Authors: Kazuma Takada, Wen Wen, Shunichi Kasahara, Tom Froese
Categories: Research, Sense of agency, Metacognition, Prediction error, Regularity detection, m-ratio
Source: Experimental Brain Research
Authors: Kazuma Takada, Wen Wen, Shunichi Kasahara, Tom Froese
The sense of agency refers to the feeling of control over one’s actions in the environment. It is typically thought to arise from comparisons between predicted action outcomes and actual sensory feedback. However, previous studies have shown that, in addition to this error detection process, a process that detects regularities between sensory input and one’s actions is also involved in the emergence of the sense of agency. It remains unclear whether these distinct perceptual processes share a common metacognitive monitoring system. We addressed this question using a control change detection task, in which participants moved a single dot on a screen and judged whether their control over the dot changed during the trial, along with their confidence in each response. Detection of a decrease in control is expected to engage the error detection process underlying the sense of agency, whereas detection of an increase in control is expected to engage the regularity detection process. Across two experiments, the results showed that detection of decreases in control was more accurate than detection of increases, whereas the m-ratio did not differ between conditions. These findings suggest that the processes underlying the detection of increases and decreases in control are distinct, but may rely on a shared metacognitive monitoring system.
The online version contains supplementary material available at 10.1007/s00221-026-07306-w.
The sense of agency is the subjective feeling that one’s own actions cause changes in the environment and that one is in control (Gallagher 2000). This subjective feeling is essential for our interactions with the environment, facilitating movement and its learning (Karsh and Eitam 2015; Tanaka and Imamizu 2025; Wen and Haggard 2018), vocalization (Ohata et al. 2020; Wen et al. 2022), and decision-making (Haggard 2017; Haggard and Chambon 2012; Haggard and Tsakiris 2009; Wen and Imamizu 2022). For example, when controlling a tool, a sense of agency arises when the actual sensory feedback matches one’s predicted (expected) outcome. Conversely, when disturbances like delays or deviations cause sensory feedback to differ from predicted outcomes, the sense of agency decays. This error detection process determines the intensity of the sense of agency by comparing the predicted outcome generated based the internal model with the actual feedback (Kawato 1999; McNamee and Wolpert 2019; Wolpert et al. 1995). For example, discrepancies between predicted and actual outcomes, as well as between predicted and actual timing, could attenuate the sense of agency (Sato and Yasuda 2005; Vigh and Limanowski 2024; Villa et al. 2018, 2021; Zama et al. 2017).
On the other hand, in highly uncertain environments or situations requiring novel control detection, the internal model has not yet been established. Because no reliable prediction is available, the comparison between predicted and actual outcomes (i.e., the basis of error detection) may fail. Under such situations, it is necessary to detect the regularities between one’s own movements and the resulting changes in the environment(Wen and Haggard 2020). Once regularity is detected (a certain degree of control is gained), the sense of agency emerges. This process is observed from infant to adult (Nobusako et al. 2022; Wen et al. 2024a, b, 2025; Wen and Haggard 2020). For example, infants who lack accurate internal models, upon perceiving that their own movements cause changes in the external environment, increase their movements (Rochat and Morgan 1995; Rovee and Rovee 1969; Zaadnoordijk et al. 2018). Adults can also use regularity detection to distinguish between self-caused events and externally caused events even when they have not yet established an internal model for controlling an object (Wen and Haggard 2020). Research targeting children aged 6 to 16 has revealed that detecting regularity involves repeating simple movements, and detection accuracy and sensitivity improve with age (Wen et al. 2025). Crucially, the degree to which one can control an object can change dynamically in the environment, for instance, when one gradually gains control during motor learning, or when control is disrupted by unexpected perturbations. The sense of agency in response to such changes may rely on different processes depending on whether control is increasing or decreasing.
These findings suggest that the sense of agency emerges by two distinct processes depending on whether an internal model has been error detection and regularity detection process. Previous research suggests these two processes may have distinct characteristics. For example, error detection process can operate both consciously (Oancea et al. 2025) and unconsciously (Pereira et al. 2023). Wen et al. (2023) also found a negative correlation between perceptual sensitivity and metacognitive sensitivity for the error detection process, but not for the regularity detection process. This dissociation suggests that error detection may operate with less conscious access, particularly in individuals with a highly sensitive sense of agency, whereas the metacognitive monitoring of regularity detection does not appear to vary depending on the sensitivity of the process.
