Single Trial Analyses in Perceptual Decision Making

Date: 30-10-2012

Student: Wouter Boekel - 5834023 - MBCS University of Amsterdam, track: Cognitive Neuroscience

Supervisor: Leendert van Maanen, PhD

Co-assessor: Max Keuken, Msc

Abstract

When analyzing data from cognitive neuroscience experiments, researchers often compute averages over

trials which reflect individual scores on a certain psychological task. However, The investigation of trial-to-

trial variability in behavior and brain processes has recently become more prominent within the field of

perceptual decision-making. In this paper, I will discuss research aimed at developing methods for single-trial

analyses of RT, EEG and fMRI data-sets. Furthermore, I will provide an overview of research into trial-to-trial

variation within perceptual decision-making and related fields. Moreover, throughout this paper I will discuss

the advantages of single-trial analyses methods, as well as the challenges for future research aimed at

investigating trial-to-trial variability in neurocognitive mechanisms underlying perceptual decision-making.

Introduction

Throughout our daily life we are constantly required to use our cognitive abilities to solve

certain problems or reach certain goals. We constantly make decisions, inhibit certain

prepotent responses, or switch our attention to different stimuli. The brain is of critical

importance in executing these behaviors efficiently, allowing us to come closer to our

goals, while simultaneously keeping us alive and healthy.

Research within Cognitive Neuroscience is mainly aimed at understanding the cognitive

processes that underlie our daily behavior, and how neural mechanisms give rise to these

cognitive processes. In general, research within cognitive neuroscience is done by having

human or animal participants perform a certain task. These experimental tasks consist of

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trials in which participants are required to respond to a certain stimulus. Seeing as there is

often large variability (e.g. in response times (RT)) on these paradigms within individuals, a

large number of trials are gathered to gain an accurate estimate of a participantʼs average

performance on a certain paradigm, and thus inform researchers about a certain cognitive

process. Neurophysiological or neuroimaging measurements can be acquired during these

paradigms in order to acquire information about the neural mechanisms underlying these

cognitive processes.

This kind of research often aims at investigating differences between groups, experimental

conditions, or single participants. Between-trial fluctuations are assumed to be a source of

noise in these experiments, and are thus ignored by computing, for example, mean RT.

This approach can help us understand cognitive processes in terms of differences

between groups, conditions or individuals. However, it is difficult to investigate the

processes themselves (more specifically, between-trial adjustments in the processes) by

using this traditional approach. Single-trial analysis methods provide a solution to this

problem, allowing researchers to investigate the between-trial variability or time-course of

certain cognitive processes. Furthermore, applying the single-trial analysis approach to

neuroimaging data allows researchers to investigate variability in neural mechanisms

underlying variability in cognitive processes.

One of the fields within cognitive neuroscience which has seen a recent increase in the

use of single-trial analysis methods is perceptual decision-making. Research in this field

employs a range of behavioral paradigms in order to investigate cognitive processes

underlying simple perceptual choices (Gold and Shadlen, 2007). One prevalent paradigm

within perceptual decision-making is the random-dot-motion paradigm. In this paradigm,

participants see a cloud of dots on a computer screen. Some of these dots are moving

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coherently to the left or to the right, and some of these dots are moving randomly.

Participants are asked to respond to the general direction in which the cloud of dots is

moving. The difficulty in this paradigm can be adjusted by specifying the ratio of coherently

versus randomly moving dots (Britten et al., 1992).

Below, I will describe an example experiment using the RDM paradigm. Subsequently I will

provide an overview of recent research in which single-trial analysis methods are used to

investigate (aspects of) perceptual decision-making and its underlying neurocognitive

mechanisms. I will use the example experiment to demonstrate how the different single-

trial analysis techniques that are described can be applied on a data set acquired from

running such an experiment. Finally, I will discuss advantages as well as shortcomings of

single-trial analysis methods.

One can easily imagine running an experiment using the RDM paradigm to investigate

how people make hard and easy decisions. In the particular design that you are using,

there are two conditions: A difficult condition, in which 5% of the dots are moving

coherently, and an easy condition, in which 15% of the dots are moving coherently.

Participants are asked to respond to the general direction in which the cloud of dots is

moving. Their accuracy scores and reaction times are gathered on every trial.

The data set that is acquired by running such a straightforward and simple design, is

already rich enough to allow multiple kinds of analyses. Accuracy scores will differ

between conditions and participants. The results will probably show us that participants

make more errors in the hard condition, and that some participants perform better on this

task than others (Palmer et al., 2005). Similarly, extracting mean or median RT per

condition (easy vs. hard), will tell us something about whether participants, overall, need

more time to reach a decision when the stimulus contains less usable information and

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more noise (i.e. lower coherence). Computing RT per participant then supplies us with a

measure of inter-individual difference in general performance on the task. Extracting these

individual RT values separately per condition provides us with an individual measure of

sensitivity to the stimulus (e.g. a participant who is more sensitive to the stimulus will show

a lower increase in RT on the difficult condition). Finally, one might try to combine both

accuracy and RT data by fitting a computational model, in order to extract measures of

certain latent cognitive processes underlying the generation of RT distributions. One of the

most validated computational models for the analysis of RT data is the drift-diffusion model

(DDM; Ratcliff, 1978). This model is based on the idea that when faced with a decision,

sensory evidence starts accumulating until a certain threshold is reached, evoking a

choice. By fitting this model to behavioral data from an RDM paradigm, one can derive

specific information about the decision process that is reflected in the parameters of the

model. This model-based approach allows researchers to investigate differences in latent

cognitive processes such as drift rate between conditions (easy vs. hard), or between

individuals.

