Motor response vigour and visual fixation patterns reflect subjective valuation during intertemporal choice.

Value-based decision-making is of central interest in cognitive neuroscience and psychology, as well as in the context of neuropsychiatric disorders characterised by decision-making impairments. Studies examining (neuro-)computational mechanisms underlying choice behaviour typically focus on participants' decisions. However, there is increasing evidence that option valuation might also be reflected in motor response vigour and eye movements, implicit measures of subjective utility. To examine motor response vigour and visual fixation correlates of option valuation in intertemporal choice, we set up a task where the participants selected an option by pressing a grip force transducer, simultaneously tracking fixation shifts between options. As outlined in our preregistration (https://osf.io/k6jct), we used hierarchical Bayesian parameter estimation to model the choices assuming hyperbolic discounting, compared variants of the softmax and drift diffusion model, and assessed the relationship between response vigour and the estimated model parameters. The behavioural data were best explained by a drift diffusion model specifying a non-linear scaling of the drift rate by the subjective value differences. Replicating previous findings, we found a magnitude effect for temporal discounting, such that higher rewards were discounted less. This magnitude effect was further reflected in motor response vigour, such that stronger forces were exerted in the high vs. the low magnitude condition. Bayesian hierarchical linear regression further revealed higher grip forces, faster response times and a lower number of fixation shifts for trials with higher subjective value differences. An exploratory analysis revealed that subjective value sums across options showed an even more pronounced association with trial-wise grip force amplitudes. Our data suggest that subjective utility or implicit valuation is reflected in motor response vigour and visual fixation patterns during intertemporal choice. Taking into account response vigour might thus provide deeper insight into decision-making, reward valuation and maladaptive changes in these processes, e.g. in the context of neuropsychiatric disorders.

Introduction

Motivation entails the willingness to perform effortful actions in order to obtain rewards. Individuals normally adapt the level of effort expended to the expected utility of a reward. An adequate adjustment of effort to expected utility is crucial to ensure reward receipt, whilst avoiding unnecessary energy expenditure. Whether a reward is worth a given effort depends on its expected (subjective) utilty. The expected utility of a reward does not equal its utility in an absolute sense, but is contingent upon both intraindividual and external factors. For instance, rewards that are temporally more distant are typically devaluated, resulting in a preference for smaller, but sooner rewards, over larger, but later rewards, a process known as temporal discounting [1, 2].

The degree of discounting delayed rewards has been linked to a range of harmful behaviours and psychiatric conditions, including impulsivity, substance abuse and addiction (for a review, see [3]). For instance, individuals suffering from substance use disorders appear to be biased towards choosing immediate compared to delayed, but larger, rewards [4, 5].

Key brain circuits involved in value-based decision-making include the medial prefrontal cortex and striatum. Here, brain activity correlates with subjective value in a variety of tasks, such as valuation of goods and intertemporal choice [6-8]. The devaluation of rewards by both cognitive and physical effort appears to be associated with BOLD activation in mostly overlapping neural structures [9].

It is well established that midbrain dopaminergic neurons play a central role in decision-making and reward processing [10, 11]. Direct evidence for the involvement of dopamine in effort-based decision-making comes from studies in patients with Parkinson’s disease (PD) and from pharmacological studies manipulating dopamine transmission. In patients with PD, effort-based decision-making appears to be disrupted—they have been found to exert less force for rewards compared to healthy controls, and to exert less force when being off compared to on their dopaminergic medication [12, 13]. In turn, pharmacological enhancement of dopamine transmission via levodopa in healthy participants increased the force levels exerted to obtain high vs. low rewards. Following debriefing, none of the participants reported to excert higher forces to obtain high rewards [14], suggesting that the behaviour reflects an implicit motivational process [14].

Pessiglione and colleagues [15] found that participants exert more force to obtain higher rewards even in cases where the rewards have only been presented subliminally. Also, across different social contexts (collaborative and competitive), force production was strongly related to subjective utility, and increased with absolute monetary value [16]. Further, subjective utility in value-based decision-making is reflected in eye movement vigour [17]. For instance, as participants approach their decision, eye movement vigour (i.e. peak velocity of a saccade as a function of amplitude) becomes greater for the preferred reward option, and the difference in eye movement vigour is closely linked to the difference in assigned subjective values of the options [18].

While value-based decision-making is a complex process requiring information integration, value computation and comparison, in most experimental settings, the process of evaluating a reward’s utility is often inferred from the participants’ choices only. However, from the above findings it appears that measures of response vigour may provide additional insights into motivation and value-based decision-making rather than measures of choice behaviour alone. In the present study, we therefore investigated if measures of response vigour, specifically handgrip force applied during choice selection, and visual fixation patterns may serve as implicit measure of outcome utility and decision conflict during intertemporal choice. There are well-established models to describe subjective valuation during intertemporal choice, allowing for a well-grounded modelling of the relationship between response vigour and subjective utility [19-21].

In contrast to the incentive force task used by Pessiglione and colleagues [15, 16], where the force applied was directly related to the payout and visually fed back to the participants, we captured implicit motivational processes by keeping the amount of force produced hidden from the participants and unrelated to the payout. Besides being instrumental in obtaining a reward, the allocation of effort may also be a correlate of the underlying evaluation process. We further included an experimental manipulation known to substantially affect reward valuation during temporal discounting, the magnitude effect [22, 23]. This effect describes the reduction in discount rates that occurs during intertemporal choice for increasing reward amounts, and we explored whether this effect is also reflected in the handgrip response.

Models of value-based decision-making, including temporal discounting, typically implement action selection using the softmax function [24]. We extend this approach by jointly modelling the choices and response times (RTs) with the drift diffusion model (DDM) [25], a form of sequential sampling model for two-alternative forced choice tasks. The drift diffusion model assumes that choices are driven by a noisy accumulation process, which terminates as soon as the level of accumulated evidence has reached one of two response boundaries. The model’s strength lies in the incorporation of both choices and RTs in the model estimation. It has proven to be a useful model in explaining choice behaviour and RTs during value-based decision-making in our and others’ prior work [19, 26–29].

We analysed the relationship between the subjective value differences as derived from the estimated drift diffusion model parameters and the force applied and fixation shifts during response selection. Further, we assessed the relationship between decision conflict, motor response vigour and visual fixation patterns. As outlined in the preregistration of our study (https://osf.io/k6jct), we tested the following hypotheses:

Delay influences reward evaluation: Participants show a tendency to devaluate rewards that are temporally distant (temporal discounting).

Differences in subjective utility modulate response times and grip force: Faster response times and stronger effort (handgrip force) in trials with high subjective value differences.

Decision conflict is reflected in motor response vigour and visual fixation patterns: Longer deliberation (response time), less vigour (grip force) and more frequent fixation shifts between the options during high-conflict decisions (choice options with similar subjective value).

Higher rewards are discounted less and elicit more effort: Lower discount rates, faster response times, and greater motor response vigour (grip force) for larger rewards (between-conditions magnitude effect).

Materials and methods

Ethics statement

The study was approved by the local institutional review board (Ethics Committee of the Medical Faculty of the University of Cologne) and all participants provided informed written consent.

Sample

Based on the effect sizes of previous studies reporting a magnitude effect for temporal discounting and handgrip force, respectively [15, 22, 23], a power analysis yielded a sample size of N = 20 (effect size Cohen’s dz = 1.1698 and dz = -0.7481, respectively, α error probability = .05, power = .95, one-tailed paired t-test). We doubled the sample size and tested 42 participants in total. As two participants had to be excluded due to technical issues, the final sample consisted of N = 40 participants (30 women, 34 right-handed, 39 with German Abitur, 1 with German Mittlere Reife or GCSE), aged 18 to 39 (M = 23.95, SD = 4.90).

The participants were recruited through university bulletins, mailing lists and by word-of-mouth recommendation. Eligibility criteria included normal or corrected-to-normal vision and German as first language (or profound German language skills). Participants with strongly impaired vision, strabismus and psychiatric disorders were excluded.

Task

The study was implemented as one-group, repeated-measures within-subject design, including two conditions. The participants performed 192 trials of an intertemporal choice task, whereby they had to choose between smaller-but-sooner (SS) and larger-but-later (LL) rewards. On one half of the trials, the SS reward was lower (10 €, low condition), and on the other half the SS reward was higher (20 €, high condition). The SS reward was always available immediately, while the LL reward consisted of combinations of sixteen ratios of the SS reward value [1.03 1.05 1.10 1.15 1.20 1.25 1.35 1.45 1.50 1.70 1.90 2.20 2.50 2.90 3.30 3.80] and six delay periods in days [1 7 13 31 58 122]. The order of the trials and the assignment of the options to the left and right side of the screen were presented in randomised order. The participants were financially reimbursed for participation and additionally received the payout from one randomly selected trial (restricted to maximum 40 €).

