Investigation of computational modelling as a tool for
decision-making strategy identification
27 EC
11 January 2017 – 16 June 2017 Farah Aulia Rahman, 11392584 Supervisor: Maël Lebreton
UvA representative: Simon van Gaal Co-assessor: Simon van Gaal
Center for Research in Experimental Economics and political Decision-making (CREED), Universiteit van Amsterdam
Abstract
In decision-making experiments, a great number of trials is often required to fulfil statistical requirement. When conducting long-duration experiments, individuals are likely to tire with time and switch their decision-making strategy to one that requires less energy which may be undesired for the research. However, there is currently no existing method to detect when individuals start to unconsciously change their decision-making strategy. Therefore, we investigated whether strategies in sensory decision making could be identified by viewing the decision-making strategy as a logistic function and investigating how the model changes with adjustments of strategy. Participants were presented with both auditory and visual stimuli simultaneously and were recurrently instructed to switch between making decisions based on visual or auditory information. Findings revealed that parameters of the model changed with different decision-making strategies. When strategy likelihood was calculated using the model and obtained parameters, the strategy likelihood of the visual strategy was higher when individuals made decisions based on visual information and the same result was found for auditory strategy.
Introduction
When making economic decisions, individuals will lean towards the choice with the best predicted outcome. The assessment to determine which alternative may give the best outcome involves assigning expected values or utility to each option and weighing the option with a higher expected value or utility (Bernoulli, 1954). This is known as expected utility maximization and is considered the rational method of decision-making. However, in economic decision-making tasks where a great number of trials is often required to fulfil statistical requirements, this rational strategy may not always be consistently used throughout the whole experiment. When conducting long-duration experiments, while individuals may initially compute each option’s expected value, they will likely tire with time and therefore switch their strategy to heuristic decision-making which requires less effort. Unlike the expected utility strategy, heuristic decision-making only considers a fraction of available information and uses simple rules to render decisions (Gigerenzer & Gaissmaier, 2011). This is a presumably faster and less effortful way of making adaptive decisions. This change in decision-making strategy may affect the choices that the individual makes and could result in inaccurate measurements, possibly confounding the conclusion regarding the desired experiment goal. Similar to economic decision-making, it is likely that individuals can also explore different ways to combine sensory information in order to comprehend the surrounding environment. Sensory information is obtained from the humans’ five sensory systems: vision, audition, olfaction, gustation, and tactioception (Kandel, Schwartz, Jessell, Siegelbaum, & Hudspeth, 2013) and each of these modalities can be further broken down into more specific decision variables (e.g. colour and shape are both variables in the visual domain). In perceptual decision-making tasks, individuals gather and combine necessary sensory information which ultimately influences the act of choosing (Heekeren, Marrett, & Ungerleider, 2008). Not only are there numerous ways of combining the accumulated sensory information, the ways in which they are integrated could also shift across time, posing a similar problem to the shifts in decision-making strategy in economical contexts.
Ideally, in such decision-making experiments participants should stop and rest when they begin to tire and shift the way in which they come to decisions to minimize deviations caused by irrelevant factors. However, there is currently no existing method to detect when individuals start to unconsciously change their decision-making strategy. Behavioural measures such as reaction time or choice patterns could be the answer to identifying these changes, however different strategies can generate similar patterns of behavioural responses. Consequently, strategies are extremely difficult to identify from behavioural measures alone.
Figure 1. Decision-making framework. Decision-making viewed from a computational perspective regards a decision-making strategy as an algorithm or function which receives decision variables or evidence as input and
utilizes these inputs to produce the final decision.
In decision-making, we absorb, perceive and combine the information available to us and take it into account for consideration before finally arriving at a decision (Gold & Shadlen, 2007; Smith, 2010). From
𝑓(𝑥)
Decision variables Strategy Final decision
Behavioural output A
B C D
a computational approach, the process of decision-making in the brain is viewed as an algorithm which receives information as the input and gives the final decision as the output (Figure 1). The received inputs are often referred to as decision variables, which are properties of the options which guide the individual towards the final decision (Glimcher, Camerer, Fehr, & Poldrack, 2009). The internal algorithm utilized to produce the output will further be referred to as a strategy: a function which weighs and combines the information in a certain way to produce a decision. The strategies in decision-making can be represented in many ways, some differing in the number of parameters, the values of the parameters, or are represented by different functions altogether. Different strategies within decision-making cases such as economic and perceptual decision making can be modelled using the same function with different sets of parameters (REF). Therefore, a switch of strategies within the same decision-making domain is likely to be indicated by a change in the combination of parameters.