The abovementioned types of analyses all have in common that trial-to-trial variability in

RT is thought of as noise. Many trials are acquired to decrease the impact of this variability

in RT, and thus ʻfilter out the noiseʼ. This approach allows researchers to gain insight into

differences in cognitive processes between certain conditions, individuals, or populations.

However, one might be interested in the time-course of the decision making process over

trials, or the occurrence of attentional lapses over trials. Computing the mean RT per

condition or participant will effectively remove the information necessary to investigate

these processes. It might still be possible to adjust experimental conditions in such a way

that one is able to extract a measure of variability in behavior by, for example, extracting

and comparing a single RT-variability score per condition. However, I will argue that it is

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much more effective to exploit trial-to-trial fluctuations to investigate variability in behavior.

I will do so by showing examples from a range of different subfields related to perceptual

decision making that all use a form of single trial analyses that leads to new insights into

perceptual decision making and its underlying neural mechanisms. In order to first provide

an overview of the different dependent measures that can be analyzed by single-trial

analysis methods, below I will describe methodological research aimed at developing

these single-trial methods for three different types of data: RT, electro- and

magnetoencephalography (EEG/MEG), and functional magnetic resonance imaging

(fMRI).

Dependent measures

In order to investigate neurocognitive mechanisms underlying trial-to-trial fluctuations in

behavior, we require measurements that reflect these mechanisms. RT is one of the most

commonly used measures in psychology, and thus many methods of analyzing RT data

have been developed. EEG and MEG are used to measure electrical and magnetic activity

non-invasively from the scalp. fMRI is a more recently developed neuroimaging technique,

which measures changes in blood flow non-invasively, and thus indirectly informs

researchers about activity in a certain brain region. These neuroimaging data-sets are

often combined with RT data to allow investigation of neural mechanisms underlying

cognitive processes. Below I will provide an overview of research aimed at developing

single-trial analysis methods which can be applied to data-sets acquired from these

measurements.

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RT

RT is one of the most used measures in experimental psychology. RT experiments gather

RT data from participants performing a large amount of trials in which, for example, a

choice has to be made between two alternatives. Mean RT values can be used to

investigate differences in RT between individuals or groups. Computational models such

as the DDM have been developed to investigate latent cognitive processes thought to

underlie a decision (Ratcliff, 1978). This model assumes that sensory evidence starts

accumulating when faced with a perceptual decision. This evidence will reach a certain

threshold, evoking a choice. By fitting this model to behavioral data from, for example, an

RDM paradigm, one can derive specific information about the decision process that is

reflected in the parameters of the model. For example, drift rate reflects the rate or speed

of accumulation, and is often thought to represent the quality of sensory information

(Ratcliff, 1978), and subsequently the difficulty of the decision. The starting point of

accumulation tells us something about the subjectʼs bias towards one of the options

(Mulder et al., 2012), and threshold values (or more accurately, the difference in between

the starting point and threshold) contain information about the trade-off between speed

and accuracy (Bogacz et al., 2010). The non-decision time reflects processes not related

to the decision, such as visual or motor processes. In addition, the model contains three

parameters for across-trial variability (variability in starting point, variability in non-decision

time, and variability in drift rate).

The abovementioned across-trial variability parameters are possible candidates for the

investigation of trial-by-trial variability. However, these are single values of variability over

the entire time-course of an experiment, and are thus averaged measures of trial-by-trial

variability. Recently, van Maanen et al. (2011) proposed a new method for estimating

single-trial parameters of drift rate and starting point, allowing researchers to investigate

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the trial-to-trial variation of these latent cognitive processes, and subsequently investigate

the underlying neural mechanisms of these processes. In a different (but related) field,

reinforcement learning models have been developed which are aimed at investigating the

time-course of a learning process. I will describe these models in more detail in the reward

learning section below.

In short, the large usage of RT data in traditional experimental psychology has led to

answers to many questions. These answers have led to new questions which could not be

answered by traditional mean-RT analyses. In order to answer these new questions,

researchers have developed analysis techniques aimed at investigating latent cognitive

processes based solely on the trial-to-trial variability in RT. The challenge of future

research utilizing RT data-sets is to investigate latent cognitive processes on a single-trial

basis, and moreover, to combine this with neuroimaging techniques to inform researchers

about the neural mechanisms underlying the trial-to-trial variability in cognitive processes.

EEG/MEG

Electroencephalography (EEG) and magnetoencephalography (MEG; although to a lesser

extent) are two of the oldest and most used non-invasive techniques to investigate neural

processes. Traditionally, EEG is measured at a high sampling rate while participants

perform a task. EEG data are then segmented based on a single event within each trial.