Experimental setup

The measurements took place at the Psychology Department of the University of Cologne. During testing, the participants were seated in a dimly lit, electrically and acoustically shielded room, with their head placed in a chinrest. Prior to the experiment, they were instructed to press the handgrip with maximal force three times in succession with their dominant hand. The procedure was disguised as calibration procedure. Following that, the participants were instructed that the level of force exerted is irrelevant to the task structure.

After presenting both options, one of the two options could be preselected through visual fixation. For this purpose, we used an eyetracking system (SensoMotoric Instruments, Model: RED 500, sampling rate: 500 Hz) to track the fixation patterns and highlight the currently fixated reward option in real-time. For highlighting the fixated option, the corresponding screen areas were defined as follows: Left area screen pixels of x-coordinate x 4, middle area screen pixels of x-coordinate x 4 and screen pixels of x-coordinate x 6, right area screen pixels of x-coordinate x 6.

The responses were logged using a hand dynamometer measuring grip force (BIOPAC Systems, Inc., Model: TSD121C, isometric range: 0–100 kgf). The force threshold to register a choice was set to 0.70 kgf. The threshold was determined in pilot measurements in such a way that false positive signals, caused by holding and slightly moving the force transducer, were avoided, while at the same time ensuring that no effort was required for a response. There was no response time limit. After having preselected an option through visual fixation, participants could still deliberate and decide for the other option as long as the force transducer had not been pressed. The measured variables included the participants’ choices, response times, fixation shift patterns and handgrip force applied during response selection, as well as their maximum handgrip force.

Data analyses

Preprocessing

All logfiles were checked for stereotypic response patterns (exclusively SS or LL choices), none were found. Choice patterns consisting of exclusively SS or LL choices may indicate that the participants proceeded heuristically rather than including values and delay periods in their reasoning. Valid response times are physiologically limited to a lower bound of around 100 to 200 ms [30, 31]. Since even implausibly fast outlier trials must be assigned a probability density > 0, modelled response time distributions for a given participant are shifted towards zero as much as required to accommodate for such response times. This may lead to poor model fits at the level of individual participants, and consequently may also impact on the fits of hierarchical models. Therefore, we excluded trials with response times below 200 ms. Further, we excluded trials with response times > 10 s. The participants were instructed that there was no time pressure for the decision, but that they should decide according to their gut feeling and not think long about the decision. Since the task was comparatively simple, long reaction times likely reflect a lack of attention rather than the process of interest. Finally, we excluded trials with maximum grip force values falling below the threshold for logging a response (technical issue with faulty signal on parallel port). In total, 139 trials (1.81% of trials) from 26 participants were excluded. The grip force data were further baseline-corrected to zero, normalised to each participant’s maximal voluntary contraction (MVC, greatest force exerted over three contractions), and smoothed with a moving average of 50 samples.

Computational modelling of behaviour

Temporal discounting model. Ensuing from previous research on the effects of immediacy vs. delay on choice behaviour, we assume temporal discounting to be hyperbolic [32, 33]. We quantified the discount rates using a model-based approach of hyperbolic discounting. To capture the choice behaviour in both conditions within a single model, we fitted a single subject-specific discount rate parameter k (estimated in logarithmic space), modelling the discount rate in the low condition, plus a subject-specific parameter s, modelling the change in the discount rate from the low compared to the high condition.

Here, SV is the subjective (discounted) value of the delayed reward and A is the amount of the LL reward on trial t. K is the (subject-specific) discount rate for the low condition (in logarithmic space), s is a (subject-specific) shift in log(k) from the low to high condition, I is a condition indicator variable (zero for low trials, one for high trials), and IRI is the inter-reward-interval.

Softmax choice rule. The softmax action selection rule is a commonly used choice rule for value-based decision making and reinforcement learning, applied in our own and others’ previous work [24, 34, 35]. Here we applied this model as a baseline or reference model. The softmax choice rule models the probability of choosing the LL reward on trial t as

SV is the subjective value of the LL option, and β is an inverse temperature parameter, describing the stochasticity of the choices (for β = 0 the choices are random, while as β increases, the choices become increasingly dependent on the values of the options).

Drift diffusion model. We further modelled the participants’ choices using the drift diffusion model (DDM), whereby the softmax choice rule is replaced by the drift diffusion choice rule. For the boundary definitions of the DDM, we applied stimulus coding, with the lower boundary defined as choosing the SS reward, and the upper boundary defined as choosing the LL reward. For this purpose, choices towards the lower boundary were multiplied by -1. When using absolute RT cut-offs, single fast trials force model parameters to adapt these trials und hence lead to a poor model fit at the single-subject level [19]. We therefore excluded each participant’s slowest and fastest 2.5% trials from the analysis. The response time on trial t is distributed following the Wiener first passage time (WFPT):

The parameter α reflects the boundary separation (modelling a speed-accuracy trade-off), τ is the non-decision time (modelling processing time unrelated to the decision process), υ is the drift rate (modelling the rate of evidence accumulation), and z is the starting-point bias (modelling a bias towards one of the boundaries). Using the JAGS Wiener module [36], z may range between 0 and 1, whereby z = .5 indicates no bias in either direction, z < .05 indicates a bias towards the lower boundary (SS option), and z > .05 indicates a bias towards the upper boundary (LL option). First, we fitted a null model (DDM0) without value modulation. This model comprises four parameters (α, τ, z, and υ), which are constant across trials for each participant. To connect the drift diffusion model with the valuation model (see Eq 1), we implemented two further models comprising a function which links the trial-by-trial variability in the drift rate υ to the value differences. First, we realised a linear model (DDMlin), following Pedersen, Frank, and Biele [37]:

The parameter υ maps the value differences onto the drift rate υ and transforms these differences to the proper scale of the DDM [37]. As a last step, we implemented a sigmoid model (DDMsig), entailing a non-linear transformation of the scaled value differences with an S-shaped function as proposed by Fontanesi, Gluth, Spektor, and Rieskamp [26], where S is a sigmoid function centred at zero with slope m and asymptote ± υ:

Ensuing from this model, we also realised a shift model (DDMshift), including the parameters s, s, s, s, , and to model changes in the parameter distributions from the low to high condition:

Since the drift rate depends on the absolute magnitudes of the values, which, in turn differ between the low and high condition, condition effects are somewhat difficult to interpret. Extending the modelling as set out in the preregistration plan, we therefore further compared the drift diffusion models using absolute vs. normalised values (normalised by the maximum value of the LL reward per magnitude condition).

Decision conflict. To assess the hypothesised relationship between decision conflict, motor response vigour and visual fixation patterns, we considered two different operationalisations of decision conflict, based on (i) the choice probability from the softmax choice rule and (ii) the trial-wise drift rate as derived from the DDM. For decision conflict based on the softmax model, we defined decision conflict from 1 (low conflict) to 5 (high conflict), with a probability of 0.5 of choosing the LL reward as maximum conflict. To provide a common scaling from low to high conflict, probabilities > 0.5 were ‘flipped’ (1 − p), implying that for instance a probability of 0.1 and 0.9, respectively, of choosing the LL reward represent an equally low decision conflict (choose SS with high probability, and choose LL with high probability, respectively). The data were grouped into five bins using MATLAB’s discretize and accumarray function (choice probabilities between 0 and 0.1 assigned to bin 1, choice probabilities between 0.4 and 0.5 assigned to bin 5, etc.).

Further, extending our planned analyses, we assessed the relationship between motor response vigour, visual fixation patterns and the subjective value differences and sums, respectively, based on the estimated parameters of the drift diffusion model (using absolute subjective values).

Motor response vigour and fixation shifts

Motor response vigour (grip response). To examine the relationship between the characteristics of the handgrip response and the choice behaviour and estimated model parameters (subjective value differences, choice probabilities and decision conflict), we modelled the handgrip response on individual trials with a Gaussian function of the form using MATLAB’s fit function, where the coefficient a is the amplitude (height of peak), b the centroid (centre of peak), c the width (width of peak) and h is a constant (to model offsets from zero). The handgrip data were fitted trial-wise per participant. To test for a magnitude effect in the grip force response, we used frequentist significance tests (one-tailed for amplitude and centroid, see section Introduction, hypothesis iv, significance threshold set at .05, not corrected for multiple comparisons).

Fixation shifts. Using the eye tracking data, we assessed the relationship between the frequency of fixation shifts between the choice options and the associated decision conflict (see section Decision conflict). We defined fixation shifts as the number of switches between the left and right option (skipping middle fixations, see section Task).