This input-algorithm-output process can generally be applied to various types of decision-making. For instance, in an economic context, a gambler would require information of the values of gains, losses, and the probability of each one (Tom, Fox, Trepel, & Poldrack, 2007) before deciding whether to take the risk or not; equally in a perceptual context, a sommelier (wine professional) requires gathering of sensory evidence such as visual, olfactory, and gustatory information to decide the quality of a glass of wine. In each of these decision-making contexts, the relevant information serves as an input which is then processed in a certain way so that it leads to a behavioural output, which is the final decision. In most cases, the decision variables are observable and often also measurable, which also holds true for the decision output. However, the internal process converting the decision variables into a decision is not yet fully understood and these decision-making strategies still remains a black box which the current study aims to explore.
The goal of the main project is to investigate strategy changes in decision-making using computational modelling as tools. For this study, a decision-making task is designed where strategy-utilization is instructed to the individual in order to demonstrate that people actually change strategies when instructed, possibly indicated by changes in the parameters of the computational model. As a starting point, the task will therefore involve strategies which are well-known to be described by good models, differing only in the set of parameters. Overall, this will be one of the first steps towards the ultimate goal of detecting strategy changes using a combination of neuroimaging and computational modelling without prior knowledge of model nor instructed strategy-switching.
Testing the hypothesis directly in an economic context however may not be the most ideal way to begin this investigation of strategy-switching detection. As previously explained, the computational decision-making framework applies to all types of decision-decision-making, not excluding economic decision-decision-making. However, in economic decision-making, a network of many inputs is involved, which include those previously mentioned in the gambling example such as probability and value. Furthermore, these variables are not completely separable from each other. As an example, a 60% probability of winning €50 will be weighted differently to a 60% probability of winning €100. Although the probability of winning is the same in both cases, the value of the prize affects its weight in the decision-making process. This interaction between value and probability is known as expected utility, which adds another extra decision variable to the equation. As a consequence, a complex function may be required to represent the decision-making process while accounting for all these inputs. Additionally, the economic decision-making process is also entwined with factors such as the attitude, perception, affect, and motive of the decision-maker (McFadden, 1999). In order to provide a proof-of-concept for likelihood calculation as a method of identifying making strategies, this study will be the first attempt to distinguish strategies in a simpler form of decision-making: perceptual decision-making.
Unlike the decision variables involved in economic situations, the information from these different modalities are separable and are less likely to interact with each other. For the purpose of simplicity, the decision variables in this study are restricted to visual and auditory stimuli only. This project will therefore investigate the identification of visual strategy and auditory strategy using computational modelling to provide proof-of-concept for strategy-identification in economic tasks. Specifically, this study will compare
the maximum likelihood of the observed data given the function representing the visual strategy and maximum likelihood of the observed data given the function representing auditory strategy during visual and auditory decision-making sessions. Ultimately, this study aims to investigate whether analysis of behavioural measures using computational priors has the power to make predictions of the strategies being utilized by calculating the maximum likelihood of observing the data when using a certain strategy.
Methods
Subjects
Twenty subjects (8 male) were recruited as subjects for the experiment. Subjects had normal or corrected eyesight, were aged 18-35 years old, and had no epileptic history. Subjects were paid a base amount of €10 for their participation and had the opportunity to gain additional money of up to €4 according to their performance in the experiment. Two participants were excluded from data analysis due to outlier performance in the calibration data.
Paradigm
The perceptual task consisted of two types of sessions; visual and auditory. The experiment was designed using Cogent Graphics and Cogent 2000 in MATLAB 2017a. In both sessions at each trial, both visual and auditory cues were always presented together. Two gabor images with different orientation angles were presented sequentially and with each visual stimuli, the participant would also hear a pitched note (Figure 2). The contrast of the gabor images were set to 0.2 and the note frequencies ranged between 300 Hz and 2000 Hz.