When considering the example experiment described above, you might create segments,

or epochs, centered around the onset of the stimulus or feedback events within a single

trial of the RDM paradigm. These epochs are averaged over trials, providing researchers

with an average of the event-related potential (ERP). Average ERPʼs can then be linked to

individual differences in behavior, or differences between groups can be investigated

(Luck, 2005). However, variability in the ERP is removed by this averaging. Moreover,

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differences in phases of single-trial ERPʼs could result in the average ERP being cancelled

out completely.

One way of solving this problem is by simply computing single trial ERPs. However, this

method still suffers from between-trial phase-shifts. Time-frequency analyses solve this

problem in a more sophisticated way, by extracting power values of specific frequencies

per trial. Seeing as the power of a certain frequency is independent of the phase of the

oscillation at stimulus onset, single-trial oscillatory power values can easily be averaged

across trials without the problem of canceling out oscillations due to across-trial phase

differences (Cohen, 2011). However, trial-to-trial variation in oscillatory power may still be

present, and in fact be informative about a certain cognitive process. MEG data-sets are

similar to EEG data-sets, in that they measure signal from the scalp at a high sampling

rate, and have thus been analyzed in a similar way.

One of the aims of methodological EEG research, is to increase reliability and signal-to-

noise ratios of single-trial analysis methods. Grandchamp and Delorme (2011) describe a

single-trial normalization method for spectral analyses of EEG data, which reduces

sensitivity to outliers. Traditionally, post-stimulus time-frequency data are baseline-

corrected by, for example, subtracting the trial-average pre-stimulus power, per frequency,

from the time-frequency signal at every time-point within the post-stimulus time window of

interest. Grandchamp and Delorme (2011) show that this method is susceptible to pre-

stimulus outliers. However, when using a single-trial baseline correction method, they

show that the influence of these outliers is reduced. This work shows that even in a pre-

processing step such as baseline-correction, averaging over trials can affect the results in

a way that is not desirable. Instead, single-trial methods should be applied to properly

account for the trial-to-trial variability.

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Gaspar et al. (2011) modeled single trial ERP amplitudes using a general linear model

(GLM) approach. This provided the researchers with an R2 (explained variance)

timecourse, representing a measure of to what extent the ERP signal at every time point

can be predicted by a specific regressor, set by the researcher. This approach is often

used in fMRI, and thus provides a way of integrating fMRI and EEG analyses (e.g. by

using two simultaneously acquired datasets to estimate parameters of a general linear

model (Kiebel and Friston, 2004)). Moreover, Gaspar et al. (2011) performed an intraclass

correlation analysis (ICC), which shows how strongly observations from the same

participants resemble each other. Using these methods, the authors showed that the

within subject correlations were much higher than the between-subject correlations in the

R2 timecourse, and concluded that this method of analyzing EEG provides reliable test-

retest results in a face processing paradigm.

One of the recurring topics of research into single-trial methods of analyzing EEG data is

single-trial classification. Kostelecki et al. (2011) describe a method of classification of

MEG data, using Granger causality. This method is based on testing to what extent a

certain time-series data-set (e.g. EEG or MEG) can be used to predict future time-series

data of another location (in the case of encephalography, another electrode or pool of

electrodes). Kostelecki et al. (2011) showed that using a single-trial classification method

based on concepts of Granger causality, it is possible to reliably classify whether

participants had to respond with a specific hand, or whether they could freely choose to

respond with either hand.

Obermaier et al. (2001) proposes an alternative method for online classification of EEG

data, and compares its performance to more traditional linear discrimination techniques.

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Obermaier and colleagues discuss prior research on classification techniques used for

online discrimination within EEG-based brain-computer-interface (BCI). One of the

problems they discuss is that “The spatio-temporal EEG patterns associated with motor

imagery are not always stable, but often demonstrate a dynamic behaviour”. Obermaier et

al. (2001) use a Hidden Markov Model, which takes into account this dynamic behavior of

brain oscillations, to more accurately perform online classification of EEG data compared

to a more traditional linear discrimination approach.

From the abovementioned research, we can conclude that the application of single-trial

analysis methods on EEG data-sets can have several useful functions, such as increasing

data quality and reliability (Gaspar et al., 2011; Grandchamp and Delorme, 2011), and

single-trial classification (Obermaier et al., 2001; Kostelecki et al., 2011). Furthermore,

these methods allow for the analysis of trial-to-trial fluctuations in the EEG signal, which

are otherwise removed by averaging over trials. The development of additional single-trial

analysis techniques for EEG data will increase the variety of methods, and thus allow

researchers to choose the most appropriate methods for the analysis of their EEG data-

sets.

fMRI

Functional Magnetic Resonance Imaging (fMRI) is a relatively new brain imaging

technique compared to EEG and MEG. One of the advantages of fMRI over

encephalography is the increased spatial resolution, while one of the disadvantages is the

decreased temporal resolution due to the sluggishness of the (blood-oxygen-level-

dependent) BOLD response. Early research into brain activity using fMRI employed

blocked designs, in which two different stimuli were repeatedly shown to a subject in

separate blocks (Huettel et al., 2009). Differences in average BOLD activation between

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blocks would then inform researchers about where in the brain these stimuli were being

processed. More recently, researchers have employed an event-related design, in which

different stimuli, or different conditions of a certain paradigm are alternated, often

pseudorandomly and including variable inter-stimulus and inter-trial intervals (Huettel et

al., 2009). GLMs are then used to model the BOLD response by convolving regressors

with for instance a hemodynamic response function (HRF; represents an assumed shape

of the BOLD response). This approach allows researchers to present participants with

more stimuli and/or conditions within a single scan-session, and thus increases the power

of data acquired from performing psychological paradigms during an fMRI scanning

session.