A critical question is how these two processes are engaged when the level of control changes dynamically. It has been proposed that each process is selected based on beliefs about error detection is engaged when one can smoothly control an object, while regularity detection is driven when one cannot control an object successfully (Wen et al. 2024a, b). Increasing control would therefore preferentially engage regularity detection, whereas decreasing control would engage error detection. Consistent with this view, Wen et al. (2020) found that the sensitivity in detecting a decrease and an increase in the level of control differed even when the starting and ending levels of control were simply reversed (i.e., a decrease from 100% to 80% vs. an increase from 80% to 100%). Given the metacognitive dissociation between the two processes (Wen et al. 2023), the direction of control change may affect not only perceptual sensitivity but also metacognitive monitoring. However, this has not been directly tested. We hypothesize that both perceptual sensitivity and metacognitive sensitivity may also differ between increasing and decreasing levels of control, reflecting the engagement of distinct underlying processes. The present study aims to test this directly. If metacognitive sensitivity differs between the directions of change, this would suggest that the conscious accessibility of these perceptual processes also differs, with one being more explicit and the other more implicit.
To address these questions, we applied signal detection theory and a metacognitive approach to a control detection paradigm in which the level of control changed during movement (Wen et al. 2020). In the task, participants manipulated a single dot on a screen, answered yes/no as to whether the dot’s controllability changed during the trial, and rated their confidence in this response. This design separates judgment biases from perceptual sensitivity (Wen et al. 2024a, b) while assessing how explicitly this movement information is recognized and contributes to the sense of agency. In this paradigm, when the level of control is high, the spatial congruency between the participant’s movements and the dot’s movements is strong, so the error detection process dominates. Conversely, when the level of control is low, the alignment is weak, so the participant engages the regularity detection process to find the rules and gain reliable control over the dot. In Experiment 1, the level of control varied within a fixed range. In Experiment 2, a staircase method adjusted the magnitude of change to standardize subjective difficulty across participants. Together, these experiments aimed to determine whether perceptual and metacognitive sensitivity differ between perceiving an increase versus a decrease in control in the sense of agency.
The sample size was determined based on a power analysis for a paired t-test. The effect size was set at 0.34 based on the m-ratio results from Charalampaki et al. (2023). The power calculation using G*Power 3.1 showed that a sample size of 55 participants (one-tailed test with α = 0.05 and a power of 0.80) was required. Because we planned to conduct the experiment using an online system, in which participant exclusion is likely to be higher and the effect size is likely to be smaller than in face-to-face experiments, we decided to recruit 110 participants for this experiment.
We recruited 110 healthy participants (mean age = 32.58, range = 20–60, SD = 9.06, 43 females, 1 other) through Prolific1. Participants were required to have an approval rate of 90% or higher on experiments conducted on Prolific. All participants were English speakers and used a computer that met the experimental system requirements. Written informed consent was obtained from all participants prior to the experiment, and they provided gender (male, female, or other) and age. After providing informed consent, they completed the experimental tasks using their own computer, and they received financial compensation after finishing all tasks. This study was approved by the local ethics committee (Okinawa Institute of Science and Technology Graduate University, ethics #HSR-2024-022).
Experiment 1 employed a within-participants design consisting of two blocks that manipulated the direction of change in the level of control (two increase/decrease). The block order was counterbalanced across participants. The level of control of the stimulus (the dot) was set at either 60% or 90%. The level of control refers to the proportion of the participant’s movement contained within the dot’s motion. The magnitude of the change in level of control was fixed at 30%. In the increase block, a single-step change from 60% to 90% was applied; in the decrease block, a single-step change from 90% to 60% was applied. This change occurred 2.5 s after the participant began moving the dot. The use of a single-step change, rather than a gradual change, was intended to reduce task difficulty and ensure that the timing of the change was clearly defined. Each block consisted of 60 main trials, including 30 change trials and 30 no-change trials. In addition, six practice trials (three change and three no-change trials) were presented before the main trials in each block. In total, each participant completed 132 trials.
Figure 1A shows the flow of a trial. Each trial consisted of a 3-second countdown, 5 s of controlling the dot, a response indicating whether a change in control occurred, and a confidence rating in their own response. After the control period, the question “Did the control of the dot change midway?” appeared on the screen, and participants pressed the Q key (“Yes, it changed”) or the W key (“No, it didn’t change”). They were then asked, “How likely do you feel that your answer is correct?” and rated their confidence on a four-point scale (“Not very likely”, “Not likely”, “Likely”, “Very likely”) by pressing the 1, 2, 3, or 4 key, respectively. When the trial involved a change, the level of control of the dot changed abruptly 2.5 s after the first movement of participants’ mouse. During the practice trials, correctness feedback for the change detection was provided after participants completed the confidence judgement.