Figure 2. Time-course of a single trial in the sensory task. (a) A fixation cross appears in the middle of the screen to capture the subject’s attention for 750 ms before the first stimuli appears. A gabor with a certain orientation is presented simultaneously with
a single beeping sound of a certain frequency for a duration of 150 ms. This is followed by a blank screen for 150 ms which appears before the second stimuli, a new set of gabor and sound, is presented. The subject then has to determine whether the second gabor orientation shifts clockwise or counter-clockwise compared to the first gabor (in visual sessions) or whether the
second sound has a higher or lower frequency compared to the first sound (in auditory sessions)
The subject will then be presented with a two-alternative forced-choice option. In visual sessions, the subject was required to make a decision based on visual cues and ignore auditory cues; press the right arrow button if the second gabor orientation shifted clockwise compared to the first gabor or press the left arrow button if the second gabor orientation shifted counter-clockwise. In auditory sessions, participants were required to press the left arrow button if the second note was lower-pitched than the first note or press the right arrow button if the second note was higher-pitched. In all sessions of the experiment, the participant receives no feedback on their responses (correct or incorrect).
The perceptual decision-making task consisted of two training sessions, two calibration sessions (one for each type of session) and followed by ten sessions of the main task. The training sessions each consisted of
5 trials each, the calibration sessions consisted of 120 trials each, and the main task consisted of 640 trials in total. From the calibration sessions, the parameters of the logistic function representing the psychometric slope was obtained for each subject to later be used to determine the difficulty level of the main task tailored for each subject. The calibration sessions were each divided into 10 blocks of 12 trials. After each block, performance was assessed. If the subject performed above 70% correct, the difficulty in the following calibration block was increased by narrowing the range of decision variables (smaller angle and frequency differences). If the subject’s performance fell below the 70% limit, the task difficulty in the following block was decreased by widening the decision variable range (larger angle and frequency differences).
Using the calibration data, the task difficulty of the following session in the main task was adjusted using a logistic function so that the probability of subjects responding correctly is 65% and 85%. The decision variable value (corresponding to these levels of difficulty was calculated using the following formula:
𝐷𝑉 = 1 𝛽1
∙ (𝑙𝑜𝑔 𝑝𝑐
1 − 𝑝𝑐− 𝛽0)
where 𝛽0 refers to the intercept point of the logistic function, 𝛽1 refers to the slope of the logistic function, and 𝑝𝑐 represents the difficulty level, which was set to 0.65 or 0.85.
This was followed by ten blocks of the perceptual task (five sessions of the visual task alternated with five sessions of the auditory task), each consisting of 64 trials. In visual blocks, the word ‘VISUAL’ is constantly presented on the screen to remind participants to make choices based on visual information while in auditory blocks, the reminder word is replaced by ‘AUDITORY’ and presented at the same location on the screen. To account for the possibility of learning and increased performance levels, the difficulty of the task was readjusted at every block. As an example, the subject performance levels in the first visual session is used to adjust the difficulty in the second visual session, the performance levels in the second visual session is used to adjust the third visual session, and so on.
Although the precise function representing the decision-making process is unknown, there is reason to believe that the logistic function can represent simple perceptual decision-making. The logistic function has often been used to assess how well individuals perform at sensory discrimination within a range of stimulus intensities (Philiastides & Sajda, 2006; Wichmann & Hill, 2001), making it likely that this function is also able to represent perceptual decision-making adequately. The probability of choice in the perceptual task is modelled as follows:
𝑃(𝐿) = 𝛽0+ 𝛽𝑉∙ 𝐷𝑉𝑉+ 𝛽𝐴∙ 𝐷𝑉𝐴
The probability of choosing the first stimuli (first gabor or first tone, using the left response button) involves two decision variables and three parameters (𝛽). 𝐷𝑉𝑉 refers to the visual decision variable, defined as the difference in angular measure (first gabor orientation – second gabor orientation), and 𝐷𝑉𝐴 refers to the auditory decision variable, defined as the difference in sound frequency (first tone – second tone). .The parameters 𝛽0 represents individual bias, 𝛽𝑉 represents the weighting of the visual decision variable, and 𝛽𝐴 represents weighting of the auditory decision variable. The fact that visual and auditory processing occurs in different areas of the brain (Kandel, Schwartz, Jessell, Siegelbaum, & Hudspeth, 2013) minimizes the chances that performance in one modality is affected by the other, allowing the function to be kept simple without interaction of the decision variables. To circumvent the strategy-identification problem, the task is designed in such a way that the changes in strategies are instructed. Individuals focus only on visual information when instructed to and ignore the auditory information and vice versa, therefore presumably no consideration or weighting will be put on the unnecessary information. This results in the assumption that the parameter for auditory strategy (𝛽𝐴) is set to 0 when instructions are given to use the visual strategy, and oppositely the parameter for visual strategy (𝛽𝑉) is set to 0 when auditory strategy is instructed.