Moreover, parametric regressors may be used, which take into account trial-to-trial

variation in behavior. A simple RT-regressor can inform researchers about the brain areas

of which the activity is significantly predicted by trial-to-trial variations in RT. In a study by

Yarkoni et al. (2009), a finite impulse response (FIR) approach is used to investigate

correlations between brain activations and trial-to-trial fluctuations in RT. While they use a

standard GLM to analyze the fMRI signal, the traditional HRF is replaced by the FIR. This

method has slightly reduced power due to the larger amount of degrees of freedom, but in

return provides the researcher with an estimation of additional parameters of the BOLD

response. Yarkoni et al. (2009) propose several potential effects of single-trial RT on

BOLD responses, which can be investigated using their method. Using the FIR approach,

they uncover an effect whereby fluctuations in RT modulate fluctuations in the onset for

the BOLD response. This work shows that a single-trial RT regressor, in combination with

a non-traditional way of analyzing the BOLD response (i.e. using FIR instead of HRF), can

provide researchers with an account of the neural mechanisms underlying variation in RT.

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Gaudes et al. (2011) describe a method of analyzing fMRI that detects BOLD-responses

on a single-trial level. This provides researchers with the possibility of investigating

processes that operate between trials and manifest themselves as trial-to-trial variation in

the BOLD response. The method that Gaudes et al. (2011) describes can be thought of as

a univariate version of an independent-component analysis (ICA; Beckmann and Smith

2004). This method is data-driven, and does not require the researcher to define the onset

and duration of events, which is traditionally done in GLM analyses of fMRI. The method

was able to detect finger tapping events within an fMRI time course, without prior

knowledge about the timing or duration of the events. Thus, this method provides

researchers with an unbiased and data-driven approach of analyzing a BOLD time course.

One example in which this method could be useful is when we are interested in neural

processes of which we are not certain when they occur, or which are not directly

detectable using behavioral measurements. For instance, task-unrelated-thoughts can be

hazardous in situations where one needs to be alert, and yet we lack tools to investigate

the occurrence of these events. Using the method described by Gaudes et al. (2011), it

could be possible to detect these events in a healthy individual performing a cognitive

task, while occasionally lapsing in attention due to a task-related thought.

One of the advantages of fMRI over other neuroimaging techniques such as EEG is its

high spatial resolution. In order to optimally exploit this advantage, multi-voxel pattern

analyses have been developed. MVPA can potentially detect fMRI activity patterns which

traditional univariate approaches cannot (Jimura and Poldrack, 2012). MVPA requires the

extraction of single-trial BOLD responses from fMRI time courses. A recent study by

Mumford et al. (2012) investigated eight methods for extracting the single-trial BOLD

response and found that the best approach entails including a regressor for the trial of

which the single-trial BOLD response is extracted, and a nuisance regressor for all other

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trials. This approach is very easy to implement, and conceptually simple, as it expands on

traditional GLM analyses of fMRI data.

The field of fMRI is still very young, and much effort is being put into the development of

new analysis techniques. Single-trial analysis methods for BOLD-data will allow

researchers to investigate trial-to-trial fluctuations in brain activity with a high spatial

resolution.

Simultaneous EEG/fMRI

EEG has a high temporal but low spatial resolution, while fMRI has a high spatial but a low

temporal resolution. Combining data-sets acquired from EEG and fMRI can potentially

increase our temporal as well as spatial understanding of a certain process. The most

direct way of combining these different methods is to acquire EEG and fMRI data

simultaneously. This allows the investigation of neurocognitive processes in the spatial as

well as temporal domain. It is not surprising that in many simultaneous EEG/fMRI studies,

single-trial analyses are employed. After all, if one werenʼt interested in the trial-to-trial

dynamics of a certain neurocognitive process, one wouldnʼt have to measure EEG and

fMRI simultaneously (i.e. separately acquired EEG and fMRI data sets are sufficient in

order to investigate individual differences or group-differences, while still informing

researchers of the spatial as well as temporal nature of these differences). Below I will

provide an overview of the single-trial analysis methods applied on simultaneous data-

sets. For a more general review on simultaneous EEG/fMRI, see Huster et al. (2012).

A much used method for the analysis of simultaneous EEG/fMRI data, is to predict BOLD

activations from EEG data. Using this method, one is able to identify the structures

underlying a certain neural process with high spatial accuracy. Eichele et al. (2005) used

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an auditory oddball paradigm, in which participants are asked to respond when an

infrequent ʻoddballʼ stimulus is presented among more frequent stimuli. Eichele and

colleagues introduced predictability in their design by alternating between random and

fixed target-to-target intervals (TTI). Amplitude modulations (AM) of ERPʼs were found as a

function of the number of times an interval was repeated. These amplitude modulations

were then correlated on a single-trial level to BOLD activations. By using a single-trial

analysis method on simultaneous EEG/fMRI data, Eichele et al. (2005) were able to

identify the brain structures underlying amplitude modulations in response to the repeated

presentation of auditory sequences. Note that because of each methodʼs specific

limitations, this result would not have been found by acquiring only EEG or fMRI data, or

even by acquiring both data-sets non-simultaneously.