The dot’s movement was generated by blending participants’ real-time movements and pre-recorded movements from other individuals. At each frame, the dot’s movement direction was computed as a weighted average (e.g., 90/10 in the 90%-control condition) of the participant’s mouse-movement angle (i.e., change in position from the previous frame) and the movement angle from a continuous sequence of pre-recorded mouse movements (Wen et al. 2020). The speed of the dot’s movement always matched the speed of the participant’s mouse movement. This ensured that the experimental manipulation was restricted to movement direction, preventing speed discrepancies from serving as an additional cue that could independently affect the change detection. When participants stopped moving the mouse, the dot also stopped on the screen. Participants were instructed to keep moving their mouse throughout the trial. Figure 1B shows examples of dot trajectories under the decrease in control and increase in control conditions. When the participant’s ratio is high, the dot’s movement closely aligns with their actual movement. However, as their ratio decreases, the prediction error increases.
Fig. 1Panel A depicts the timeline of the control change detection task. Experiment 1 and Experiment 2 used the same task design, but the magnitude of the change differed between them. Each trial began with a 3-seconds countdown, after which a dot appeared at a random position on the screen. Participants then freely moved the dot using a mouse for 5 s. Five seconds after their first mouse movement, the dot froze in place, and participants indicated whether their control over dot’s movement had changed during the trial by pressing the Q or W key. They then rated their confidence in their judgment on a 4-point scale using the 1, 2, 3, and 4 keys. Panel B illustrates an example of blending the participant’s movement with a pre-recorded movement. The blending ratio varies depending on the condition. In the “decrease in control” condition, the dot’s movement initially tracks the participant’s actual movement. However, the weight of the pre-recorded movement increases after 2.5 s, causing the dot to deviate from the participant’s input. Conversely, in the “increase in control” condition, the pre-recorded movement is dominant initially, but the participant’s contribution increases after 2.5 s, resulting in the dot moving closer to the participant’s actual trajectory
The experiment was conducted using an online experimental platform (Kasahara and Takada 2021). Participants were eligible for the experiment if their laptop or desktop met the following Full HD or higher resolution, browser size of 1600 × 940 or larger, refresh rate of 60 Hz, macOS or Windows operating system, and use of Google Chrome as the browser. These requirements were checked by the platform. Participants who did not meet these requirements were declined from participation. For the experimental task, participants were asked to use a wired mouse and keyboard. To prevent the OS pointer from moving outside the experimental window in the browser, participants were first asked to click the center of the screen. This locked the OS pointer to the browser window and made it invisible. During the experimental task, mouse position at each frame was acquired to generate the dot’s movement. If a participant wished to withdraw from the experiment, they could press the ESC key to unlock the pointer and then close the browser window. A message explaining this withdrawal option was always displayed in the lower left corner of the screen.
The experiment consisted of two blocks–an increase block and a decrease block. At the beginning of each block, participants were informed of the direction in which their control over the dot might change in the upcoming trials. Participants pressed the A key to start a block. This allowed them to take a short break before starting the second block. The first six trials of each block were practice trials. The level of control over the dot’s movement changed in three trials and remained unchanged in the other three trials. The trial order was randomized. During the practice trials, participants were shown whether their response of control change detection was correct or not after they had rated their confidence. After the practice trials, the main trials were conducted. Each block consisted of 60 main trials, with half containing a change in control over the dot’s movement and the other half containing no change. The trial order was randomized for each participant. In total, participants completed 132 6 practice trials and 60 main trials in each of the two blocks. The experiment lasted approximately 45 min, including the time participants spent reading the informed consent and instructions before the task.