Effects of conflict, value difference and value sum

To assess the effects of conflict, we regressed motor response vigour (single-trial Gaussian grip force model parameters) and the number of fixation shifts onto the response conflict measures. We fitted a hierarchical Bayesian linear regression of the form where y is the conflict on trial t, operationalised either (1) based on the choice probabilities from the softmax model (see section Decision conflict), (2) as the trial-wise drift rate, based on the estimated parameters of the best fitting drift diffusion model, or (3) as the value difference between the (discounted) LL and SS reward on trial t, based on the estimated subject-specific k parameters of the DDM (see Eq 1).

Since we observed no relationship between motor response vigour, number of fixation shifts and conflict, neither for choice probability (softmax model) nor trial-wise drift rate (DDM), we extended our analyses plan and also regressed motor response vigour and number of fixation shifts on the (absolute) subjective value differences. We reasoned that this might be attributable to the fact that both predictors are insensitive to increasingly higher value differences: in the softmax model, these are mapped to a conflict of 0, whereas in the DDM these are mapped to a maximum drift rate of v. As we observed a magnitude effect for grip force amplitude, we carried out a further exploratory analysis to test whether the total value (sum across options) would likewise show an association with response vigour. To this end, we regressed grip force and the number of fixation shifts onto the sum of the LL and SS option amounts (see Section 5 and Fig F in S1 Text of the supplementary material) and onto the sum of the subjective LL and SS option values, based on the discount rates estimated from the drift diffusion model. These models were not preregistered.

The estimated grip force parameters a, b, and c, and the number of fixation shifts were within-subjects z-standardised before entering the regression. The parameter d corresponds to the absolute number of fixation shifts between the options. Since we excluded each participant’s slowest and fastest 2.5% of trials within the scope of the drift diffusion model (see section Drift diffusion model), the respective trials were likewise removed from the grip force and gaze data.

We report Bayes factors (BFs) for directional effects [38] for the β—hyperparameters, via kernel density estimation in MATLAB (The MathWorks, Inc., version R2019a). The Bayes factors are defined as the ratio of the integral of the posterior distribution from—∞ to 0 versus the integral from 0 to ∞. We consider BFs between 1 and 3 as anecdotal evidence, BFs between 3 and 10 as moderate evidence, BFs between 10 and 30 as strong evidence, BFs between 30 and 100 as very strong evidence, and BFs above 100 as extreme evidence for the H1. The inverse of these values reflect the corresponding evidence for the H0 [39, 40]. We further report the posterior highest density intervals (HDI) along with the regions of practical equivalence (ROPE, limits for β = ±0.05 as for standardised variables) [41] for the posterior distributions of the regression coefficients.

Parameter estimation and model comparison

The parameter distributions of the softmax, drift diffusion and regression models were estimated through Markov chain Monte Carlo (MCMC) simulation as implemented in JAGS [42, version 4.3.0], using MATLAB (The MathWorks, Inc., version R2019a) and the MATJAGS inferface for JAGS (Steyvers, 2018, version 1.3.2). We implemented a hierarchical Bayesian framework, in which the parameters for each subject are drawn from group-level gaussian distributions. We ran two chains with a burn-in period of 50,000 samples and thinning of two. We determined chain convergence of the chains such that [43]. For comparing the variants of the drift diffusion models, we ranked them according to the deviance information criterion [44, DIC].

Posterior predictive response time distributions

To ensure that the best-fitting model reflects and reproduces the observed data, we simulated 10,000 datasets based on the posterior distributions of the respective hierarchical model. For each individual participant, the model-predicted RT distributions were smoothed with a kernel smoothing function using density estimation (using MATLAB’s ksdensity function) and overlaid onto the observed RT distributions.

Results

Model-free analyses

The participants made significantly more LL selections in the high (M = 63.00, SD = 19.28) as compared to the low (M = 53.30, SD = 21.09) magnitude condition (t(39) = -10.12, p < .001, one-tailed), reflecting the predicted magnitude effect. However, such a magnitude effect was not present in the response time patterns. The mean RTs were not significantly different between the low (M = 3.03, SD = 0.69) and high (M = 3.03, SD = 0.67) condition (t(39) = -0.01, p = .498, one-tailed).

Softmax choice rule

We modelled the choices using the softmax choice rule, using both the absolute and normalised reward values. As hypothesised, we found a magnitude effect for temporal discounting, indicated by the negative shift parameter s, which models the change in log(k) from the low to the high condition (see Table 1). We observed a close correspondence of the parameter estimates from the softmax model based on absolute vs. normalised values, except for β (see Fig 1), which scales with the value differences (see Eq 2).

Table 1

Group-level mean estimates and 95% HDIs of log(k), slog(k) and β using the softmax choice rule.

	SMabs	SMnorm
log(k)	-4.44 (-5.07 to -3.79)	-4.44 (-5.04 to -3.82)
s log(k)	-0.80 (-0.90 to -0.70)	-0.74 (-0.86 to -0.64)
β	0.43 (0.05 to 0.72)	27.23 (14.80 to 38.54)

HDI: highest density interval; SMabs: softmax model using absolute values; SMnorm: softmax model using normalised values; log(k): discount rate (in logarithmic space); slog(k): shift parameter for the changes in log(k) value from the low to high magnitude condition; β: inverse temperature parameter.

Fig 1

Posterior distributions of the group-level parameter means from the softmax models based on absolute (SMabs) and normalised (SMnorm) values.

log(k): discounting parameter, s: shift in log(k), β: inverse temperature parameter. Horizontal solid lines indicate the 85% and 95% highest density interval.

Drift diffusion modelling

Model comparison

We compared the fit of different variants of the DDM, including models with a linear (DDMlin) and non-linear scaling (DDMsig, and DDMsig-shift) of the drift rate by the subjective value differences, and a model including parameters to model changes in the parameter distributions from the low to high condition (DDMsig-shift). As a baseline comparison, we formulated a model comprising no value modulation (constant drift rate, DDM0). Further, we assessed the fit of all models using absolute vs. normalised values (see section Computational modelling of behaviour). The models implementing a non-linear scaling of the drift rate provided a superior fit to the data compared to models with a linear scaling. This was true for models operating on absolute and normalised values. Also, both the linear and non-linear models provided a superior fit compared to the DDM0, see Tables 2 and 3.

Table 2

Model comparison of the variants of the drift diffusion models of temporal discounting using absolute values.

	Value scaling	Value function	DIC	Rank
DDM0	-	-	26830	4
DDMlin	Linear	Hyperbolic	24769	3
DDMsig	Sigmoid	Hyperbolic	22213	2
DDMsig-shift	Sigmoid	Hyperbolic + shift	22179	1

DIC = deviance information criterion; 0: no value scaling of the drift rate; lin: linear value scaling of the drift rate; sig: sigmoid value scaling of the drift rate. The DDMsig-shift includes additional shift parameters for α, τ, z, υ, υ, and υ to models changes from the low to high condition.

Table 3

Model comparison of the variants of the drift diffusion models of temporal discounting using normalised values.

	Value scaling	Value function	DIC	Rank
DDM0	-	-	26830	4
DDMlin	Linear	Hyperbolic	24286	3
DDMsig	Sigmoid	Hyperbolic	22210	2
DDMsig-shift	Sigmoid	Hyperbolic + shift	22170	1

DIC = deviance information criterion; 0: no value scaling of the drift rate; lin: linear value scaling of the drift rate; sig: sigmoid value scaling of the drift rate. The DDMsig-shift includes additional shift parameters for α, τ, z, υ, υ, and υ to models changes from the low to high condition.

Comparing the models based on absolute vs. normalised values, we observed a good correspondence of all model parameters, with the exception of v and , which of course scale directly with value differences.

To verify that the best-fitting model can reproduce the observed RT distributions, we examined the posterior predictive RT distributions per participan. The posterior predictive RT distributions of the DDMsig-shift (using normalised values), along with the observed response time distributions, are depicted in Fig 2 (see Fig A in S1 Text of the supplementary material for the posterior predictive response time distributions of the DDMsig-shift using absolute values). The comparison showed that the model captures the characteristics of the response time distributions well.

Fig 2

Posterior predictive response time distributions (in blue) of the DDMsig-shift (using normalised values) for each participant, overlaid on the histograms of the observed RT distributions.

The negative response times arise from the boundary definitions of the DDM. We defined the lower boundary as choosing the SS reward, and the upper boundary as choosing the LL reward. For this purpose, choices towards the lower boundary were multiplied by -1. Negative response times indicate SS choices, positive response times indicate LL choices.

Analysis of model parameters

We observed a positive association between the value differences and trial-wise drift rates, as indicated by the consistently positive drift rate coefficient parameter v (see Tables 4 and 5).

Table 4

Parameter group means and 95% HDIs of the posterior distributions of the drift diffusion models using absolute values.

