted by concurrent electrode recordings. In addition, we offer a broad discussion regarding what our findings do and do not say about local neural activity underlying imaging signals.NeuroImage 04/2011; 55(4):1413-8. · 6.25 Impact Factor
When people make decisions quickly, accuracy suffers. Traditionally, speed–accuracy tradeoffs (SATs) have been almost exclusively
ascribed to changes in the amount of sensory evidence required to support a response (“response caution”) and the neural correlates
associated with the later stages of decision making (e.g., motor response generation and execution). Here, we investigated whether
performance decrements under speed pressure also reflect suboptimal information processing in early sensory areas such as primary
of sensory evidence accumulation. However, these relationships were not observed when subjects emphasized speed. Collectively, our
Fast decisions are typically more error prone, while precise deci-
sions require more time, a phenomenon known as the speed–
accuracy tradeoff (SAT) (Woodworth, 1899; Fitts, 1966;
not enough sensory information has been accumulated to sup-
port an accurate judgment (i.e., response thresholds are too low)
(Bogacz et al., 2006; Ratcliff and McKoon, 2008). On this “re-
anisms of late-stage decision processes that immediately precede
the initiation of motor responses (Forstmann et al., 2008, 2010;
van Veen et al., 2008; Bogacz et al., 2010). A complementary—
and largely untested—hypothesis is that speed pressure also in-
fluences the efficiency with which sensory evidence is
accumulated during decision making (“sensory-readout” hy-
pothesis). This is an important possibility given that the rate of
sensory evidence accumulation necessarily limits the efficacy of
downstream decision making and motor control processes.
we designed a perceptual decision making task that required hu-
man observers to discriminate between two orientated grating
stimuli (Fig. 1) (see Materials and Methods) under either speed
emphasis (SE) or accuracy emphasis (AE) conditions. Impor-
tantly, subjects had to discriminate a small rotational offset (5°)
supporting such fine discriminations are tuned away from the
target feature (hereupon termed “off-target” neurons) (Fig. 2)
(Regan and Beverley, 1985; Hol and Treue, 2001; Schoups et al.,
2001; Purushothaman and Bradley, 2005; Butts and Goldman,
2006; Jazayeri and Movshon, 2006; Navalpakkam and Itti, 2007;
work thereby provides a benchmark pattern of optimal sensory
We investigated how the SAT influenced information pro-
the LBA, the single-trial linear ballistic accumulator (STLBA)
(van Maanen et al., 2011). These models revealed an impact of
task instruction on the amount of information required to initi-
ate a decision (“response caution”) and on the rate of sensory
evidence accumulation (the “drift rate”); the later effect suggests
Author contributions: T.H., S.B., and J.T.S. designed research; T.H. and J.T.S. performed research; T.H., S.B.,
L.v.M., B.U.F., E.-J.W., and J.T.S. contributed unpublished reagents/analytic tools; T.H., S.B., and J.T.S. analyzed
Correspondence should be addressed to either Tiffany Ho or John T. Serences, Department of Psychology,
7992 • TheJournalofNeuroscience,June6,2012 • 32(23):7992–8003
that the SAT may affect sensory processing (Hu ¨bner et al., 2010;
Vandekerckhove et al., 2011). We then used a forward encoding
model (Brouwer and Heeger, 2009, 2011) (for review, see Nase-
laris et al., 2011; Serences and Saproo, 2012) to examine how
(V1) are associated with behavioral performance and with the
rate of sensory evidence accumulation under different SAT con-
ditions. Our results suggest that theoretically optimal response
accumulation—but only when accuracy is emphasized over
of California, San Diego (UCSD) (La Jolla, CA) community. All had
normal or corrected-to-normal vision. Each subject gave written in-
formed consent per Institutional Review Board requirements at UCSD
and completed a single 1 h session in a climate- and noise-controlled
subject room outside of the scanner and a single 1.5–2 h session in the
ing and $20/h for scanning. Subjects received an additional reward for
task compliance according to a point system described below (mean
due to improper slice stack selection during fMRI scanning that resulted
in no data being collected from large portions of primary visual cortex,
the main area of interest in this study.
Stimuli and task. Visual stimuli were generated using the Psychophys-
sion 7.1; MathWorks), presented at a frame rate of 60 Hz, and projected
onto a screen at the entrance of the scanner bore that subjects viewed
through a mirror. Button press responses were made on an fMRI-
compatible response box using the index and middle fingers of the right
Subjects were shown a centrally presented oriented grating (with a
diameter of ?14°) at full contrast which flickered at 6 Hz (83.33 ms on,
pseudorandomly selected with equal probability from one of nine possi-
ble orientations (0, 20, 40, 60, 80, 100, 120, 140, 160°) with a small
amount of pseudorandom jitter added (up to ?6°, selected from a uni-
form distribution). On one-half of the trials, the same stimulus was pre-
sented at every “flicker” (“match” trials), but for the remaining trials
(“mismatch” trials), the orientation of the grating was offset by 5° on
every other flicker, with the rotational offset of the deviant grating (i.e.,
clockwise or counterclockwise) fixed on a given trial and counterbal-
tive was to make a match/mismatch judgment
hand. The order of match and mismatch trials
was pseudorandomized and counterbalanced
a response any time after the stimulus onset;
the stimulus was present for 3 s, after which it
was replaced with a white centrally presented
fixation circle for 3.5 s. We omitted all trials in
or emitted a response faster than 200 ms
that responses quicker than 200 ms should be
regarded as definite blind guesses. In total, a
tal trials and 14 null trials consisting of just a
fixation circle) and lasted 336 s including an
run. Across the 36 experimental trials, each of
the 9 possible orientations was presented 4
times. Before each run, subjects were in-
structed by the experimenter to emphasize ei-
ther response accuracy or speed. Subjects
earned points based on their performance: ?10 for correct responses on
accuracy trials, ?10 for incorrect responses on accuracy trials, ?10 for
correct responses on speed trials within the response deadline, ?0 for
incorrect responses on speed trials, ?10 for any responses exceeding the
response deadline. At the end of the experiment, subjects were paid an
being scanned (rounded to the nearest dollar). During training in the
laboratory, subjects were given trial-by-trial feedback, but feedback was
delayed until the end of each run during the scanning session.