From the calibration session, the parameters (𝛽0and 𝛽1) for the visual strategy function and the auditory strategy function are obtained for both the visual and auditory sessions. Within each session (visual and auditory), the slope parameter for the visual strategy (𝛽1𝑉) and the auditory strategy (𝛽1𝐴) is contrasted using the paired t-test to evaluate which stimuli information contributed more in the decision-making process (indicated by a significantly higher slope parameter). Using the obtained parameters, the likelihood of using the visual or auditory strategy is then calculated. For each sensory block (visual and auditory), the likelihood of using the visual strategy and the likelihood of using the auditory strategy is compared using the paired t-test to confirm whether visual information was used to make decisions in the visual blocks and auditory information was used for decision-making in the auditory blocks.
Results
Participants were required to do a perceptual task in which they were presented with visual and auditory stimuli simultaneously and had to make decisions based on either one of the sensory stimuli according to instruction. The visual stimuli were gabors with tilted orientations at various angles and the auditory stimuli were tones were of various frequencies. Each gabor was presented simultaneously with a sound and at each trial, two sets of images and sound tones were presented consecutively. When instructed to make decisions based on visual information, the participant is required to judge whether the orientation of the second gabor shifts clockwise or counter-clockwise relative to the first gabor image and ignore the auditory stimuli. When instructed to make decisions based on auditory information, the participant must decide whether the second tone is of higher or lower frequency than the first tone and ignore the visual stimuli.
In this study, the problem of identifying strategies is approached by viewing the decision-making strategy as a computational model and then investigating how the model changes with adjustments of strategy. The model receives decision variables as input and uses it to compute the behavioural output. Under the assumption that the visual and auditory strategies are described by the same model and differentiated only by different sets of parameters, the probability that a certain strategy is used is equivalent to the posterior probability of the parameters, given the data and the model (Daw, 2011). This can be described using the Bayes formula:
𝑃(𝜃 | 𝐷) =𝑃(𝐷 | 𝜃) ∙ 𝑃(𝜃) 𝑃(𝐷)
where the probability of the strategy being used given the observed data is equal to the product of probability of the data given the parameters or strategy (most often referred to as likelihood) and the probability of the parameters, divided by the probability of observing the data. When considered independently of the model, the probability of observing the data would be the same therefore 𝑃(𝐷) can be neglected in comparisons of strategies. In the case of strategy comparison such as the current study, different computational models can be considered to have equal probability of occurrence regardless of the data. Consequently, the probability of strategies given the observed data is proportional to the likelihood of observing the behavioural choices given the strategy. Comparison of strategies can therefore also be conducted by comparing the likelihood of observing the behavioural data given different strategies, which is the approach that the current study adopts.