	DDM0	DDMlin	DDMsig	DDMsig-shift
α	2.72 (2.59 to 2.86)	2.90 (2.76 to 3.04)	3.27 (3.09 to 3.43)	3.23 (3.05 to 3.41)
s α	-	-	-	0.09 (-0.01 to 0.19)
τ	1.30 (1.22 to 1.39)	1.30 (1.23 to 1.39)	1.23 (1.15 to 1.31)	1.23 (1.15 to 1.31)
s τ	-	-	-	0.01 (-0.01 to 0.04)
z	0.53 (0.52 to 0.55)	0.53 (0.51 to 0.56)	0.51 (0.49 to 0.52)	0.50 (0.49 to 0.52)
s z	-	-	-	0.02 (0.00 to 0.03)
υ	0.18 (0.04 to 0.31)	-	-	-
υ coeff	-	0.05 (0.04 to 0.05)	0.77 (0.61 to 0.94)	0.78 (0.62 to 0.95)
s_υ_coeff	-	-	-	-0.08 (-0.17 to 0.01)
υ max	-	-	1.07 (0.98 to 1.16)	1.10 (1.01 to 1.19)
s_υ_max	-	-	-	-0.04 (-0.11 to 0.03)
log(k)	-	-4.42 (-5.08 to -3.78)	-4.45 (-5.07 to -3.83)	-4.47 (-5.07 to -3.85)
s log(k)	-	-0.52 (-0.71 to -0.34)	-0.82 (-0.93 to -0.71)	-0.77 (-0.89 to -0.65)

HDI: highest density interval; 0: no value scaling of the drift rate; lin: linear value scaling of the drift rate; sig: sigmoid value scaling of the drift rate; α: boundary separation; τ: non-decision time; z: starting-point bias; υ: drift rate; υ: value difference to drift rate mapping; υ: asymptote for υ; log(k): discount rate (in logarithmic space); s: shift parameter for the changes in parameter value from the low to high magnitude condition.

Table 5

Parameter group means and 95% HDIs of the posterior distributions of the drift diffusion models using normalised values.

	DDM0	DDMlin	DDMsig	DDMsig-shift
α	2.72 (2.59 to 2.86)	2.95 (2.81 to 3.09)	3.27 (3.10 to 3.45)	3.24 (3.05 to 3.41)
s α	-	-	-	0.07 (-0.03 to 0.18)
τ	1.30 (1.22 to 1.39)	1.30 (1.22 to 1.38)	1.23 (1.15 to 1.31)	1.23 (1.15 to 1.31)
s τ	-	-	-	0.02 (-0.01 to 0.04)
z	0.53 (0.52 to 0.55)	0.53 (0.51 to 0.56)	0.51 (0.50 to 0.52)	0.50 (0.49 to 0.52)
s z	-	-	-	0.02 (0.00 to 0.03)
υ	0.18 (0.04 to 0.31)	-	-	-
υ coeff	-	3.00 (2.68 to 3.32)	39.44 (31.68 to 47.92)	38.11 (30.11 to 46.90)
s_υ_coeff	-	-	-	2.58 (-0.24 to 4.40)
υ max	-	-	1.07 (0.99 to 1.16)	1.05 (0.96 to 1.14)
s_υ_max	-	-	-	0.04 (-0.02 to 0.10)
log(k)	-	-4.19 (-4.78 to -3.60)	-4.48 (-5.13 to -3.87)	-4.49 (-5.14 to -3.88)
s log(k)	-	-0.75 (-0.90 to -0.60)	-0.79 (-0.92 to -0.68)	-0.76 (-0.89 to -0.64)

HDI: highest density interval; 0: no value scaling of the drift rate; lin: linear value scaling of the drift rate; sig: sigmoid value scaling of the drift rate; α: boundary separation; τ: non-decision time; z: starting-point bias; υ: drift rate; υ: value difference to drift rate mapping; υ: asymptote for υ; log(k): discount rate (in logarithmic space); s: shift parameter for the changes in parameter value from the low to high magnitude condition.

Magnitude effects on model parameters. For all models with value modulation of the drift rate, we observed an effect of reward magnitude on s (see Table 4), reflecting reduced discounting in the high compared to the low magnitude condition. This was also true for the models operating on normalised values (see Table 5). The starting point parameter z was close to 0.5, indicating no strong bias towards either decision boundary, (SS rewards), with a rather small shift towards the upper boundary in the high magnitude condition. The effects of reward magnitude on the other parameters were negligible.

Effects of value normalisation. Comparing the models based on absolute vs. normalised values, we observed a good correspondence of all model parameters, with the exception of v and , which of course scale directly with value differences.

Motor response vigour (grip force)

The time between visual preselection of an option and choice registration with the grip force transducer was on average 0.03 seconds (SD = 0.11). The grip force responses were modelled with a Gaussian function (see Fig 3, 1 term plus constant, mean (range) goodness-of-fit across all trials and participants: R-squared = 0.98 (0.29–1.00), adjusted R-squared = 0.98 (0.29–1.00), root-mean-square error = 0.004 (0.0002–0.16). The parameter means (amplitude, centroid and width) per condition (low, high) are listed in Table 6, for mean values per participant and condition, and within-subject differences see Figs B and C in S1 Text of the supplementary material.

Fig 3

Grip response and grip response model of three trials from a single participant.

The grip responses were modelled with a Gaussian function with parameters for amplitude, centroid, width, and a constant. A: trial 14, b: trial 152, c: trial 180. R-squared = 0.983, 0.998 and 0.997, respectively. Blue: preprocessed (baseline-corrected, normalised to maximal voluntary contraction [MVC], and smoothed) grip response data, black: modelled grip response. The unit of the x-axis and centroid parameter has been converted to seconds (sampling frequency: 2000 Hz, 1 s = 2000 samples).

Table 6

Parameters of the gaussian-modelled grip force responses (means and standard deviations).

	Low condition	High condition
Amplitude	0.2142 (0.1414)	0.2179 (0.1448)
Centroid	3.15 (1.54)	3.15 (1.52)
Width	0.13 (0.05)	0.13 (0.05)

Amplitude has been normalised to MVC (maximal voluntary contraction). Centroid and width are reported in seconds.

Since the data were non-normal (as assessed with Lilliefors tests yielding p < .001 for all tests), we performed Wilcoxon signed-rank tests to check for parameter differences between the low and high condition. In line with our preregistered hypothesis, the amplitude was significantly higher for the high compared to the low condition (z = 1.90, p = .029, one-tailed). In contrast to our preregistered hypothesis, the centroid, and also the width, did not differ between conditions (z = 0.73, p = .768, one-tailed, and z = 1.75, p = .081, two-tailed).

Decision conflict effects

Conflict based on choice probability (softmax model). Our first operationalisation of response conflict was based on the softmax choice probabilities. Because condition effects are more straightforward to interpret in the normalised model (see section Softmax choice rule), the following analyses are based on this model. The mean values for amplitude, centroid and number of fixation shifts for trials of a given response conflict (binned from 1 to 5) are depicted participant-wise in Fig 4 and listed in Table 7. The Bayesian regression is based on a continuous conflict measure (probabilities > 0.5 are ‘flipped’ to provide a common scaling from low to high conflict, whereby .5 represents the maximum conflict). The posterior distributions of the group-level parameter means for the regression coefficients are depicted in Fig 5 (medians: α = 0.12 [intercept] β1 = -0.01 [amplitude], β2 = 0.02 [centroid], β3 = -0.004 [width], β4 = 0.001 [N fixation shifts]).

Fig 4

Mean amplitude, centroid and width of the Gaussian-modelled grip force response and mean number of fixation shifts (from SS to LL, and vice versa) for trials of a given (binned) response conflict for each participant.

Thick lines depict the mean values across participants. Conflict is defined from 1 (low conflict) to 5 (high conflict), with a probability of .5 of choosing the LL reward as maximum conflict. Amplitude has been normalised to MVC (maximal voluntary contraction). Centroid and width are reported in seconds.

Table 7

Mean amplitude, centroid, width and number of fixation shifts per conflict bin.

	1	2	3	4	5
Amplitude	0.2188	0.2128	0.2102	0.2135	0.2137
Centroid	2.9427	3.2680	3.2063	3.2789	3.3160
Width	0.1328	0.1340	0.1336	0.1317	0.1330
Fixation shifts	2.79	3.52	3.05	3.17	3.42

Conflict is defined from 1 (low conflict) to 5 (high conflict), with a probability of .5 of choosing the LL reward as maximum conflict. Amplitude has been normalised to MVC (maximal voluntary contraction). Centroid and width are reported in seconds.

Fig 5

Hierarchical Bayesian regression results. Regression of the parameters of the Gaussian-modelled grip force response and number of fixation shifts onto the trial-wise response conflict based on the choice probabilities (softmax model).