Fuglø et al. (2011) describe an experiment in which a basic visual stimulation paradigm

was used in order to assess the between-subject reliability of single-trial EEG-fMRI

correlations. The authors found that when combining the amplitudes of two commonly

reported visual evoked potentials (VEP; more specifically the P1 and N1) in the EEG

domain, they found high correlations with BOLD activation in visual areas, which were

consistent across all participants. Several other studies have utilized simple experimental

paradigms in conjunction with single-trial simultaneous EEG/fMRI methods in order to gain

insight into the spatial locations of previously investigated electrophysiological phenomena

(Esposito et al., 2009; Goldman et al., 2009; Mulert et al., 2010; Scheibe et al. 2010;

Becker et al., 2011; Yuan et al., 2011)

Debener et al. (2005) used a Flanker task while recording simultaneous EEG/fMRI.

Participants had to report the direction of an arrow displayed in the center of a screen,

surrounded by either congruent (same direction) or incongruent (opposite direction)

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arrows. Debener and colleagues found that single-trial error-related negativity (ERN)

amplitudes were predictive of the magnitude of the increase in RT on the subsequent trial

(post-error slowing; PES). Moreover, trial-to-trial coupling of EEG and fMRI showed that

the ERN was predictive of BOLD activation in the rostral cingulate zone (RCZ), which is

often associated with performance-monitoring (Ridderinkhof et al., 2004). By combining a

single-trial EEG-behavior method with a single-trial EEG-fMRI method, the authors were

able to identify both neural mechanisms underlying performance monitoring with high

temporal as well as spatial precision.

More sophisticated methods for the analysis of simultaneous EEG and fMRI data-sets are

being developed. Correa et al. (2010) describe a method for the fusion of two data-sets

using multi-set canonical correlation analysis (M-CCA). This multivariate method is data-

driven and allows the researcher to investigate connectivity across functional networks. To

discuss the specifics of this method is unfortunately beyond the scope of this review.

The research described above shows that much effort is being put into developing new

methods for the analysis of RT, EEG and fMRI data. Furthermore, combining techniques to

acquire simultaneous RT/EEG/fMRI data will allow researchers to more precisely

investigate (latent) cognitive processes, and their underlying neural mechanisms, both in

the temporal as well as in the spatial domain.

Application of single-trial analyses in perceptual decision making

The research described above provides us with a wide array of methods to apply to

different types of data-sets. From this section onward, I will discuss the application of

these single-trial analysis techniques in perceptual decision making. I will start by generally

discussing perceptual decision making, followed by three sections on aspects related to

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perceptual decision making.

General

As described in the dependent measures section, methods from machine learning have

been adjusted to provide researchers with analysis techniques which can be applied to M/

EEG and fMRI datasets. Furthermore, computational models are being applied to

investigate latent cognitive processes underlying perceptual decision making. Below, I will

discuss perceptual decision making research using some of these single-trial analysis

methods.

Kamitani and Tong (2006) show that by using MVPA on data acquired from participants

performing a RDM paradigm during fMRI scanning, they were able to train a classifier to

reliably distinguish trials with different directions of motion, from BOLD activations in early

visual areas V1 through V5. In addition, they showed that it is possible to classify the

attended motion direction when two opposite motion directions were displayed

simultaneously. Using this method, Kamitani and Tong (2006) provide an alternative

method for investigating visual direction selectivity in humans, with a higher spatial

resolution (through the use of MVPA) than conventional fMRI analyses.

Philiastides and Sajda (2005) used a face-car discrimination task with multiple levels of

coherence (much like the example experiment described above, but with images of faces

and cars instead of dots moving to the left or right), and showed that they were able to

train a classifier to distinguish between face and car trials using single-trial EEG data from

an early and a late ERP component. The accuracy of this classifier was highest in the

high-coherence condition, and lowest in the low-coherence condition. Moreover, they

found that the optimal time-window for classification in the late (but not in the early) EEG

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component was shifted for more difficult conditions in which stimuli were more ambiguous.

The authors suggest that as opposed to the early face-selective ERP component, this late

ERP component is representative of the accumulation of evidence, given that it shifts

temporally based on the difficulty of the stimulus (and thus the increase in RT). Using this

single-trial method, the authors were able to more specifically investigate ERP

components, and draw more sophisticated conclusions about two ERP components, which

would, in a more traditional analysis, otherwise simply be interpreted as being correlated to

the process of distinguishing cars from faces. In a later study, Philiastides et al. (2006)

expand on their earlier work by employing a diffusion model, and correlating the strength

of discrimination of the late ERP component to the mean drift rate per condition.