Calibration
At the beginning of each run, each participant first goes through two calibration sessions. In these sessions, the participant is instructed to answer based on visual information in the visual calibration session and answer based on auditory information in the auditory calibration session. From these sessions, parameters 𝛽0 and 𝛽𝑉 or 𝛽𝐴 (depending on the calibration session type) are obtained for each individual and this represents their bias and psychometric slope in the visual task and auditory task, respectively. The main purpose of obtaining these parameters for each individual is to use them to estimate the difference in visual angles or frequency which sets the task at a desired difficulty. Large differences in angle or frequency are
presumed to be distinguished correctly more often than small differences, yet the task needs to be adapted according to each individual’s performance levels in order to be difficult enough to capture attention but easy enough to keep the participant motivated. Under the assumption that the parameter for auditory strategy (𝛽𝐴) is set to 0 when instructions are given to use the visual strategy and the parameter for visual strategy (𝛽𝑉) is set to 0 when auditory strategy is instructed, within each session, the two parameters are calculated separately using the following formulae:
𝑧 = 𝛽0+ 𝛽𝑉∙ 𝐷𝑉𝑉 (E.3) 𝑧 = 𝛽0+ 𝛽𝐴∙ 𝐷𝑉𝐴 (E.4)
where 𝐷𝑉𝑉 stands for the visual decision variable (the angle difference between the first and second gabor) and 𝐷𝑉𝐴 stands for the auditory decision variable (the difference in frequency between the first and second tone). Using the observed behavioural data, the parameters for visual information are estimated using glmfit function in MATLAB (with a logit distribution due to the binomial distribution of the responses) given the various angle differences of the visual gabors. The beta parameters for auditory information given the frequency differences of the presented sounds is also estimated separately using the same method. These parameters represent weighting of each sensory information for the decision-making process as well as the performance level of perceptual discrimination.
The obtained parameters show that in the visual session, more weight is put on visual information than auditory information in the decision-making process (Figure 1). This is indicated by the significantly higher value of 𝛽𝑉 (M = 1.77, SD = 1.22) compared to 𝛽𝐴 in the visual calibration session for each individual (M = 0.01, SD = 0.26), t(17) = 5.53, p < 0.001. As predicted, the value of the auditory parameter (𝛽𝐴) in the visual session is very close to 0. The opposite results are observed in the auditory calibration session. The value of 𝛽𝑉 (M = 0.24, SD = 0.18) deviates slightly from 0, implying that participants’ choices in the auditory calibration session may have been mildly affected by the visual information. Nonetheless, 𝛽𝐴 was still found to be significantly higher than 𝛽𝑉 for each participant (M = 1.44, SD = 1.07), t(17) = -4.81, p < 0.001.
Figure 2. (a) Histogram of mean parameter values of the calibration sessions choice behaviour pattern during the calibration sessions (b). The top graphs show parameters obtained from the visual calibration session and the lower graphs show parameters
obtained from the auditory calibration session. The histograms show mean values of the weighting parameters for both visual and auditory strategies in visual and auditory sessions. Higher values indicate more weighting of the decision variable during the
decision-making process. | (b) Choice behaviour patterns for visual and auditory stimuli in visual and auditory calibration sessions. The graph shows the certainty of choosing left (approaching 1; counter-clockwise shift or descending frequency) over choosing right (approaching 0; clockwise shift or ascending frequency). Black data points represent the observed behaviour data averaged over participants. Red lines show the modeled choice behaviour at various angle differences (visual session). Blue lines
show the predicted choice behaviour at various differences in frequency (auditory session).
Using the obtained parameters, choice behaviour patterns of visual strategy and auditory strategy are generated with the logistic function approach and compared. In sessions where the strategy is instructed, the observed data points appear to form a more sigmoidal curve than the horizontal graph in sessions where the strategy was not instructed. In the calibration sessions where the strategy was not instructed, the probability of choice did not seem to deviate far from chance. The levelled blue line representing the probability of choice given the auditory information in the visual calibration session shows that with various frequency differences, the probability of choice did not change but remained in a stable range. The probability of choice given the visual information in the auditory calibration session was also probabilistic, however a mild slope is observed in the curve. This confirms the observation based on the parameter values that visual information was assigned a small weight in the auditory decision-making process; it is possible that participants’ may have made decisions based on visual data on several trials although instructed to focus on the auditory information. The auditory discrimination performance in the auditory calibration session however and seemed to be unaffected and still followed a logistic-curve shape.
Task
Similar to the calibration session, the participant makes decisions based on either visual or auditory information in the main task. The main task is divided into 10 blocks consisting of 5 blocks of each task type (visual instructed or auditory instructed) in an alternating pattern. At each block, task performance is reassessed and new function parameters are generated. The new parameters will then be used to determine new values of adapt the task difficulty of the following block. This accounts for the possibility of learning although answer feedback is not given to the participant.