Posterior distributions of the group-level parameter means. α: intercept, β1: coefficient for amplitude, β2: coefficient for centroid, β3: coefficient for width, β4: coefficient for fixation shift. Horizontal solid lines indicate the 85% and 95% highest density interval. Vertical solid lines indicate x = 0, and vertical dashed lines indicate the lower and upper bounds of the region of practical equivalence (ROPE).

The Bayes factors for the regression coefficients for amplitude, centroid, and width of the grip response, and for the numbers of fixation shifts provide only anecdotal evidence for values greater than zero vs. smaller than zero (BF for β1: 0.95, BF for β2: 1.25, BF for β3: 0.97, BF for β4: 1.09). Since the 95% HDIs of all the posterior distributions fall neither completely inside nor outside the ROPE, we remain undecided for all three β regression coefficients.

Conflict based on subjective value differences (DDM). The second operationalisation of response conflict was based on the trial-wise drift rate calculated based on the estimated parameters of the highest-ranked DDM using normalised values (DDMsig-shift). Since we found no evidence that any of the regression coefficients for motor response vigour and number of fixation shifts were greater than vs. smaller than zero (or vice versa), we refer the reader to Section 3 and Fig D in S1 Text of the supplementary material.

Finally, we regressed the estimated grip force parameters amplitude, centroid and width, and the number of fixation shifts onto the subjective value differences between the (discounted) LL and SS rewards, based on the subject-specific k parameters of the highest-ranked model using absolute values (DDMsig-shift). Recall that the analysis of the magnitude effect yielded an effect of condition, i.e. higher grip force amplitudes in the high compared to the low condition. Because condition differences in reward magnitudes are eliminated in the DDM based on normalised values (see Section 4 and Fig E in S1 Text of the supplementary material), the regression on subjective value differences is based on the DDM using absolute values.

The mean values for amplitude, centroid and number of fixation shifts for trials of a given value difference bin are depicted participant-wise in Fig 6. The posterior distributions of the group-level parameter means for the regression coefficients are depicted in Fig 7. The medians of the group-level posterior distributions were as follows: α = 3.33 (intercept) β1 = 0.46 (amplitude), β2 = -1.20 (centroid), β3 = 0.19 (width), β4 = -0.48 (N fixation shifts).

Fig 6

Mean amplitude and centroid of the Gaussian-modelled grip force response and mean number of fixation shifts (from SS to LL, and vice versa) for trials of a given value difference bin.

The (absolute) value differences were z-standardised and binned participant-wise into 3 groups of equal size (based on quantile ranks of the values, 1: lower value differences, 3: higher value differences). Thick lines depict the mean values across participants.

Fig 7

Hierarchical Bayesian regression results. Regression of the parameters of the Gaussian-modelled grip force response and number of fixation shifts onto the subjective value differences (DDM).

Posterior distributions of the group-level parameter means. α: intercept, β1: coefficient for grip force amplitude, β2: coefficient for grip force centroid, β3: coefficient for grip force width, β4: coefficient for fixation shift. Horizontal solid lines indicate the 85% and 95% highest density interval. Vertical solid lines indicate x = 0, and vertical dashed lines indicate the lower and upper bounds of the region of practical equivalence (ROPE).

The Bayes factors provide very strong evidence that the coefficient for amplitude is greater than zero vs. smaller than zero (BF for β1: 79.50), extreme evidence that the coefficient for centroid is below zero vs. above zero (BF for β2: > 10308), moderate evidence that the regression coefficient for grip force width is greater than zero vs. smaller than zero (BF for β3: 5.06), and very strong evidence that the coefficient for number of fixation shifts is smaller vs. greater than zero (BF for β4: 69.61). For β3 we remain undecided, since the 95% HDI of the posterior distribution is neither completely inside nor outside the ROPE. For β2 we reject the null value (95% HDI of posterior distribution entirely outside ROPE). For β1 and β4 we also reject the null value, since the 95% HDIs do not include zero and only 0.23% and 1.41%, respectively, of the 95% HDI overlap with the ROPE. This indicates higher grip force amplitudes, faster response times and a lower number of fixation shifts for trials with higher subjective value differences between the options.

Value sum effects

To analyse the association between motor response vigour, fixation shifts and total value, we regressed the parameters of the Gaussian grip force model and the number of fixation shifts onto the sum of the subjective LL and SS option values (based on the drift diffusion model using absolute subjective values). The medians of the group-level posterior distributions were as follows: α = 0.59 (intercept), β1 = 0.62 (amplitude), β2 = -0.47 (centroid), β3 = 0.01 (width), β4 = -1.11 (N fixation shifts) (see Fig 8). The Bayes factor for the regression coefficient for amplitude provides extreme evidence for values greater than zero vs. smaller than zero (BF for β1: 111.18). For the centroid coefficient, the Bayes factor provides strong evidence for values smaller than zero vs. larger than zero (BF for β2: 16.37). For the width coefficient, the Bayes factor provides only anecdotal evidence for values greater than zero vs. smaller than zero (BF for β3: 1.04). The regression coefficient for fixation shifts provides extreme evidence for values smaller than zero vs. larger than zero (BF for β4: 10933.53).

Fig 8

Hierarchical Bayesian regression results. Regression of the parameters of the Gaussian-modelled grip force response and number of fixation shifts onto the total sum of the subjective option values from the drift diffusion model (DDM).

Posterior distributions of the group-level parameter means. α: intercept, β1: coefficient for grip force amplitude, β2: coefficient for grip force centroid, β3: coefficient for grip force width, β4: coefficient for fixation shift. Horizontal solid lines indicate the 85% and 95% highest density interval. Vertical solid lines indicate x = 0, and vertical dashed lines indicate the lower and upper bounds of the region of practical equivalence (ROPE).

For β1 and β4 we reject the null value (95% HDI of posterior distribution entirely outside ROPE). For β2 and β3 we remain undecided, since the 95% HDI of the posterior distribution is neither completely inside nor outside the ROPE. Accordingly, this analysis shows higher grip force amplitudes and fewer fixation shifts for trials with high value sums across the options. Running separate regressions on value sums of the low and high magnitude condition revealed that this effect was driven by the high magnitude condition (see Section 6, Figs G and H in S1 Text of the supplementary material).

Discussion

We explored whether value computation and response conflicts during intertemporal choice are reflected in motor response vigour and visual fixation patterns. For this purpose, we measured the handgrip force applied during choice, and the concurrent fixation shift patterns between the choice options. Assuming hyperbolic discounting, we compared variants of the softmax and drift diffusion model and assessed the relationship between the estimated model parameters, motor response vigour and fixation shifts. The intertemporal choice task comprised two conditions, a low and high magnitude condition (low vs. high SS reward), which allowed us to directly assess the impact of overall smaller vs. larger reward magnitudes on response vigour. To represent both conditions in a single model, we included shift parameters to model the changes in parameter values from the low to the high magnitude condition.

We compared models with a linear and non-linear (sigmoid) modulation of the drift rate by the subjective value differences, and, since the drift rate parameter is dependent on the absolute magnitude of the options’ values, models using absolute vs. normalised option values. We then analysed the relationship between decision conflict and response vigour, in particular the trial-wise amplitude, centroid and width of the Gaussian-modelled grip force response and the number of fixation shifts between the options. Further, we investigated if the magnitude effect, which describes reduced discounting for higher amounts [22, 23], is also reflected in the grip force strength.

As hypothesised, participants discounted rewards as a function of delay. The choice and response time (RT) data were best accounted for by a DDM including a non-linear modulation of the drift rate by the subjective value differences. As in previous studies, [23, 29], and in accordance with our hypothesis, we found a magnitude effect for temporal discounting, indicating that higher rewards were discounted less. This effect was also evident in motor response vigour: higher forces were applied in the high vs. the low magnitude condition. In addition, trials with higher subjective value differences between the options were associated with higher grip forces, faster response times and a lower number of fixation shifts.

In general, the estimated non-decision times τ were longer than in typical laboratory experimental setups (> 1000 ms) [19, 29]. The non-decision time parameter τ models time that is not related to the decision process, such as stimulus encoding and motor response execution. Our estimated non-decision times were comparable to the estimated non-decision times from a recent study using a VR environment, where the participants logged their responses using VR-compatible controllers, as opposed to simple response keys [45]. This is likely due to the task’s requirement of first preselecting an option through visual fixation before finally selecting it using the hand dynamometer. However, since τ reflects both motor and non-motor components, which of these processes is affected cannot be inferred from τ alone. There is preliminary work on the decomposition of the non-decision time of drift diffusion models using electro-myographical activity [46]. The authors conclude that stimulus encoding does not necessarily end when evidence accumulation begins, and that the onset of the motor response does not necessarily denote the end of the deliberation process. Further, the non-decision time may be influenced by participants’ adjustments in response to task instructions. Therefore, a meaningful comparison of non-decision times across experiments with different response schemes may only be made if all other experimental parameters are kept constant. Still, applying the DDM works well in settings with different task demands and response modes.