First, we conducted a paired t-test (increase - decrease) on accuracy and confidence ratings to evaluate whether task difficulty differed between conditions. To estimate metacognitive performances, we employed a hierarchical Bayesian framework for the joint estimation of d´, meta-d´, and m-ratio (Fleming 2017), implemented in hmetad2 package. This approach offers several advantages over conventional signal detection theory (Green and Swets 1966) and maximum likelihood estimation of meta-d´ (Maniscalco and Lau 2012). First, because meta-d´ is derived from d´, the hierarchical model propagates the uncertainty in d´ into the estimation of meta-d´ and m-ratio within a single generative model. Second, hierarchical estimation regularizes individual-level estimates toward the group-level, which stabilizes estimation for participants with low d´ and obviates the need for exclusion criteria such as d´ ≤ 0. Third, this method eliminates the need for ad hoc adjustments (e.g., log-linear correction) typically required when hit or false–alarm rates reach extreme values of 0 or 1. In this framework, the m-ratio is parameterized in log space (log(meta-d´/d´) with a normal prior, thereby constraining m-ratio to positive values and avoiding the complications associated with negative point estimates based on the signal detection. Posterior samples were exponentiated to recover the m-ratio on its original scale for reporting.
The model in this study included condition (Increase vs. Decrease) as a fixed effect and participant-level random intercepts and slopes for condition on all estimated parameters (d´, criterion, and the confidence-criterion parameters), with a full covariance matrix across random effects. We ran four MCMC chains, each with 10,000 total iterations including 5,000 warmup iterations, yielding 20,000 post-warmup posterior samples in total.
For each condition, we derived group-level posterior distributions for d´, meta-d´, and m-ratio. We calculated the median of each distribution and the difference between conditions (Increase minus Decrease), along with 95% highest density interval (HDI) and the probability of direction (pd) (Makowski et al. 2019). Following previous work (Nagamura et al. 2025), differences were considered robust if the 95% HDI did not overlap with zero and pd exceeded 95%. To assess the stability of individual differences across conditions, we estimated posterior distributions of the between condition Pearson correlation coefficient for each metric (d´, meta-d´, and m-ratio). Specifically, for each MCMC draw, we obtained participant-level parameter estimates for both conditions and computed the correlation, yielding a full posterior distribution of ρ that incorporates uncertainty in the individual-level estimates. Correlations were considered robust if the 95% HDI did not overlap with zero and pd exceeded 95%. We also conducted paired t-tests (Increase - Decrease) on accuracy and confidence ratings to evaluate differences in task difficulty and confidence level between conditions.
Rather than using d´ exclusion criterion, we applied exclusion criteria based on accuracy rate and diversity of confidence ratings. First, participants who used only a single confidence rating level were excluded. Because meta-d´ is estimated from the joint distribution of performance and confidence, and a lack of variance in ratings yields a flat likelihood function, rendering the parameter estimate overly dependent on the prior distribution. Second, participants whose accuracy fell below chance level (50%) in both conditions were excluded, as this pattern indicates inattentiveness or random responding. These exclusion criteria were applied in the main analysis. In the supplementary analysis, stricter accuracy thresholds were applied; excluding participants whose accuracy was at or below 70% in both condition and in either condition. We verified whether the results were consistent with those of the main analysis.
We excluded 8 participants who used only a single confidence rating in either condition, as well as 3 participants whose accuracy fell below 50% in both conditions. Consequently, these participants were excluded from all subsequent analyses, resulting in a final sample of 99 participants in Experiment 1. A paired t-test was conducted on the accuracy, and a significant difference was observed between two conditions (t(98) = − 12.410, p < .001, Cohen’s d = − 1.247). Accuracy was higher in the decrease condition (mean = 85.5%) than the increase condition (mean = 56.8%). Figure 2A shows the result of group-level posterior distribution of d´ estimated by the hierarchical Bayesian modeling. The posterior median differences of d´ between condition was − 1.937, indicating a credible advantage for the decrease condition (95% HDI [− 2.253, − 1.596], pd = 1.000; Fig. 2C). Figure 2B illustrates the posterior distribution of meta-d´ and there were also credible advantage for the decrease condition (median ∆meta-d´ = − 1.675, 95% HDI [− 2.030, − 1.295], pd = 1.000; Fig. 2D). These results indicate that changes in level of control were detected more accurately and with higher metacognitive sensitivity in the decrease in control condition than in the increase in control condition. Furthermore, the results of a paired t-test for confidence rating showed that there was a significant difference between conditions (t(98) = − 7.297, p < .001, Cohen’s d = − 0.733). In other words, for the same magnitude of change, participants were more confident about their sense of agency in the decrease condition. The correlation analysis showed that there were moderate positive correlation across conditions in d´ (ρ = 0.520, 95% HDI [0.442, 0.600]; Fig. 2E), as were moderate positive correlation in meta-d´ (ρ = 0.436, 95% HDI [0.337, 0.543]; Fig. 2F). These results indicate that moderate positive correlations were observed across the two conditions for both perceptual sensitivity (d´) and metacognitive sensitivity (meta-d´), suggesting some consistency in individual differences between conditions.