While diffusion models do take into account entire RT distributions, they lack the ability to

provide single-trial estimates of parameters such as drift rate and threshold. Some efforts

have been made to solve, or circumvent this drawback. For instance, Ratcliff et al. (2009)

use the early and late ERP components acquired on a face-car discrimination task to

divide the data into more face-like and more car-like groups, and then fit a diffusion model

to the separate groups. They find that differences in drift rate were found between groups

when the data were separated based on the late ERP component, while this was not the

case for when the data were separated based on the early ERP component. This result

reinforces the notion that the late component is associated with evidence-accumulation.

To more accurately investigate the underlying neural mechanisms of latent cognitive

processes such as evidence accumulation, a single-trial implementation of drift-diffusion

type analyses is required. Van Maanen et al. (2011) describe a single-trial implementation

of the linear ballistic accumulator model (STLBA). The LBA (Brown and Heathcote, 2008)

differs from the DDM in that it contains accumulators for each option separately, meaning

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that it is possible for the LBA to fit multiple-choice data-sets. In addition, the LBA achieves

RT variability by including variability in drift rate and starting point. While the drift-rate

distribution is gaussian, the starting point distribution is uniform. Van Maanen et al. (2011)

Use the gaussian nature of the drift-rate distribution to estimate single-trial values of drift-

rate and starting-point. More specifically, a default LBA model is fit to provide the

researcher with average drift rate and starting point values and decision time. The mean

drift rate is then set as the most likely drift rate for every trial. Corresponding starting point

values are then selected, based on the decision time. If the starting point value required

for the decision-time on a single trial, using the mean drift rate, is an invalid one (i.e. falls

outside of the distribution of starting points), the drift rate for that trial is adjusted to provide

the most likely combination of drift rate and starting point, given the single trial decision-

time. Van Maanen et al. (2011) use an RDM paradigm with a speed-accuracy-tradeoff

manipulation, and show that when participants were instructed to switch between speed

and accuracy conditions, single-trial starting point values were correlated with single-trial

BOLD estimates in medial frontal gyrus (MFG), anterior cingulate cortex (ACC) and

Striatum. In addition, when participants were specifically instructed to speed up their

responses, a correlation between these measures in pre-supplementary motor area

(preSMA) was found. In a control analysis, van Maanen et al. (2011) show that performing

similar analyses using single-trial RT instead of model parameters results in a large

amount of unspecific brain areas associated with RT. Using this single-trial model-based

approach is more specific and allows investigation of latent cognitive processes such as

evidence accumulation or response caution on a single trial level.

Reward learning

Reward learning is an important aspect of perceptual decision-making. When we make

perceptual decisions, we might be influenced by the previous outcomes of similar

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decisions. In order to benefit from previous experience, we need to be able to learn

stimulus-reward associations (OʼDoherty et al., 2004). Research into reward learning

naturally invites methods of analyses which take into account the time-course of certain

learning processes. The learning of stimulus-reward associations can be modeled by a

model-based framework known as reinforcement learning theory (Sutton and Barto, 1998).

These models provide a computational account of how certain stimulus-reward

associations are formed over time, and how reward-rate is subsequently optimized. A

recent study by Cavanagh et al. (2010) utilized a specific model derived from

reinforcement learning theory: Q-learning. This approach estimates action values and

prediction errors per trial, providing the researcher with a single-trial measure of the

subjectʼs reward expectation and subsequent prediction error. Cavanagh et al. (2010)

showed that following negative prediction errors, RT slowed down, while it speeded up

after positive prediction errors. Furthermore, they showed that there was a relation,

especially in incorrect trials, between single-trial prediction error and single-trial theta

(4-8hz) power over the medial prefrontal cortex (mPFC). mPFC theta power was also

predictive of the next-trial change in RT. Additional single-trial analyses showed that theta

power in the lateral prefrontal cortex (lPFC) was related to prediction error, as well as to

the RT change on the subsequent occurrence of the same stimulus as opposed to the

current one. Finally, theta phase synchrony between mPFC and lPFC was related to the

single-trial prediction error estimates. Using these single-trial analyses, Cavanagh et al.

(2010) were able to investigate the role of theta oscillations during the time-course of the

reinforcement learning process in much more detail than simple trial-averaging would have

allowed them.

Several other studies have employed single-trial analyses to investigate reinforcement

learning processes. For example, Cavanagh et al. (2011) investigate the exploitation/

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exploration trade-off and find that frontal theta power is predictive of single-trial parameters

reflecting uncertainty and unexpectedness. Cohen and Ranganath (2005) used a

reinforcement-learning paradigm while measuring functional MRI, and found that individual

differences in value functions can be linked to individual differences in BOLD activations,

and that future decisions can be predicted by neural activity on previous trials. In a later

study, Cohen (2006) estimated single-trial prediction errors and found a correlation with

BOLD activity in a network of areas including left Substantia nigra, dorsal cingulate cortex,

bilateral PFC, and right cuneus. Wunderlich et al. (2009) used reinforcement learning

theory in conjunction with functional MRI to investigate neural correlates of trial-to-trial

fluctuations in action values, and found that the BOLD signal in SMA predicted single-trial

action value estimates irrespective of which action was chosen, while BOLD signal in the

ventromedial prefrontal cortex (vmPFC) and intraparietal sulcus were specifically related to

the action values for the chosen actions.