Model comparison

The choice and RT data were best accounted for by a drift diffusion model specifying a non-linear mapping between the subjective value differences and trial-wise drift rates. Following the DIC criterion, the variants of the DDMs implementing a transformation of the scaled value differences using a sigmoid function [26] provided a superior fit to the data compared to both the DDM using a linear modulation and the DDM involving no value modulation. We found a close correspondence between the observed response time distributions and the response time distributions simulated using the estimated posterior parameter distributions, demonstrating that the best-fitting model captured the characteristics of the response time distributions reasonably well.

Magnitude effect

Replicating previous findings [22, 23, 29], and in accordance with our hypothesis, we found a magnitude effect for temporal discounting, such that higher rewards were discounted less. While the model-free analysis revealed more LL choices in the high compared to the low magnitude condition, the magnitude effect was further reflected in the log(k) parameter, which was consistently negative in all variants of the softmax and drift diffusion models. Importantly, as predicted, this magnitude effect was also reflected in motor response vigour: Looking at the amplitude parameter of the Gaussian-modelled grip force response, we found that stronger forces were exerted in the high compared to the low magnitude condition. Contrary to our hypothesis, the RTs were not significantly different between the two conditions. The effect of reward magnitude on the discount rate (reduced discounting for higher rewards) appears to be a consistent effect [22, 23, 29], and our data reveal that this effect is reflected in both choice behaviour and motor response vigour (grip force amplitude) during response selection.

Based on this finding, we carried out a further exploratory analysis, replacing subjective value differences with total value. In line with the idea that subjective (rather than objective) option dimensions shape behaviour [7], the associations with amplitude and centroid were more pronounced for the model that used subjective (DDM-based) rather than objective (absolute magnitude) values for the computation of total value (see section Value sum effects and Section 5 and Fig F in S1 Text of the supplementary material). Further, comparing the results for conflict and subjective value differences and total value, respectively, it appears that total value was most strongly associated with grip force amplitude and number of fixation shifts. These effects share some similarity with other modulatory effects of pavlovian cues, such as pavlovian instrumental transfer, where conditioned stimuli affect the vigour with which an action is executed [47, 48]. However, the present effects of value sum on motor response vigour were not instrumental, as grip force was decoupled from outcome.

Decision conflict effects

First, we carried out a model-based analysis of the trial-wise grip force time courses. A gaussian model, decomposing grip force time courses into amplitude, centroid and width parameters for each trial provided an excellent fit to the single-trial grip force trajectories (mean R-squared = .98). We then analysed the relationship between decision conflict, the grip force parameters and fixation shifts, operationalising decision conflict based on the choice probability as derived from the softmax choice rule, and based on the trial-wise drift rate, as derived from the best-fitting DDM. Contrary to our hypothesis, however, we found no relationship between decision conflict and motor response vigour, response times, or fixation shifts. However, regressing motor response vigour and fixation shifts directly on the subjective value differences (based on the estimated parameters of the best-fitting DDM, we found that the amplitude and centroid of the grip response, as well as the number of fixation shifts were significantly related to these. As predicted, grip force amplitudes increased, and response times (centroids) decreased with increasing subjective value differences between options. In addition, the number of fixation shifts decreased with increasing subjective value differences. Looking at the models regressing motor response vigour and fixation shifts onto subjective value differences and value sum, respectively, the negative relationship with the centroid parameter appeared to be most pronounced for value difference. In the model with objective value sum (model-free, see Section 5 and Fig F in S1 Text of the supplementary material) the effect was not visible at all. Hence, the centroid (response time) effect appeared to be relatively specific for response conflict, whereas the grip force amplitude effect was observed in both models, albeit more pronounced for the value sum model.

The null effects for the conflict measure based on the softmax model likely arise because for large value differences, the conflict predictor approaches zero. The second regression was based on the drift diffusion model using a non-linear (sigmoid) scaling of the drift rate by the subjective value differences, so we speculate that the null effects for conflict based on the drift rate arise because the drift rate does not scale linearly with the value differences (as the value difference exceeds an individual threshold, the corresponding drift rate is mapped to v). We therefore assume that the effects we found when regressing motor response vigour and fixation shifts directly on the subjective value differences are driven by trials with large absolute value differences. Taken together, these results suggest that the observed associations between value differences, grip force parameters and fixation patterns are driven by absolute value differences, rather than decision conflict.

This suggests that valuation or implicit motivation could be reflected in these measures. In contrast to Pessiglione and colleagues [15], where the force produced was related to the payout (reward height magnitude was presented subliminally), we kept the force produced unrelated to the payout. Therefore, even when the force produced is unrelated to the payout (and the participants are unaware that force production is being measured), it is nonetheless related to the subjective value difference and even more so, the value sum. [49, 50] In the present study, the participants applied more force in trials with higher value differences, and in particular a higher subjective value sum of the options. This suggests that motivational processes are also reflected in motor response vigour.

Summarising the findings with respect to our hypotheses, as expected, participants discounted rewards as a function of delay (hypothesis i). In accordance with our predictions, we further found evidence that differences in subjective utility modulated response times and grip forces, such that response times decreased and grip forces increased with increasing subjective value differences between options (hypothesis ii). Unlike what we thought, we found no relationship between decision conflict and grip force, response time or fixation shifts (hypothesis iii). Yet, in line with our hypothesis, higher rewards were discounted less and elicited stronger effort (magnitude effect). Contrary to our hypothesis, however, the response times were not significantly different between the two magnitude conditions (hypothesis iv).

Dopamine and response vigour

Although dopamine neurotransmission was not measured in the present study, the observed effects might be mediated by dopamine. A number of studies suggest that the anterior cingulate cortex and its dopaminergic pathways are involved in the integration of effort and reward [51-54]. Pharmacological enhancement of dopamine transmission increases the willingness of animals to accept delays and to expend effort to obtain rewards (for a review, see [55]). Three studies with human subjects also reported higher force production in states with augmented dopamine transmission [12-14]. In a rewarded odd-ball discrimination task, Beierholm and colleagues [56] demonstrated that L-DOPA modulated reward-related response vigour (reaction times). The results suggest that the influence of reward rate on response vigour is mediated by dopamine transmission. Further, augmented dopamine transmission increased response vigour (reduced reaction times) in a temporal discounting and reinforcement learning task [29, 57, 58]. In addition to dopamine, noradrenaline is also involved in force production [59] and conflict resolution [60, 61]. However, manipulating noradrenaline levels does not appear to affect reward sensitivity [62].

Relevance

Our results suggest that in addition to choices and response times, measures of response vigour may provide information regarding valuation during intertemporal choice. Other tasks involving subjective evaluation of options may also conceivable. Since several maladaptive behaviours and psychiatric conditions, including impulsivity, substance use disorders and behavioural addictions, have been linked to increased discount rates (see, e.g. [4, 5, 63, 64]), this task is particularly interesting from a clinical perspective.

Using response vigour as an implicit measure of utility may open up the possibility to assess utility in cases where explicit reports are not possible, i.e. in different patient groups. In the area of statistical learning, patients with hippocampal damage show impairments in certain processes when the patients are required to explicitly report regularities or patterns [65, 66]. When testing for implicit knowledge in a motion discrimination task, patients with hippocampus damage showed a similar performance to controls [67]. Experimental approaches such as those employed in the present study might be informative in such patient populations.

Limitations

Finally, there are some limitations to our study. For the present task, it would have been interesting to also include pupillometry and more comprehensive analyses of e.g. saccade reaction times and velocities [17, 68]. Since the usage of a force transducer functions as a single key, some method of preselecting one of two options was necessary. Choice selection was thus implemented such that an option was preselected by visual fixation and selected by subsequently pressing the force transducer. Hence, an option could only be chosen if it was concurrently fixated, which may have restricted the fixation patterns. Therefore, we limited the analyses to the shifts of fixation. Further, since we did not specifically construct isoluminant stimuli, the analysis of pupil dilation would be confounded by differences in luminance between the stimuli and conditions.

Although, based on the literature, an involvement of dopamine in the effects examined here is likely, dopamine neurotransmission was neither measured nor manipulated. Future studies would benefit from examining this in greater detail.