Fig. 2Results of the estimated d´ and meta-d´ after exclusion in Experiment 1 (N = 99). Panel A and B show the posterior distributions of d´ and meta-d´ respectively. Panel C and D depict the posterior distributions and there is substantial evidence for differences between the two conditions for each metrics. These result suggests that sensitivity in the two processes and its reflection have different characteristics. Panel E and F shows the posterior distributions of correlation in d´ and meta-d´ across two conditions. Although the correlation is positive, they were moderate evidence
Next, we calculated the m-ratio for 99 participants and analyzed their differences and correlation. Figure 3A shows the group-level posterior distribution of m-ratio and no substantial evidence for a difference were observed (median ∆m-ratio = 0.058, 95% HDI [-0.108, 0.222], pd = 0.746; Fig. 3B). The results from the correlation analysis showed that m-ratios in the two conditions were not correlated (median ρ = -0.027, 95% HDI [-0.764, 0.872]; Fig. 3C). In addition to the absence of these differences and the lack of correlation, substantial individual difference was observed (Fig. 3D). For example, participants were observed not only with similar m-ratios across both conditions, but also with extremely large m-ratios in one condition. A supplementary analysis using stricter exclusion criteria yielded similar results, confirming the robustness of the findings (See Supplementary material S1.1).
Fig. 3Results of m-ratio after exclusion. Panel A shows the posterior distributions of estimated m-ratio under each condition, and there was no substantial evidence in ∆m-ratio between the two conditions (Panel B). In addition to this, no strong correlation was observed across two conditions as shown in Panel C. Panel D depicts the individual differences in m-ratio between conditions. These results demonstrate that individual sensitivity depends on the direction of change in level of control. For example, some participants were better monitoring to increases in level of control, others to decreases, and some showed similar sensitivity to both directions of change
In Experiment 2, we used a staircase method for adjusting the magnitude of change in control to equate participants’ subjective difficulty levels. The experimental task, apparatus, and procedure were identical to those in Experiment 1.
The sample size was determined in the same way as in Experiment 1. We recruited 110 healthy participants (mean age = 37.19, range = 20–60, SD = 10.38, 48 females, 2 others) through Prolific. Participants had an approval rate of 90% or higher on experiments conducted on Prolific, their native language was English, and the computers they used met the experimental system requirements. Written informed consent was obtained from all participants prior to the experiment, and they provided gender (male, female, or other) and age. After providing informed consent, they worked on the experimental tasks using their own computer, and they received financial compensation after finishing all tasks. This study was approved by the local ethics committee (Okinawa Institute of Science and Technology Graduate University, ethics #HSR-2024-022).
Experiment 2 employed a within-participants design consisting of two blocks manipulating the direction of change in the level of control (two increase and decrease), as in Experiment 1. The block order was counterbalanced across participants. In experiment 2, the range of level of control changes (the difficulty of detection) was adjusted using a staircase method. The higher end of the level of control was fixed at 90% (i.e., control either increased from a lower level to 90% or decreased from 90% to a lower level). The staircase adjusted the lower end of the level of control, which was initially set at 60% at the beginning of each block. Lowering the lower end reduced task difficulty, whereas raising it increased task difficulty. The task difficulty was adjusted using a 2-up/1-down algorithm. On trials in which the level of control changed (change trials), the difficulty increased by one step if a participant responded correctly on two in a row. After any incorrect response on a change trial, the difficulty decreased by one step immediately. Furthermore, for difficulty to increase, the correct answer rate over the previous 30 trials with changing the level of control had to exceed 71%. The step size for changes in level of control was 2.5%. These procedures were designed to achieve an approximate 71% accuracy rate for participants across two conditions, enabling evaluation of change detection in level of control and its cognitive processing.
As in Experiment 1, the change in the level of control occurred 2.5 s after the participant began moving. Each experiment block consisted of 110 trials. The first 10 trials in each block were not adjusted based on the staircase. The next 100 trials were organized into 25 sets of four within each set, two trials contained a change in the level of control and two trials did not, and the order of change and no-change trials was randomized within each set. In each block, the participant performed 6 practice trials, containing three change trials and three no-change trials before the main trials. During practice trials, feedback on the correctness of change detection was provided at the end of each trial. Each participant completed a total of 232 trials.