Response deadline on speeded trials. All participants were trained
before the scan session for a minimum of 180 trials. During training,
subjects received point feedback on a trial-by-trial basis according to
the reward scheme outlined above. Participants practiced the task
without any speed pressure until they felt comfortable and performed
at ?90% accuracy. Subjects were then asked to repeat the task by
responding as quickly as they could without guessing. The median of
their RT distribution on this block was then set as their response
deadline for both the subsequent speeded training blocks and the
speeded blocks during the fMRI session.
LBA model. Behavioral data were modeled using the LBA, which is a
peting accumulator model (Usher and McClelland, 2001; Brown and
On each trial, two racing accumulators begin with a random activation
level (the “starting point”) that is independently drawn from a uniform
distribution on [0, A]. Activity in each accumulator increases linearly,
and a response is triggered as soon as one accumulator crosses the re-
sponse threshold. The predicted response time is the time taken to reach
the threshold, plus a constant offset time (“nondecision time”). The rate
mal distributions for each accumulator (with the SD of these distribu-
tions being arbitrarily fixed at 1). The means of the normal distributions
reflect the quality of the perceptual input. For example, a salient mis-
match between the orientated gratings would lead to a large mean drift
bution for each accumulator (match or mismatch).
The distance from the starting point to the response threshold is a
measure of response caution as this distance quantifies the average
amount of evidence that needs to be accumulated before a response is
initiated. Changes in response caution are usually assumed to originate
from adjusting the response threshold; however, adjusting the response
threshold is mathematically equivalent to adjusting the starting point;
of the grating was offset by 5° on alternating flickers (either clockwise or counterclockwise, counterbalanced across trials). On
Hoetal.•SpeedPressureandSensoryProcessing J.Neurosci.,June6,2012 • 32(23):7992–8003 • 7993
which the starting points were drawn (although the starting points nev-
ertheless vary trial to trial) (Ratcliff, 1978; Ratcliff and Rouder, 1998;
Forstmann et al., 2010; Wolfe and Van Wert, 2010; van Maanen et al.,
2011). As a result, we hereon use the response threshold to represent
response caution since the maximum of the start point distribution is
fixed across the SE and AE conditions.
LBA model analyses. The parameters of the LBA model were esti-
mated using the method of maximum likelihood. Likelihood was
optimized using simplex searches (Nelder and Mead, 1965). Initial
parameter values for searches were generated two ways: using heuris-
tic calculations based on the data, and using start points determined
of these methods and extensive discussion of alternative approaches
are provided in the study by Donkin et al. (2011a)]. We fit the match
and mismatch trials simultaneously, fixing all parameters between
these two trial types to be constant except for the drift rate (which is
presumably determined by the stimulus). Different drift rates were
estimated for the accumulator corresponding to a mismatch response
on trials with a mismatch stimulus (i.e., “correct” drift rate) and on
trials with a match stimulus (i.e., “incorrect” drift rate; see Table 2).
Similarly, different drift rates were estimated for the accumulator
corresponding to a match response on trials with a match stimulus
(correct drift rate) and on trials with a mismatch stimulus (incorrect
drift rate; see Table 2). Each different design for constraining model
subject’s data. One subject, however, only made one incorrect re-
sponse among the AE mismatch trials, thereby providing little con-
straint on the model estimate for that condition. The parameter
estimates for that subject were therefore set to the group average for
that condition. The overall grouped BIC value provided very strong
support for the design that allowed three parameters to vary between
SE and AE conditions [response threshold (b), drift rate (v), and
nondecision time (t0)]. To quantify that support, we approximated
be ?1010times more likely than the next best design (see Results).
STLBA. Response times and accuracy vary on each trial due to envi-
ronmental changes and/or internal noise in a subject’s cognitive state. It
is therefore important not only to map overall mean behavioral patterns
with parameters that quantify relevant cognitive processes (as can be
done with the standard LBA) but also to link estimates of these parame-
ters and BOLD responses on a trial-by-trial basis.