Conclusion

In the present work, we investigated motor response vigour, specifically grip force applied during response selection, and fixation patterns as an implicit measures of subjective utility during intertemporal choice. Comparing variants of the drift diffusion model, we found that the choices and response times were best accounted for by a drift diffusion model that included a non-linear scaling of the drift rate by the subjective value differences. A magnitude effect for temporal discounting was apparent in both choice and motor response vigour, such that higher rewards were discounted less and selected with higher grip force. The magnitude effect was evident not only between conditions, but also in the form of an association between total value (sum of discounted values across conditions) and response vigour. Further, the peak forces (grip force amplitudes), response times (grip force centroids) and the number of fixation shifts were related to the subjective value differences between the options. Normalising the options’ values across conditions eliminated these effects. We conclude that the effects were likely driven by large absolute (discounted) value differences between the options. A further exploratory analysis revealed that the subjective value sum across options showed an even more pronounced association with the trial-wise grip force amplitudes and number of fixation shifts. The force applied was unrelated to the payout and the participants were not informed that force production was measured. Nonetheless, it was related to the subjective value differences between the options, suggesting that valuation or implicit motivation is reflected in motor response vigour. Future studies might explore the extent to which neuropsychiatric disorders associated with impairments in decision-making and effort are likewise associated with changes in such implicit measures of motivation.

Fig A: Posterior predictive response time distributions of the DDMsig-shift (using absolute values) for each participant, overlaid on the histograms of the observed RT distributions. Fig B: Parameters of the modelled grip response (mean values per participant and magnitude condition). Fig C: Within-subject differences of the parameters of the modelled grip response between the low and high magnitude condition. Fig D: Hierarchical Bayesian regression of the parameters of the Gaussian-modelled grip force response and number of fixation shifts onto the trial-wise response conflict based on the drift rate (DDM). Fig E: Hierarchical Bayesian regression of the parameters of the Gaussian-modelled grip force response and number of fixation shifts onto the subjective value differences (DDM). Fig F: Hierarchical Bayesian regression of the parameters of the Gaussian-modelled grip force response and number of fixation shifts onto the total sum of the option amounts (model-free). Fig G: Hierarchical Bayesian regression of the parameters of the Gaussian-modelled grip force response and number of fixation shifts onto the total sum of the subjective option values from the drift diffusion model (DDM) for the low magnitude condition. Fig H: Hierarchical Bayesian regression of the parameters of the Gaussian-modelled grip force response and number of fixation shifts onto the total sum of the subjective option values from the drift diffusion model (DDM) for the high magnitude condition. Section 3: Conflict based on trial-wise drift rate (DDM). Section 4: Conflict based on subjective value differences (DDM using normalised values). Section 5: Sum of larger-later (LL) and smaller-sooner (SS) amounts (model-free). Section 6: Sum of the subjective larger-later (LL) and smaller-sooner (SS) option values (DDM) per magnitude condition.

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14 Dec 2021

Dear Dr. Smith,

Thank you very much for submitting your manuscript "Motor response vigour and fixations reflect subjective preferences during intertemporal choice" for consideration at PLOS Computational Biology.

As with all papers reviewed by the journal, your manuscript was reviewed by members of the editorial board and by several independent reviewers. In light of the reviews (below this email), we would like to invite the resubmission of a significantly-revised version that takes into account the reviewers' comments.

In particular, the authors should pay careful attention to strengthening the analyses that establish the links between visual fixations / grip force, and the two computational variables, as the manuscripts claims hinge on this link. (Note: one of the reviewers' attachment was incomplete; we have attached the complete version IN ADDITION to the incomplete one)

We cannot make any decision about publication until we have seen the revised manuscript and your response to the reviewers' comments. Your revised manuscript is also likely to be sent to reviewers for further evaluation.

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Reviewer's Responses to Questions

Comments to the Authors:

Reviewer #1: Uploaded as as attachment

Reviewer #2: The manuscript reports the results of a pre-registered study that investigated how implicit behavioral measures (gaze fixations and grip force) are affected by the subjective values of options presented during an intertemporal choice task. Of interest, there were links with the overall value of the option pair and the difference between option values.

Among the strengths of the paper is an original choice task in which options are selected by visual fixation and confirmed by pressing a handgrip. Another is the sophistication of the computational analyses and the use of Bayesian techniques for model selection. My global impression however is that the paper lacks focus and fails to identify the main questions of interest. As stated in my summary above, the analyses should target the links between the two implicit measures (visual fixations and grip force) and the two computational variables (value sum and difference). This could be done in a model-free analysis that would be straight and simple. In the current paper, these analyses are buried within tons of computational variants that address no meaningful issue at the conceptual level. For instance, whether the DDM provides a better account of RT when taking as input an affine or a sigmoid transformation of value difference will not change our understanding of how the brain works. My main suggestion would be to streamline the analyses around the questions that might bring some conceptual advance. I understand there is the issue of pre-registration, which constrains the authors to sticking on their first ideas. While I understand the virtue of pre-registration in the context of a replication study (where one wants protection against false positives), I think it is problematic in the context of an exploration study (where one wants protection against false negatives) that examines novel potential effects, as we have here. I would therefore encourage the authors to go beyond their pre-registered analyses (which could be moved in supplementary material) and explore their data in a more systematic approach.

More specific concerns:

1) The introduction does not provide a justification for the design. If the idea is to test the link between response vigor and subjective value, then why using intertemporal choice, and why manipulating reward so as to induce a magnitude effect? It also introduces useless or misleading concepts, such as effort discounting, that are never used later in the paper.

2) Among the four predictions, only the second and third ones (ii and iii) relate to the main question (correlates of value sum and difference). The first prediction, as it is phrased, is trivially false (participants do not always prefer smaller-sooner over larger-later rewards, it obviously depends on rewards and delays). The fourth prediction about the magnitude effect could be reduced to the second (whether value sum affects response vigor). The questions about whether delay and reward magnitude have an influence on choices, which are conflated with predictions (i) and (iv) could be side-tracked as already answered in many previous studies.

3) There are fluctuations in the notion of response vigor, which designates grip force specifically in some instances (such as in the abstract and title) and all non-instrumental measures (including number of fixations) in other instances (such as in the first sentence of the conclusion).

4) I have nothing against using DDM to predict RT, but in the context of this paper it seems like an unnecessary complication. The proxy for confidence (or inverse conflict), i.e. value difference, could be taken directly from the softmax function. Similarly, fitting a response function with 3 parameters to force pulses seems like a good idea, but probably weakens the analyses testing the link between grip force and value-related variables. This is because these correlated parameters compete to explain the same variable in the multiple regression model. I suggest using a model-free measure (like the area under the curve) for a more sensitive and straightforward analysis.

5) The discussion is essentially a reiteration of the results, while it should provide perspectives for the conceptual advances and limitations for the interpretations.

Minor concerns:

1) There are a lot of typos and mistakes throughout the manuscript, which should be checked carefully. For examples:

- Maximum conflict (page 9) should be 0.5 and not .05.

- Right graphs in Fig. 1 (page 12) should be labeled SMnorm and SNabs (and/or colored in grey and black)

- ‘shift’ should be deleted in the depiction of the DDMsig model in Table 2 (page 13)

- There are three parameters in the force response function but only two are reported in Table 7 and reported in Fig. 4 (page 19).

- Two studies are announced in the conclusion paragraph but three references are provided.

2) I would suggest to replace ‘fixations’ by ‘visual fixation pattern’ in the title, which would stand symmetrically to ‘motor response vigor’. Also, these measures did not reflect ‘subjective preferences’, as suggested in the title, but value sum and difference (unsigned). This is critical because some passages seem to suggest that one can know which option is preferred by looking at grip force, while this is clearly not the case.

3) Doubling the number of participants required by the power calculation means that the power calculation was not taken seriously. I agree that for an explorative study, testing a new effect, power calculation is meaningless (because one cannot know the expected effect size). But then providing a power calculation sounds like showing off superficial rigor.

4) The link with dopamine suggested in the discussion is interesting but not the only possibility. For instance, there is a literature relating conflict to noradrenalin (and anterior cingulate cortex) that the authors may want to cite.

5) The application to neuropsychiatric conditions is too far-fetched. Removing it would not undermine the interest of the study, in my opinion. Besides, that effort processing is impaired in Parkinson’s disease makes the grip force measure more problematic, not more relevant.

6) Some details are missing now and then.

- what is the unit for delays? (Presumably, days for the first and months for the last one)?

- What is the force threshold that must be reached to confirm a choice?

- How was conflict binned into 5 levels?

Reviewer #3: In this paper Smith and Peters use an inter temporal choice task to examine how non-voluntary (or non-instrumental) vigor of a motor response can be influenced by subjective estimation of reward options. Several previous studies have shown links between reward processing and vigor of motor responses, with a possible mediator of Dopamine.

Vigor was here measured through grip-force, while eye tracking was used to examine visual fixation.

The two main findings were

1. There is a magnitude effect causing higher rewards to be discounted less, and with higher vigor

2. For easier trials (large subjective value differences between options) had larger vigor, shorter response times, and few shifts in fixation between the options.

Neither of these results are very surprising but the paper is well written, and the methods all seem very solid. The results are interesting, and worth publishing in PLoS Comp Bio.

It would have been interesting if more fine grained results could have been squeezed out of the eye tracking data, but that may be for future work (latency in saccade initiation? pupilometry?).