In short, reinforcement learning models have been shown to provide researchers with an

excellent tool with which they can investigate the time-course of reward-learning

processes.

Other types of single-trial analyses have also been applied in the field of learning and

memory (Behrens et al., 2007; Nieuwenhuis et al., 2011). Behrens et al. (2007) use a

Bayesian account of learning to estimate single-trial values of volatility, which is a measure

of to what extent recent experiences are more predictive of future events than distant

experiences. They showed that this parameter was correlated on a single-trial level to

BOLD activity within the SMA, and volatility related activity in the ACC was related to

individual differences in learning rates. Nieuwenhuis et al. (2011) measured functional

connectivity by correlating single-trial oscillatory power between areas involved in

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associative memory, and found that functional connectivity between the left anterior

temporal lobe (ATL) and the posterior parietal cortex (PPC) and fusiform face area (FFA)

increases over time when face-location associations are learned. This experiment

provided evidence for the emergence of memory representations within neocortical areas,

and suggested that the development of single-trial gamma-power correlations over time

could be an underlying process.

The abovementioned methods can be used and adapted to investigate the reward-

learning aspects of perceptual decision-making. Imagine adapting the example experiment

described above to only reward participants on a subset of correct trials. You might

reinforce correct “left” decisions on only 50% of all trials, while reinforcing “right” decisions

75% of all trials. over time, participants might develop a bias towards choosing the “right”

decision. As described in the previous paragraph, you could apply a reinforcement

learning model to your data in order to estimate single-trial prediction errors or action

values, and subsequently correlate them to single trial EEG or BOLD measurements.

Based on the studies discussed one can argue that single-trial analysis methods are

broadly being used in the field of reward-learning. Within this field, neuroimaging methods

such as EEG/MEG and fMRI are being combined with computational models to inform

researchers about the underlying neural mechanisms of reward-learning.

Attention

The research field of attention is one that easily links to perceptual decision making. A

decision-maker needs to attend to different options in order to properly choose between

them. One of the questions within attention is whether it is possible to predict lapses in

attention from brain activity. Weissman et al. (2006) investigated whether single-trial

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performance on a global/local selective task could be predicted by single-trial BOLD

activity. In this task, participants are shown a letter that consists of smaller letters.

Participants are instructed to report either the global or the smaller local letters. Trials can

be incongruent or congruent, depending on whether the global and local letters are

different or the same. The authors specifically looked at trial-to-trial variation in reaction

times, and predicted that larger reaction times would be linked to smaller BOLD activity in

frontal control regions. The results indeed showed this effect, and the authors interpreted

the reduction in BOLD activity in these areas as reflecting attentional lapses, which

resulted in longer response times. In addition, longer response times were found to

correlate to increased activity within regions of the default-mode network. The default-

mode network is often found to be activated when participants are instructed to do nothing,

meaning that participants are not actively engage in a task., and deactivated when

participants engage in a task (although this is not a clear dichotomy; see Spreng (2012)).

This effect again suggests the increased response times are linked to a lapse in attention.

Eichele et al. (2008) followed up on this by investigating whether specific patterns of

activation can predict the occurrence of an error. In this study, a Flanker task was used in

which participants were asked to report on a target stimulus, which is surrounded by

distractor stimuli, which can be either congruent or incongruent to the target stimulus.

Eichele et al. (2008) used independent component analyses (ICA) of fMRI data to

specifically extract components of activity consisting of areas associated with the default

mode network, as well as components which represented a network of areas associated

with engagement in a task. It was found that activity in the default mode network gradually

increases (or rather, deactivation gradually decreases), preceding an error. Activation in

task-relevant brain areas gradually decreased preceding errors. In addition, just shortly

before errors occurred activity in sensorimotor areas abruptly declined. Shortly after the

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error occurred, these activity patterns reversed. These effects show that errors can be

predicted by fluctuations in brain activity more than one trial preceding the erroneous

behavior. This suggests that averaging over pre-error trials might not be the most powerful

method to investigate brain activity leading to errors. Instead, investigating multiple trials

preceding errors (and thus, employing a single-trial analysis method) might provide a

better insight into what causes an error to occur. Moreover, it might even be beneficial to

combine neuroimaging techniques, by simultaneously measuring fMRI and EEG (the latter

of which has a much greater temporal resolution) in order to more closely investigate trial-

to-trial variation, and even within-trial variation in brain activity.

More recently, Prado and Weissman (2011) performed an fMRI study using a simple

detection task containing both visual and auditory cues. Participants had to report on

either the visual or auditory cue, while suppressing the distractor cue. Similar to the

studies described above, the paradigm contained congruent and incongruent trials. The

authors found that an increase in functional connectivity between posterior cingulate

cortex (PCC) and dorsolateral prefrontal cortex (DLPFC) was associated with slower

responses in current trials, but faster responses in the next trial. These results are

supportive of the default-mode interference hypothesis, which states that activity in default-

mode areas interferes with task-related processing, thereby decreasing performance or

producing attentional lapses. However, the authors acknowledge that the positive

influence that they found on future performance is less clear. Given that this effect

inherently entails fluctuations in behavior and brain activity between trials, future studies

should continue to use single-trial analyses to investigate fluctuations in attention.