In the standard LBA model (as in other decision making models)
(Ratcliff, 1985; Ratcliff and Rouder, 1998), drift rates are normally
distributed across trials, with independent distributions for each re-
spective accumulator. This assumption of normally distributed drift
rates implies that drift rates that are close to the mean of the distri-
points for each accumulator. These considerations yield the following
(0° offset on the abscissa axis) exhibit small changes in firing rates (?1) in response to two
denoted by ?2). B, The information available for supporting a fine discrimination—here
selective to all possible orientations (with 0° on the abscissa axis indicating the target). As
discrimination. C, Increasing the gain of the informative off-target neurons serves to further
the orientation discrimination task. The stimulus grating (top) provides information to two
racing accumulators; the first accumulator to reach threshold determines the response, and
thus the decision processing time. One accumulator corresponds to each possible response
The final response time is the time taken for the first accumulator to reach threshold plus a
7994 • J.Neurosci.,June6,2012 • 32(23):7992–8003 Hoetal.•SpeedPressureandSensoryProcessing
maximum-likelihood estimates for a single-trial drift rate (di) and a
single-trial starting point (ai) given a trial with response time (ti):
b ? A
if ti?b ? A
? t0? ti?b
ifb ? A
if ti?b ? A
? t0? ti?b
b ? ?ti? t0? ? v
ifb ? A
of the distribution of starting points (A), and the nondecision time (t0),
respectively. Note that the assumed independence between estimated
parameters that is found in the standard LBA model is no longer pre-
served with the STLBA. Nevertheless, parameter recovery studies show
that the STLBA can explain much of the variance in the true parameter
values [van Maanen et al. (2011), see the text surrounding their Fig. 3].
As in the main LBA analysis, we computed single-trial estimates of
drift rate based on a model where response threshold (b), drift rate (v),
fixed (for exact values, see Table 2). Constraining the model in other
reasonable ways (e.g., fixing the nondecision time parameter) yielded
qualitatively similar results. Note also that the single-trial estimates for
the starting point here are mathematically equivalent to single-trial esti-
mates of the response threshold since what is actually being calculated is
the relative distance between the two.
fMRI data acquisition and analysis. All scanning was performed on a
UCSD. Anatomical images were acquired using a FSPGR T1-weighted
sequence that yielded images with a 1 ? 1 ? 1 mm resolution. Whole-
ms; TE, 30 ms; flip angle, 90°; image matrix, 64 ? 64; field of view, 192
mm; slice thickness, 3 mm; 0 mm gap).
Data analysis was performed using BrainVoyager QX (version 1.91;
Brain Innovation) and custom time series analysis routines written in
MATLAB (version 220.127.116.114; MathWorks). Data from the main exper-
response instruction type, respectively). EPI images were slice-time cor-
rected, motion-corrected (both within and between scans), and high-
pass filtered (3 cycles/run) to remove low-frequency temporal
observer was then z-transformed on a run-by-run basis to normalize the
mean response intensity across time to zero. This normalization was
differences related to the composition of a voxel or by its distance from
the coil elements). We then estimated the magnitude of the BOLD re-
sponse on each trial by shifting the time series from each voxel by four
1.5 s TRs (6 s) to account for the temporal lag in the hemodynamic
response function, and then extracting data from the two consecutive
1.5 s TRs that correspond to the duration of each 3 s trial (Kamitani and
Tong, 2005; Serences and Boynton, 2007a,b; Serences et al., 2009). The
two data points extracted from these two consecutive TRs were then
voxel on each trial. These trial-by-trial estimates of the BOLD response
amplitude were subsequently used as inputs to the forward encoding
model (see below, Estimating feature-selective BOLD response profiles
using a forward encoding model).
Functional localizer scans. Each subject participated in two runs of an
independent functional localizer scan to identify voxels within primary
visual cortex that were responsive to the spatial position occupied by the
oriented grating stimulus used in the primary experiment. The localizer
stimulus was comprised of a full-contrast counter-phase modulated (8
Hz) checkerboard that exactly matched the size of the oriented grating
stimulus used in the main task. On each trial, the checkerboard stimulus
was reduced by 30% for a single video frame at six pseudorandomly
selected time points. Subjects were instructed to make a button press
response with their right index finger every time they detected a contrast
decrement. Each 10 s trial was then followed by 10 s of passive fixation.
a general linear model (GLM) with a single regressor that was con-
structed by convolving a boxcar model of the stimulus sequence with a
of positive response, 5 s; time to peak of negative response, 15 s; ratio of
sion, 1). Voxels were retained for analysis in the main experimental task
if they passed a false discovery rate corrected single-voxel threshold of
p ? 0.05.
Retinotopic mapping. A meridian mapping procedure consisting of a
was used to identify V1 (Engel et al., 1994; Sereno et al., 1995). Subjects
the peripheral stimulus. The data collected during these scans were then
projected onto a computationally inflated representation of each sub-
ually defined according to the representations of the upper and lower
vertical meridian following standard practices (Wandell et al., 2007).
Estimating feature-selective BOLD response profiles using a forward en-
coding model. The goal of encoding models is to adopt an a priori as-
sumption about the important features that can be distinguished using
hemodynamic signals within an ROI, and then to use this set of features
(or basis functions) to predict observed patterns of BOLD responses
(Gourtzelidis et al., 2005; Thirion et al., 2006; Dumoulin and Wandell,
V1 voxel represents the pooled activity across a large population of
orientation-selective neurons, and that the distribution of neural tuning
preference is biased within a given voxel due to large-scale feature maps
(Freeman et al., 2011) or to random anisotropies in the distribution of
orientation-selective columns within each voxel (Kamitani and Tong,
2005; Swisher et al., 2010). Thus, the BOLD response measured from
and Heeger, 2011; Freeman et al., 2011).
patterns in V1, we first separated the data from the 8–10 scanning runs
obtained for each subject into train and test sets using a “leave two out”
holding one AE and one SE run out for use as a test set, we ensured that
the training set had an equal number of trials of each type. For each run
in the training set, we then computed the mean response evoked by each
of the nine orientations, separately for each voxel. The mean responses
were then sorted based on stimulus orientation and run (i.e., mean re-
sponse to orientation 1 was first, then orientation 2, . . . , orientation 9).