I don’t have any major comments, but just wanted to raise on potential issue with the model specification.

Twelve parameters (for the largest model) is a lot, making me a bit worried about over-fitting. But as DIC is meant to correct for that, I will take the numbers at face value.

I have some minor comments:

Page 6

“ sixteen percentages of the SS reward value “ are these percentages or ratios?

Are the delay periods really [1 7 13 31 58 12], i.e. 12 as the last? Are these given in seconds? Hours? Days?

“track the gaze patterns and to give real-time feedback to the participant,” what feedback was given? Or was it just to highlight the current fixated reward option

“All logfiles were checked for stereotypic response patterns” should that be non-stereotypic? Maybe rephrase

Incidentally, having a figure showing the experimental setup (even if very simple) could be useful

Page 9

I did not understand how the decision conflict was operationalised as a number from 1 to 5. Please explain

Page 11

The variable d is used for both the grip model and the number of fixation shifts, please change one of them.

Page 12

Figure 1, make clearer that the two right most plots are for the same parameter but different models.

Page 15

Figure 2, I would suggest to make this bigger

Also, are the RTs split by L/R? I.e. why are there negative RTs?

Page 18

Table 6 and Fig 3, why report the centroid in number of samples instead of time?

Also, is there a reason gap force width is not reported here?

For the discussion on Dopamine or future work: The authors may also find Beierholm et al 2013 (https://www.nature.com/articles/npp201348) interesting, showing that Dopamine modulated reward-related vigour in a reaction time task, thus building on the work by Niv et al 2007 (https://link.springer.com/article/10.1007/s00213-006-0502-4).

A few of the references are incomplete, e.g. Moreira & Barbosa, as well as Schultz

Reviewer #4: PCOMBIOL-D-21-02032

This study investigates whether response vigor serves as an additional implicit measure of subjective utility during intertemporal choice. They find that motor response vigor reflects the difference in subjective value between the options and is also includence by the absolute value of the options. Subject grasp earlier and with more force the greater the difference int subjective value between the options and to some extent, the greater the absolute value of the two options.

This is an interesting and novel study. It has been previously shown that relative saccade vigor during deliberation between two options correlates with the difference in subjective value between the options. This study shows that grasp vigor when selecting between two options also correlates with the difference in subjective value. This demonstrates that vigor of multiple effectors (eyes, hand) may simultaneously reflect subjective utility. Overall, I am excited to see these results. However, I have a few comments and suggestions that I believe would strengthen and extend their findings.

General Comments

1. I am not sure why the authors do not simply measure peak grasp force as their main vigor measure. Instead there is a model that is fit to the profiles. I understand that they show there is a good fit between model and data, but It would be helpful if they also performed their same analysis using peak grasp force.

a. The authors could also consider looking at rate of grasp force development and time to required force as additional measures of vigor.

2. I think the magnitude effect on response vigor is quite interesting. As I understand it the magnitude effect suggests that for the two pairs of options with the same relative difference in subjective value, the pair with the greater magnitude will have a greater response vigor. Related to this, I have the following questions:

a. The authors seems to suggest that the magnitude effect on response vigor is in addition to the effect of the difference in subjective value, which is potentially very interesting. However, could the increase in vigor in the high magnitude condition be due to greater relative values differences between options in high magnitude condition compared to the low magnitude condition?

b. If indeed there is a magnitude effect then this could potentially be seen across all trials and not just between conditions. Do the authors see an effect of the total value (sum of both options) on response vigor?

Minor Comments

1. Please provide additional detail about the deliberation phase of the experiment. For example, how much time did the subjects have to indicate their choice?, how much time was allowed to pass between pre-selection and the grasp response?

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Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

Reviewer #4: No: The subjects did not consent this, thus the data is available on a private server.

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Reviewer #1: No

Reviewer #2: No

Reviewer #3: Yes: Ulrik R Beierholm

Reviewer #4: No

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Submitted filename: PLOS_Comp_Bio_review_11252021.docx

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10 Feb 2022

Submitted filename: Response_to_reviewers.pdf

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8 Mar 2022

Dear Dr. Smith,

Thank you very much for submitting your manuscript "Motor response vigour and visual fixation patterns reflect subjective valuation during intertemporal choice" for consideration at PLOS Computational Biology. As with all papers reviewed by the journal, your manuscript was reviewed by members of the editorial board and by several independent reviewers. The reviewers appreciated the attention to an important topic. Based on the reviews, we are likely to accept this manuscript for publication, providing that you modify the manuscript according to the review recommendations.

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Reviewer's Responses to Questions

Comments to the Authors:

Reviewer #1: The authors have provided thoughtful responses to all of the questions I have previously raised. I also believe that the authors have done a great job in revising the manuscript to include additional explanation of their analytical frameworks, results, and discussion. The present manuscript addresses an important and timely topic which will have a wide-reaching impact in field of decision-making and human cognition.

I only have one further comment which I hope the authors could help clarify – in your response about t0. I’m not sure I necessarily agree with this statement: “In particular, if all trials were included, the non-decision time would necessarily adjust, shifting the modeled

RT distribution towards zero as much as required to ensure a probability density

> 0 for fast outlier trials.” Could the author please expand on this idea a bit more? Also, relatedly, I’m wondering if the authors think t0 could inform us something meaningful across experiments that use the same exact stimulus setup but with different response schemes (e.g., gaze shifting/grip force vs button press vs continuous dial response)?

Reviewer #2: The authors did a great job in their revision. I still think the paper could be clearer at the conceptual level, but the analyses are technically sound and the results certainly deserve publication. There is no need to prolong this review process with more iterations, but here is a couple of points that could be improved:

1) The paper is introduced with the notion of effort discounting (how a reward is devalued by the effort required to get it), which is not the question of interest in this paper. The authors justify this introduction by stating that their paper reveals another aspect of effort – in addition to reflecting a cost, it would reflect motivational process. But the two aspects are the two sides of the same coin: if motivation is measured by the cost one is willing to pay for a given reward, then accepting a higher cost (exerting more effort) reveals stronger motivation without changing the basic notion that effort is a cost. In other words, the literature on effort discounting also uses effort to reveal motivation, there is no novelty here. The difference, as stated later by the authors, is that effort is an implicit measure in the present study because it is not instrumental in getting a reward. The question of interest (whether implicit measures can provide further insight into subjective valuation during decision-making) without the misleading detour through effort discounting.

2) The interest of the approach is sold with the perspective of applications to neuropsychiatric diseases. I know everyone does that and I’m not particularly shocked, except by the justification that response vigor (grip force) measurement would be informative in conditions where effort processing is impaired (like Parkinson’s disease). To put it bluntly, this is like saying that eye-tracking would be helpful to investigate blind people because their visual exploration is impaired. The paper is interesting enough to attract attention without using this sort of twist.

Reviewer #3: I am happy with the changes

Reviewer #4: Thank you to the authors for their responses and additional analysis. I have a few additional comments:

1) Please report the times (mean, sd) observed between pre-selection and choice registration with the force transducer. This is useful information for future studies investigating similar questions. For example, one could ask how close does the time of the decision need to be to the motor response for this vigor effect to be observed. If the motor response is much delayed (say 1 min) would it still reflect the decision variables? Thus providing the numbers observed in this study will be helpful for others.

2) I am not clear what the second hypothesis is stating. As written, it says: "(ii) Subjective utility modulates response times and grip force: Faster response times and stronger effort (handgrip force) for choices with high utility (subjective value)."

It seems they mean ‘the difference in subjective utility’ rather than simply ‘subjective utility’? If not, then please clarify subjective utility of which option will modulate response times and grip force.

3) In section ‘3.4.2 Value sum effect’, please add a sentence at the end of the paragraph to summarize the main findings.

4) The results are a little difficult to follow. It would be helpful if the authors let the readers know when results supported their hypotheses (and specificy which hypothesis). Even better, would be a summary at the end of the results or in the discussion where there was a recap of the hypotheses and what was supported or rejected.

5) Can the authors clarify whether the new analysis of the effect of total value on response vigor hold true even within a condition? Is the effect they observe driven by the condition effect (high vs low), or is this something observed even with the low condition or high condition, independently?

**********

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Reviewer #1: Yes

Reviewer #2: None

Reviewer #3: Yes

Reviewer #4: Yes

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5 Apr 2022

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12 Apr 2022

Dear Dr. Smith,

We are pleased to inform you that your manuscript 'Motor response vigour and visual fixation patterns reflect subjective valuation during intertemporal choice' has been provisionally accepted for publication in PLOS Computational Biology.

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26 May 2022

PCOMPBIOL-D-21-02032R2

Motor response vigour and visual fixation patterns reflect subjective valuation during intertemporal choice

Dear Dr Smith,

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