To prove the concept of using strategy modeling to identify the strategies individuals use, out-of-sample predictions are made for each individual. The likelihood of using a visual strategy is calculated using the parameters of the previous visual session meanwhile the likelihood of using an auditory strategy is calculated using parameters generated from the previous auditory session. The obtained results show that participants
were able to follow the instructions to switch strategies and this was revealed through analysis of the strategy likelihood over time. Figure 3a shows the strategy likelihood over time for one participant (averaged per 8 trials). At most time points, the visual strategy likelihood indicated by the red line is higher than the auditory strategy likelihood in sessions where the visual strategy was instructed (odd-numbered sessions). Oppositely, the likelihood of using the auditory strategy tends to be higher than the visual strategy in sessions where the auditory strategy was instructed (even-numbered sessions).The pattern is visibly more prominent in analysis of the trial-by-trial average likelihood of using strategies over time (Figure 3b).
(a)
(b)
Figure 4. Time series of strategy likelihood of one participant (a) and of the average of all participants (b). Red lines represent the likelihood of the observation given the visual strategy and blue lines represent the likelihood of the observed data given the auditory strategy. Vertical black lines mark switches in instructed strategy between visual and auditory strategies, starting with the
first time period being the visual strategy. Estimation of strategy likelihood using computational modeling
Analysis of the average likelihood over all sessions and participants show that as predicted, when participants were instructed to make choices based on a certain strategy, the likelihood of the instructed strategy is indeed higher than the likelihood of the uninstructed strategy (Figure 3). In blocks where visual information is utilized, the likelihood that the visual strategy was used (M = 0.58, SD = 0.06) is higher than the likelihood that the auditory strategy was used (M = 0.50, SD = 0.01), t(17) = 5.33, p < 0.001. Conversely, when auditory information is used to make decisions, the likelihood of using the auditory strategy (M = 0.63, SD = 0.04) is higher than the likelihood of using the visual strategy (M = 0.51, SD = 0.02), t(17) = -9.80, p < 0.001. These results ultimately provide evidence that strategies with known models can be used to make predictions of subsequent data and estimate the strategy being used for the decision-making process.
Figure 3. Histogram of averaged likelihood of observing the choice data given the strategies (visual and auditory) in the visual and auditory blocks. The connected white dots represent the likelihood of the visual and auditory strategy for each participant, averaged over five sessions for the visual block and auditory block each. Most participants show a trend of having a higher likelihood of observing the data when the instructed sensory strategy is congruent with the sensory session (visual strategy in visual sessions; auditory strategy in auditory sessions) compared to incongruent combinations (visual strategy in auditory session;
auditory strategy in visual session), showing that strategies can indeed be identified through modeling of choice behaviour.
Discussion
Results of the study has shown that strategy likelihood estimation can be used to distinguish a visual decision-making strategy from an auditory strategy, although with instructed decision-making behaviour, the observed results are highly expected. Considering the within-subject design of the experiment, the significant result also supports the idea that this concept could potentially be applied to identify strategy-switches at the individual level. However, it is important to consider that this study is a very early step towards establishing computational priors as tools to detect strategy changes and further research is still required. The limitations of this method also need to be recognized before considering transferability of the concept to strategy-detection in economic decision-making.
First of all, in the current study, strategy-changes were manipulated to occur at a single point in time, instead of gradually over time (Barraclough, Conroy, & Lee, 2004). Changes of strategy were explicitly instructed to the participant by a word displayed on the screen. This resulted in sharp transitions from the visual strategy to the auditory strategy and vice versa, giving clear boundaries of data inclusion and exclusion for analysis of the likelihood that a certain strategy was used. However, the gradual strategy change which would likely occur in economic decision-making experiments will give no definitive cut-off boundary for strategy likelihood analysis. The challenge is therefore to identify the beginning and end of the time range during which the decision-making strategy gradually changes. This study has found that strategies can be identified using different parameters of the same function, rendering a possibility that the change in strategy could be reflected by gradual changes in the values of these parameters with increasing amounts of data included in the calculation. For example, strategy likelihood analysis using the first 150 trials may result in a lower beta value for expected value (the product of value and probability (Bernoulli, 1954)) compared to analysis using only the first 100 trials, possibly indicating that the weighting of expected value in the decision-making process has started to decrease somewhere in between the two time points. However, to see the changing trend in parameter values, the strategy likelihood will need to be recalculated with every added trial. Not only will this method need to be tested for validity, it is also inefficient. Furthermore, more research will be
required to determine the definite magnitude of value increase or decrease for a change to be identified as the beginning or end of a strategy-switch.