Thus, each training set had 54 observations for subjects who underwent
8 runs in the scanner (6 runs in training set ? 9 orientations), and 72
the training set ? 9 orientations). Note that, as described below, data in
function was estimated for every trial.
Adopting the terminology of Brouwer and Heeger (2009, 2011), let m
be the number of voxels in a given visual area, n1be the number of
observations in the training set (either 54 or 72), n2be the number of
Hoetal.•SpeedPressureandSensoryProcessing J.Neurosci.,June6,2012 • 32(23):7992–8003 • 7995
trials in the test set, and k be the number of hypothetical orientation
matrix) be the test data set. Under the assumption that the observed
responses, we generated a matrix of hypothetical channel outputs (C1,
k ? n1) composed of nine half-sinusoidal functions raised to the sixth
power as a basis set (Fig. 4). The training data in B1were then mapped
that was estimated using a GLM of the following form:
where the ordinary least-squares estimate of W is computed as follows:
W ˆ? B1C1T(C1C1T)?1.
The channel responses C2(k ? n2) were then estimated based on the test
data (B2) using the weights estimated in Equation 3 as follows:
Cˆ2? (W ˆTW ˆ)?1W ˆTB2.
The first steps in this sequence (Eqs. 2, 3) are similar to a traditional
the model (in this case, one weight for each hypothetical orientation
channel). Equation 4 then implements a multivariate computation be-
cause the channel responses estimated on each trial (in C2) are con-
of responses observed across all voxels on that trial in the test set. Thus,
one key feature of this approach is that a set of estimated channel re-
voxels is greater than the number of channels. If there are fewer voxels
than channels, then unique channel response estimates cannot be de-
rived as the number of variables being estimated exceeds the number of
tuning profile on each trial is exploited when comparing channel re-
sponses on correct and incorrect trials and when correlating channel
responses with accuracy and drift rates on a trial-by-trial basis (see
The shape of the basis functions used in C1has a large impact on the
half-sinusoidal functions that were raised to the sixth power to approxi-
mate the shape of single-unit tuning functions in V1, where the 1/?2
half-bandwidth of orientation tuned cells is ?20° (although there is a
considerable amount of variability in bandwidth) (Schiller et al., 1976;
Swindale, 1998; Ringach et al., 2002a,b; Gur et al., 2005). Given that the
half-sinusoids were raised to the sixth power, a minimum of seven lin-
early independent functions was required to adequately cover orienta-
tion space (Freeman and Adelson, 1991); however, since we presented
nine unique orientations in the experiment, we used a set of nine evenly
distributed functions. The use of more than the required seven basis
basis functions based on physiology studies, all results that we report are
robust to reasonable variations in this value (i.e., raising the half-
based on the documented variability of single-unit bandwidths). Note
that, since the magnitude of the channel responses is scaled by the am-
y-axes of all data plots are in arbitrary units. Importantly, however, scal-
ing the basis functions to some other common value would not change
the differential response between conditions.
Using this modeling approach, the center position of each function in
the basis set can be systematically shifted across orientation space to
estimate the response in a channel centered at any arbitrary orientation
(as long as the channels remain linearly independent) (Freeman and
Adelson, 1991). While this method of shifting the center of each channel
across orientation space could in principle be used to generate channel
response profiles with a resolution of 1° (or even smaller), we opted to
reconstruct the response functions in 5° steps as no additional insights
were gained by estimating the responses at a higher resolution. After
generating a channel response function on each trial in 5° steps across
orientation space, each function was circularly shifted to a common
stimulus-centered reference frame, and these recentered response func-
tions were averaged across left and right V1 and across all trials of a like
response functions were found to be symmetrical about their center
point, we averaged data from corresponding offsets on either side of the
orientation tuning functions. Note that, in the process of collapsing
across channels centered on both positive and negative offsets from 0°,
we necessarily collapsed across mismatch trials in which there was either
a clockwise or a counterclockwise offset between sequentially presented
gratings within a trial. However, sorting the data by the rotational offset
of the deviant grating had no qualitative impact on any of our results,
presumably because the two gratings were flickering back and forth on
sequential presentations over the course of the 3 s trial (Fig. 1) and
because there was a random jitter of up to ?6° introduced on each trial
(see task description above), which was on the same order as the offset
between sequential gratings on mismatch trials (?5°).