To illustrate the effectiveness of single-trial analyses in this field, imagine adapting our

example experiment to induce attentional lapses. You might increase the difficulty and

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length of the paradigm, while simultaneously depriving participants of sleep and/or coffee.

Participants will surely become fatigued and start making errors (Ratcliff and van Dongen,

2009, 2011), possibly because they werenʼt paying attention when the stimulus was

presented. The single-trial analyses described above can easily be adjusted to

accommodate analyses of RT data from the adjusted RDM paradigm. You might

investigate functional connectivity or increased activity within the default-mode network, to

investigate whether longer RTʼs are associated with default-mode network activation.

Alternatively, you might employ a single-trial model such as the STLBA method (van

Maanen et al., 2011). Attentional lapses might result in a temporary decrease in sensitivity

to the stimulus, which would be reflected in a decrease in single-trial drift rate parameter

values. These single-trial values could then be linked to BOLD activity, which could

potentially provide a more specific view into the underlying neural mechanisms of

attentional lapses, than one would get when using mean RTʼs.

Spontaneous brain fluctuations

The attentional and reward-learning aspects of perceptual decision making have in

common that the processes involved in these aspects are not random, and contain a

certain functionality. However, random processes in the brain might also have an influence

on perceptual decision making.

Research into spontaneous brain fluctuations directly investigates the question why there

is variability in the brain, and how this variability manifests itself in terms of behavior (For a

review on spontaneous brain fluctuations, see Fox et al. (2007a)). It is obvious that

researchers in this field would use single-trial analyses, seeing as averaging over trials

effectively removes the temporal variability that is being investigated when looking at

intrinsic brain fluctuations.

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Fox et al. (2006) investigated intrinsic spontaneous fluctuations in BOLD activity by

exploiting the correlation of intrinsic activity between left and right somatomotor cortex

(SMC). Participants were first instructed to passively view a movie, during which fMRI was

measured. During a second movie viewing, participants were instructed to press a button

with their right index finger on specific occasions. The left SMC was functionally defined by

the button press condition (i.e. the area in which activity corresponded to a button press

was defined as the SMC). Then, the right SMC was defined by using a functional

connectivity analysis. Lastly, the BOLD activity in the right SMC was subtracted from

activity in the left SMC. This resulted in a decrease in noise of the task-related BOLD

response in left SMC, while still retaining the average response that was found in the initial

analysis. Furthermore, they showed that the magnitude of the event-related BOLD

response could be predicted by whether the time of the event occurred in a trough or peak

of the intrinsic BOLD response. By doing this, they showed that event-related activity can

be influenced by event-unrelated intrinsic activity. Fox et al. (2007b) expanded on their

earlier experiment by linking the variability in BOLD activity to variability in button press

force. While they didnʼt employ a purely single-trial analysis, they did show that the shape

of the BOLD response could predict whether the associated button press was attributed to

the “hard” or “soft” bin. Furthermore, this effect was extinguished by regressing out the

BOLD time-course of the right SMC. This result suggests that intrinsic fluctuations can

influence subsequent event-related BOLD activity, which in turn is associated with

variability in behavior.

The research described above shows us that intrinsic fluctuations in brain activity can be a

source of trial-by-trial variability in behavior. In our example experiment, intrinsic brain

fluctuations might underlie trial-to-trial variation in RT. One of the challenges of future

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research into spontaneous brain fluctuations is to develop models that can take into

account these fluctuations in a data set acquired from healthy participants performing a

psychological task, like the RDM.

Conclusion

In this review, I have provided an overview of research into trial-to-trial variation in

perceptual decision-making and related fields. I have shown that much work is being done

to develop single-trial analysis methods which can be applied to RT, EEG/MEG, and fMRI

data-sets. In addition, I have shown many examples of experiments employing single-trial

analysis methods to investigate perceptual decision-making and related cognitive and

neural processes such as reward learning, spontaneous brain fluctuations, and attention.

Despite the many promising single-trial methods that have been developed and applied,

many studies do not explicitly show that by using a single-trial analysis method, results are

found which could not have been obtained by using traditional averaging methods. For

future research, it is important to emphasize the advantage of these single-trial analysis

methods by reporting both results from traditional averaging and single-trial analysis

methods. This will provide a more clear picture of when single-trial analyses can, and

when they cannot, provide researchers with a better insight into trial-to-trial variability in

perceptual decision making.

In conclusion, the application of single-trial analysis techniques as opposed to trial-

averaging potentially provides researchers with the possibility to investigate cognitive

processes and their underlying neural mechanisms in more detail. Whereas more

traditional research has looked into the difference of a specific process between groups or

individuals, single-trial methods allow researchers to investigate the time course of the

26

process itself, informing the researcher of how the process develops over time. The

challenges of future research aimed at investigating trial-to-trial variation in perceptual

decision making is two-fold: First, future methodological research will have to integrate

simultaneously acquired data-sets from different neuroimaging techniques, and

subsequently develop analysis methods which take into account trial-to-trial variability.

Second, future research will have to develop new psychological paradigms in which trial-

to-trial variability in cognitive and neural processes can be investigated, using these single-

trial analysis techniques.

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