Secondly, the functions describing the different strategies in investigation must already be known prior to detection of strategy switches. The current study identifies which strategy was used in each session through comparison and not based on characteristics unique to that certain strategy. The concept therefore can only be used to identify which strategy was used, but not to define what strategy was used. The computational framework adopted in this study illustrates the decision-making process as a function operation in the brain. For this experiment, the function representing the perceptual decision-making process was predicted based on previous research and theories (Fox & Poldrack, 2009; Philiastides & Sajda, 2006; Wichmann & Hill, 2001) and previously tested for validity in pilot studies. As also seen the calibration session results, the participants’ behaviour indeed follows a sigmoidal logistic curve when the stimuli variable (e.g. gabor angle) is congruent with the calibration session (e.g. visual session). In this study, one function was able to represent two strategies; each was differentiated from the other by a different set of parameters. Similar to the perceptual task in the current study, economic decision-making strategies could also possibly be represented by a single function, considering that the expected-value and heuristic decision-making strategies involve the same variables, differing only in the way that the information is combined, indicated by different weights that are assigned to each variable. However, there is a wide range of possible computational models to represent economic decision-making. Pilot studies of applying the method in this study to economic decision-making has shown that the same logistic function can represent economic decision-making involving three variables: value, probability, and expected value. The drift diffusion model (DDM) in particular has succeeded in modelling choice behaviour in simple value-based decision-making (Krajbich, Lu, Camerer, & Rangel, 2012), making it a suitable candidate to describe economic decision-making strategies. Tests for goodness of fit will be necessary in order to investigate the most suitable computational model to represent the economic decision-making strategy in question while keeping in mind that there will be a trade-off between accuracy and simplicity of the function.
Third, the decision variables involved in economic decision-making are not completely separate from each other, unlike the variables in the current study. Visual processing and auditory processing involve disparate sensory organs and brain areas, therefore occurring separately from each other (Kandel et al., 2013). A small effect of visual processing was indeed observed in the auditory calibration session, indicating that some
choices may have been made on the grounds of visual instead of auditory information. This is because vision is more dominant in most individuals than towards other sensory information (Posner, Nissen, &
Klein, 1976). Regardless of this small effect, calculations of strategy likelihood still leaned towards a higher likelihood of the auditory strategy. On the other hand, in economic decision-making, the subjective values of each variable are influenced by one another and cannot be disentangled completely, therefore the contrast between the parameters for each variable may be less profound than observed in this study. Furthermore, each individual may be more sensitive to certain information. As an example, a great number of individuals are risk-aversive whereas others are risk-seekers (Tom et al., 2007). The risk-aversive group may be more sensitive to the probabilities of loss than the value of rewards in economic decision-making compared to the risk-seeking. The computational model will therefore need to accommodate the interactions between variables and also general individual differences.
Last but not least, the predictive power of likelihood calculations could be further strengthened by coupling it with neural measurements during decision-making. For confirmation of function suitability, behaviour can be analysed along with fMRI measurements to observe whether the activity of brain regions known to be involved with decision-making strategies are correlated to changes in the function parameters. For a more practical approach, EEG can be used to measure changes in EEG waves over different areas of the brain involved in processing of economic variables.
In summary, the current study has succeeded in providing a proof-of-concept for detecting strategy-switching in decision-making using computational modelling. However, further research will still be required to achieve the final goal of detecting real-time strategy-switches in economic decision-making. The
likelihood calculation concept could be firstly tested in an instructed-strategy, simple economic decision-making task such as a gambling task involving only gains, probability, and expected value. The perceptual decision-making design of this study could be applied again in early attempts to combine computational data with neurophysiological recordings. The separate processing locations of the sensory modalities in the brain will make it easier to match the strategy function to the corresponding brain area. Although this study is still a very early step towards the final goal, the results have provided positive insight into detection of strategy changes in decision-making.
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