Bootstrapping/randomization procedure for evaluating statistical signif-
icance. Because the basis functions used to estimate channel responses
overlapped—thus violating the independence assumption of traditional
statistical tests—we estimated statistical significance using a nonpara-
metric bootstrapping/randomization procedure. Note that this boot-
matrix (W) that estimates the magnitude of the response in each voxel in each of the nine
Schematic of the forward encoding model. A, Basis set comprised of nine half-
7996 • J.Neurosci.,June6,2012 • 32(23):7992–8003Hoetal.•SpeedPressureandSensoryProcessing
accuracy, AE logistic regression ? weights vs SE logistic regression ?
vs single-trial correlations between SE responses and drift rate). First, a
along the two tuning curves differed significantly (using a threshold of
p ? 0.05 for each individual t test). We then generated a new data set by
randomly selecting 14 participants with replacement and then reassign-
ing the condition label associated with data from each participant with a
probability of 0.5. A series of paired t tests was performed on the resa-
mpled and randomized data set using the same procedure applied to the
observed data. This resampling plus randomization procedure was then
iterated 10,000 times to determine the probability of obtaining the pat-
null hypothesis that the two conditions are equivalent (i.e., interchange-
times we observed a pattern of significant t tests in the resampled data
that matched the pattern obtained in the observed data. Note that the
behavioral data were evaluated using conventional parametric statistical
subsequent analyses (including model fitting procedures de-
scribed below) (see Materials and Methods). Two-way repeated-
measures ANOVA with factors for response-emphasis (speed vs
accuracy emphasis, or SE and AE trials, respectively) and trial
type (match vs mismatch) was used to assess accuracy and RT
data collected during the scanning session (for a summary of the
SAT effect: participants responded faster on SE trials compared
a corresponding drop in accuracy on SE trials (F(1,13)? 71.975;
p ? 0.001; Table 1).
On average, subjects gave a match response 55% of the
time, which is significantly greater than chance (one-sample t
test, t(13)? 2.49, p ? 0.03). In addition, RTs were slower and
accuracy slightly better on match trials compared with mis-
match trials (F(1,13)? 13.26, p ? 0.01; F(1,13)? 5.4, p ? 0.05;
Table 1), which is consistent with the bias to respond match
over mismatch and commensurate with the well known pro-
pensity for making confirmatory responses (Clark and Chase,
1972). There was an interaction between response-emphasis
and trial type for RTs (F(1,13)? 12.6; p ? 0.01; Table 1), with
interaction between response-emphasis and trial type for ac-
curacy rates (F(1,13)? 0.61; p ? 0.45; Table 1).
Accuracy rates and RTs might be lower on SE trials compared
rate at which sensory evidence is accumulated. Therefore, we
used a mathematical model of decision making (Fig. 3) to inves-
tigate how emphasizing either speed or accuracy influenced the
rate of sensory evidence accumulation (as captured by the drift
rate parameter) and response caution (as captured by the dis-
Materials and Methods). Given that the neuronal mechanisms
thought to support fine orientation discriminations are reason-
ably well characterized (Fig. 2) (see below, Predicting feature-
our analyses on mismatch trials (data from match and mismatch
trials were nonetheless fit simultaneously) (for more details, see
sions of the LBA model of Brown and Heathcote (2008) were fit
by allowing all combinations of three different parameters (drift
rate, response caution, and nondecision time) to either vary
freely across SE and AE conditions or to be fixed across those
conditions, while keeping the maximum starting point always
fixed across AE and SE conditions (Fig. 3) (for more details, see
Materials and Methods, LBA model and LBA model analyses).
We then used the Bayesian information criterion (BIC) to select
used measure that evaluates the tradeoff between model com-
plexity and goodness of fit (Schwarz, 1978; Raftery, 1995). The
model yielding the best BIC was the one that estimated different
values for the parameters corresponding to response caution,
drift rate, and nondecision time on AE trials compared with SE
trials (for a summary of the parameter fits to data averaged over
all the subjects, see Table 2). Based on approximated posterior
LBA model analyses), this design was found to be ?1010times
more likely than the next best design. Individually, this design
was also the modal result: the BIC values for 6 of 14 subjects
preferred this design. Four subjects had best-BIC designs that
included an effect on drift rate but not response threshold, while
three had best-BIC designs that included an effect on threshold
but not drift rate. Only one subject had a best-BIC design that
included no effect at all of the experimental manipulation.
response time distributions from the data. This figure estimates
the distributions using quantiles plotted against response proba-
bution plots” and are a standard method for evaluating the
All parameters were fixed to be constant across match and mismatch trials except for the drift rates, which are
tion (drift rates) between correct and incorrect accumulators on accuracy emphasis trials compared with speed
Hoetal.•SpeedPressureandSensoryProcessingJ.Neurosci.,June6,2012 • 32(23):7992–8003 • 7997
quality of fit for response time models, as they provide a much
more rigorous test than histograms [for introductions to this
method and related discussion, see the study by Ratcliff and
Tuerlinckx (2002) or the study by Donkin et al. (2011a)]. The
model fits the data quite well, matching the probability (as
indicated by the height on the graph) of each response type in
each condition accurately. The latency of each part of the
response time distribution (abscissa axis) is also accurately
captured by the model. For example, in the SE and AE condi-
LBA predicted value by ?25 ms.
In any choice task, it is possible that participants occasionally
in which error rates were relatively high. However, since the de-
cision model fits the response time distributions from both con-
ditions very well (Fig. 5, left panel), we assume that simple
random guessing is not a plausible explanation for observed dif-
ferences in parameters between the SE and AE conditions. Nev-
ertheless, to avoid having the model results overly biased by
contaminant processes such as guessing, we incorporated a mix-
ture process with the assumption that each response had a 98%
probability of arising from the LBA choice process, and a 2%
probability of arising from a guessing process with random re-
sponses and uniform RT over the observed range [for details, see
the studies by Ratcliff and Tuerlinckx (2002) and Donkin et al.
(2011a)]. With this built-in assumption, the decision model fit
the response time distributions from both conditions very well
(Fig. 5), consistent with the hypothesis that participants were
making informed decisions on the vast majority of trials.
response caution (Table 2) (Ratcliff, 1985; Ratcliff and Rouder,
1998; Voss et al., 2004; Palmer et al., 2005). Moreover, we ob-
served a larger difference in the rate of evidence accumulation
associated with correct and incorrect accumulators on AE trials
compared with correct and incorrect accumulators on SE trials
with no main effect of stimulus type nor interaction between
when the accumulator corresponding to the correct response for
corresponding to the incorrect response. The larger difference in
drift rates between correct and incorrect accumulators on AE
trials therefore suggests that sensory information about the cor-
rect response is being selectively accumulated at a higher rate
when subjects make decisions in the absence of speed pressure.
Such selectivity represents a departure from the typical assump-
tion used by mathematical psychologists that the rate of sensory
evidence accumulation is fixed across AE and SE conditions [for
extensive discussion, see Ratcliff and Rouder (1998)], as well as
evidence for a change in drift rates with task demands (Vande-
kerckhove et al., 2011), and we speculate that the effect may be
even more apparent in the present task because subjects were
engaged in a difficult perceptual discrimination in which the
quality of sensory representations critically determined behav-
ioral performance [for a more theoretical treatment, see also the
ences in the time taken for nondecision processing between SE
and AE conditions (Table 2) are sometimes observed as a conse-
quence of task instructions, but these differences are not usually
of interest when the main purpose of the manipulation is to in-
In general, the parameter estimates from the LBA model have
been shown to be in agreement with the corresponding parame-
ters in the Ratcliff diffusion drift model (Donkin et al., 2011b).
Nevertheless, to demonstrate that our modeling results are not
specific to our choice of model and fitting procedures, we also fit
our behavioral data using the Diffusion Model Analysis Toolbox
linckx, 2007, 2008). We used DMAT to fit the same eight models
tested in our LBA analysis (i.e., all possible combinations of drift
eters fixed). Group BIC values for each model design were calcu-
lated in the same manner as those computed for the LBA models
(see Materials and Methods, LBA model analyses). Consistent
with the results of the LBA model, the diffusion model design
with the best BIC was the one that estimated different values for
the parameters corresponding to drift rate and response thresh-
rates, t(13)? 4.93, p ? 0.01; and AE response thresholds were
higher than SE response thresholds, t(13)? 5.94, p ? 0.01). We
which only drift rate and response threshold varied yielded the
probabilities were close to 0).
We next sought to establish a relationship between feature-
selective BOLD responses in early visual areas and behavior. In
stimuli (as in the present experiment in which orientations on
mismatch trials were offset by only 5°), neurons tuned to off-
ence of mismatching orientations (Fig. 2) (Regan and Beverley,
and Bradley, 2005; Butts and Goldman, 2006; Jazayeri and
Movshon, 2006; Navalpakkam and Itti, 2007; Scolari and Ser-
ences, 2009, 2010). Hence, we focused our analyses on mismatch
Data are shown separately for the speed emphasis condition (left panel) and the accuracy
emphasis condition (right panel). In each panel, the upper lines and symbols show quantile
and model predictions were generated separately for each individual participant and then
averaged. The height of the graphs shows response probability. Nine quantile estimates are
7998 • J.Neurosci.,June6,2012 • 32(23):7992–8003Hoetal.•SpeedPressureandSensoryProcessing
trials in which the activation of off-target neurons is predicted to
support such decisions. Given the relatively large difference in
drift rates associated with correct and incorrect accumulators on
AE trials should be associated with more activation in off-target
The difference between the drift rates associated with the correct
and incorrect accumulators on SE mismatch trials, however, is
much smaller (Table 2). We would therefore expect a small dif-
ference between off-target activation on correct SE mismatch
trials compared with incorrect mismatch SE trials.
We used fMRI and a forward encoding model of BOLD responses
(Brouwer and Heeger, 2009, 2011) (for review, see Naselaris et al.,
2011; Serences and Saproo, 2012) to estimate how the SAT modu-
subsequently reported p values associated with TFs were estimated
using a nonparametric randomization procedure due to the non-
independence of adjacent data points; see Materials and Methods).
However, when examining only the AE mismatch trials, we found a
65° away from the target orientation showed larger responses on
correct trials compared with incorrect trials. The observation of
more activation in these off-target channels on correct trials is con-
sistent with our predictions, as these neural populations should
better signal small changes in orientation. In turn, more gain in
being sent to downstream decision mechanisms and thus increase
rect and incorrect SE trials (p ? 0.90; Fig. 6C), and the difference
between off-target channel responses on correct and incorrect AE
trials was significantly larger than the difference on correct and in-
correct SE trials (p ? 0.01; Fig. 6D). This interaction is consistent
with the relatively large difference in drift rates associated with cor-
rect versus incorrect accumulators on AE trials compared with SE
As shown in Figure 6B, we observed more activation in off-
the AE condition. To further test the relationship between the
magnitude of off-target responses and behavior, we performed a
between-subject correlation between the change in drift rate and
the change in off-target activation on correct and incorrect AE
trials (where our measure of off-channel activation was the area
between the TFs associated with correct and incorrect responses
across channels tuned 25–65° from the target orientation) (Fig.
6B). Across subjects, larger differences between correct and in-
correct accumulator drift rates were positively correlated with
larger differences in off-target activation on correct compared
with incorrect AE trials (Fig. 7A; R2? 0.36; t(12)? 2.59; p ?
0.025). This relationship was still observed even when the total
area between the TFs associated with correct and incorrect AE
rates (R2? 0.30; t(12)? 2.24; p ? 0.05), demonstrating that the
positive correlation did not strongly depend on the exact points
along the TFs that were entered into the analysis. This between-
subjects relationship between BOLD and behavior suggests that
individual differences in the degree of off-target activation in
V1—and by inference, individual differences in the amount of
cision making when subjects are not under speed pressure.
The correlation analysis presented in Figure 7A establishes a
subject-by-subject relationship between off-target responses in
V1 and the rate of sensory evidence accumulation. To further
explore this relationship on a within-subject basis, we next used
logistic regression to map fluctuations in the magnitude of the
response in each orientation channel to accuracy on a trial-by-
trial basis. A positive fit coefficient (? coefficient) indicates that
higher activation in a given channel predicts a higher probability
of a correct behavioral response; negative ? coefficients indicate
an inverse relationship between BOLD activation levels and be-
channels tuned to the target (0° offset) were associated with a
higher probability of incorrect responses, whereas larger re-
sponses in channels tuned ?40–60° from the target were associ-
ated with a higher probability of a correct response (Fig. 7B). In
contrast, the ? coefficients on SE trials fluctuated around zero.
This pattern gave rise to a significant crossover interaction be-
with the increased off-target activation on correct AE trials (Fig.
6B) and the corresponding relationship with the rate of sensory
TFs for the AE data (gray) and SE data (black) are plotted as a function of the offset of each
set to 0°; note that channel responses were collapsed across clockwise and counterclockwise
Tuning functions for mismatch AE trials. A comparison of tuning functions for correct (gray)
different from incorrect responses, with greater activation in channels offset by 35–60° on
parison of tuning functions for correct (gray) versus incorrect (black) SE trials. There was no
Hoetal.•SpeedPressureandSensoryProcessingJ.Neurosci.,June6,2012 • 32(23):7992–8003 • 7999
evidence accumulation on a between-subject basis (Fig. 7A), this
nel responses and behavioral performance suggests that percep-
tual decisions are tightly coupled to activation levels across
informative off-target sensory neurons, but only when subjects
emphasize accuracy over speed.
Given the data presented thus far that off-target activation levels
in V1 predict behavior on AE trials, we would also predict a
positive correlation between trial-by-trial estimates of the rate of
sensory evidence accumulation and the magnitude of the BOLD
response in off-target channels. To evaluate this relationship, we
correlated trial-by-trial estimates of off-target channel responses
and trial-by-trial estimates of drift rates derived from the STLBA
model on a within-subject basis.
sensory evidence accumulation (drift rate), response caution, and
was fixed). Next, we estimated both channel responses and single-
correlation between these metrics across all trials for each subject.
trials in channels tuned 30–55° away from the target. This pattern
produced a significant crossover interaction between task instruc-
accumulation on AE trials. This finding converges with the prior
subject correlation (Fig. 7A), and within-subject logistic regression
(Fig. 7B), and is consistent with the idea that responses in informa-
tive sensory neurons are strongly coupled with behavioral perfor-
mance, but only in the absence of speed pressure. However, this
analysis more directly links trial-by-trial fluctuations in off-target
channel responses with the rate of sensory evidence accumulation
Note that the correlations shown in Figure 7C were expected to
be small because both measures (model parameters and BOLD re-
sponses) are extremely variable when estimated on a trial-by-trial
basis. Nevertheless, even though they were small in magnitude, the
tions about how model parameters were constrained across condi-
tions. For example, the same general pattern was observed using a
of the model parameter corresponding to the rate of sensory evi-
dence accumulation: correlating V1 channel responses to raw re-
sponse times or to trial-by-trial estimates of the parameter
The selectivity of the correlations presented in Figure 7C thus illus-
When subjects emphasized accuracy, higher off-target activation
lation (Fig. 7A), logistic regression revealed a trial-by-trial relation-
ship between behavioral accuracy and BOLD activation levels in
trial-by-trial estimates of the latent cognitive processes involved in
perceptual decision making (van Maanen et al., 2011) revealed a
correlation between activation levels in off-target channels and the
dict behavioral performance on AE trials suggests that decision
mechanisms can selectively pool inputs from the most informative
incorrect accumulators is positively correlated with the difference in off-target activation on
on a trial-by-trial basis. Positive coefficients indicate that larger BOLD signals correspond to
drift rate and then computed a correlation coefficient across trials per subject. The r values
A, Between-subject correlation between differences in off-target channel re-
8000 • J.Neurosci.,June6,2012 • 32(23):7992–8003Hoetal.•SpeedPressureandSensoryProcessing
2009). However, this reliance on informative off-target channels
during decision making only appears to happen on AE trials, as
fluctuations in off-target responses do not predict behavior under
speed pressure. This observation leads to an interesting prediction:
expected that off-target activation levels on SE trials more closely
pare A, B). Contrary to this prediction, we instead observed that
tuning functions in the SE condition more closely resemble tuning
ulations of sensory neurons in an optimal manner during decision
parent failure to rely on informative off-target neural responses on
cise readout of sensory information when response speed is at a
One interpretation of the relationship between behavior and
off-target modulations on AE trials holds that top-down atten-
tional signals originating in frontal and parietal cortex differen-
basis. This type of attentional-feedback account is consistent by
many theories of attentional control (for review, see Desimone
and Duncan, 1995; Kastner and Ungerleider, 2000; Corbetta and
Shulman, 2002; Serences and Yantis, 2006; Yantis, 2008; Nou-
visual cortex and concomitant changes in performance across
mediate perceptual decisions (Heekeren et al., 2004, 2008; de
Lafuente and Romo, 2005, 2006; Gold and Shadlen, 2007; Ho et
al., 2009; Herna ´ndez et al., 2010; Kayser et al., 2010; Lemus et al.,
2010; Purcell et al., 2010). However, since we did not directly
manipulate attention in this study, it is difficult to dissociate
sources of variability in V1 that are due to fluctuations in top–
down biasing signals as opposed to sources of variability that are
local to visual cortex. Future studies could more critically exam-
attention cue to determine whether speed pressure selectively
impairs a subjects’ ability to use prior information to appropri-
ately bias population response profiles in visual cortex.
In addition to suboptimal usage of sensory information dur-
ing decision making, it is likely that performance under speed
pressure in our task is further limited by other neural mecha-
responses are emphasized (Forstmann et al., 2008, 2010; van
Veen et al., 2008), consistent with a response threshold account
that only motor and frontal areas are involved in mediating the
SAT (Ratcliff, 1985; Ratcliff and Rouder, 1998; Forstmann et al.,
2008, 2010; Ivanoff et al., 2008; van Veen et al., 2008; Wenzlaff et
al., 2011). In contrast, our findings provide support for the
sensory-readout account, which posits that perceptual perfor-
mance under speed pressure is also limited by how efficiently
sensory information is integrated during decision making.
The forward encoding model that was used to estimate re-
sponses in different orientation channels is a proxy for the actual
This leads to an inevitable loss of resolution as a single V1 voxel
rons can be highly variable. Therefore, it is difficult to pinpoint
the exact orientation offset at which off-target BOLD modula-
lying neural responses. However, the observation of increased
responses starting in channels tuned 25–30° from the target is
V1 (Schiller et al., 1976; Ringach et al., 2002a,b; Gur et al., 2005).
More generally, the robust relationship between off-channel ac-
tivation levels and behavior supports the functional importance
of the observed modulations, and is consistent with established
models of optimal gain during fine discriminations (Fig. 2).
Generating channel tuning functions also depends critically
on the ability of fMRI to reliably measure orientation-selective
responses in primary visual cortex. In V1, it is likely that these
feature-selective response biases depend to a large degree on rel-
atively coarse maps of orientation space that unfold across the
cortical surface (Leventhal, 1983; Schall et al., 1986; Sasaki et al.,
2006; Mannion et al., 2009; Zhang et al., 2010; Freeman et al.,
et al., 2006; Zhang et al., 2010; Freeman et al., 2011). Thus, neu-
rons with spatial receptive fields in (say) the upper right visual
field tend to respond more to oblique orientations around 45°,
and so on. Given the robust retinotopic organization of V1, this
radial bias would generate an orderly representation of orienta-
tion across patches of cortex that represent each visual quadrant
(Sasaki et al., 2006; Zhang et al., 2010; Freeman et al., 2011). In
addition to this coarse orientation map across V1, voxel-level
orientation selectivity may also reflect contributions from ran-
dom anisotropies in the distribution of orientation-selective col-
umns within a voxel (Haynes and Rees, 2005; Kamitani and
Tong, 2005; Swisher et al., 2010) (for a useful graphical illustra-
index feature-selective responses arising from neural signals at
both coarse and fine spatial scales.
Despite this link, we do not claim that orientation-selective
response functions are solely related to neural spiking activity, as
tic input from both local and distant inputs, tuned local field
potentials, and even responses in astrocytes (Heeger et al., 2000;
Logothetis et al., 2001; Buxton, 2002; Heeger and Ress, 2002;
Logothetis and Wandell, 2004; Schummers et al., 2008; Sirotin
and Das, 2009; Kleinschmidt and Muller, 2010; Das and Sirotin,
2011; Handwerker and Bandettini, 2011a,b; Jia et al., 2011).
However, given that neurons in early sensory areas like V1 are
massively interconnected (Douglas and Martin, 2007), changes
in the BOLD signal related to synaptic activity should be highly
correlated with changes in local spiking activity. Despite these
caveats, the robust predictive relationship between off-target
channel modulations and behavior strongly supports the func-
tional significance of these indirect BOLD assays of neuronal
The instruction-dependent change in the reliance of decision
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variables leading up to the ultimate choice (Purushothaman and
Bradley, 2005; Law and Gold, 2008, 2009; Pestilli et al., 2011).
Similarly, Rahnev et al. (2011) observed that manipulating prior
expectation increased functional connectivity between posterior
and frontal areas, consistent with an increase in the rate of sen-
sory evidence transfer from earlier visual areas to putative deci-
Hoetal.•SpeedPressureandSensoryProcessingJ.Neurosci.,June6,2012 • 32(23):7992–8003 • 8001
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