In Experiment 2, we applied an additional exclusion criterion based on the range of the staircase, in addition to the criteria used in Experiment 1. Participants who reached the minimum stimulus level of control of 2.5% in either condition (i.e., an increase from 2.5% to 90% or a decrease from 90% to 2.5%) were excluded from all analyses. After applying this criterion, we estimated d´, meta-d´ and m-ratio using hierarchical Bayesian modeling and calculated the difference between the increase and decrease condition, following the same procedure described in Experiment 1. Furthermore, we used the correlation coefficients estimated simultaneously with the above metrics to examine the relationships between conditions and among metrics. All estimations were performed using the hmetad library, with same MCMC settings as in Experiment 1. We also conducted a paired t-tests (increase – decrease) on the mean level of control to assess whether the threshold of change detection differed between conditions. In addition to this main analysis, we conducted a supplementary analysis using a stricter exclusion criterion for accuracy, as in Experiment1, to verify the consistency of the main analysis results.
First, 23 participants who reached the lowest level of control within the range of staircase were excluded. In addition, 4 participants were excluded based on the diversity of confidence rating. After excluding these participants, no participants met the exclusion criteria based on accuracy. Therefore, the final sample size for subsequent analyses was 83 participants. Paired t-tests showed a significant difference in mean level of control between conditions (t(82) = − 7.955, p < .001, Cohen’s d = − 0.873; Fig. 4A and B). As shown in Fig. 4C, the median of the group-level d´ was 1.626 under the decrease condition and 0.780 under the increase condition, with a median difference of − 0.845. The 95% HDI of the difference distribution was [− 1.047, − 0.639], which did not include 0, and since pd was 1.000, substantial evidence was observed, similar to Experiment 1, that perceptual sensitivity was higher in the decrease condition than in the increase condition (Fig. 4E). For meta-d´ as well, the posterior distributions differed substantially across conditions (Fig. 4D), and substantial differences were observed between conditions (median of ∆meta-d´ = − 0.735, 95% HDI [-0.956, − 0.517], pd = 1.000; Fig. 4F). In the confidence rating, there was a significant difference between conditions based on paired t-test (t(82) = − 3.672, p < .001, Cohen’s d = − 0.403).
Fig. 4Results in Experiment 2, after exclusion based on the minimum level of control, few confidences rating, and accuracy (N = 83). Panel A shows the level of control transition in each condition and Panel B demonstrates the distribution of the mean level of control that participant reached. A significant difference was observed in the required change magnitude for detection between increases and decreases in the level of control. Panel C and D show the posterior distribution at group-level d´ and meta-d´. A substantial differences were observed in d´ and meta-d´. These result suggests that a decrease in level of control is easier to detect with confidence, as in Experiment 1
To examine the consistency of performance across the two conditions, we estimated the group-level correlation coefficient (ρ) at the group-level for both d´ and meta-d´. The results showed a modest positive correlation for each metric (d´: median ρ = 0.308, 95% HDI [0.198, 0.420]; meta-d´: median ρ = 0.210, 95% HDI [0.048, 0.371]). Furthermore, to investigate the relationship between participants’ metacognitive sensitivity and difficulty, we performed the linear regression analyses between the mean level of control across conditions, and between the mean level of control and meta-d´ for each condition. The results showed a positive correlation for the mean level of control, but with considerable variability (r(81) = 0.504, p < .001, R^2^ = 0.254). This indicates that the magnitude of changes in level of control required to detect changes in movement across conditions is consistent. However, the low coefficient of determination suggests that there are significant variability and individual differences. Regarding the relationship between meta-d´ and the mean level of control, a positive correlation was observed in increase condition (r(81) = 0.434, p < .001, R^2^ = 0.188), while no correlation was observed in the decrease condition(r(81) = 0.004, p = .970, R^2^ = 0.000). These results suggest that, under the increase condition, changes in the level of control are associated with metacognitive sensitivity, whereas under the decrease condition, metacognitive sensitivity remains constant regardless of changes in the level of control.
Fig. 5Correlation results in Experiment 2 after exclusion (N = 83). Panel A and B show the posterior distribution of correlation coefficient. The modest differences were observed in both conditions. Panel C shows the correlation in the mean level of control through staircase across conditions and there was a significant positive correlation. Panel D shows the correlation between median meta-d´ from each participants’ posterior distribution and the mean level of control. While there was a significant positive correlation in the increase in control condition, there was no correlation in the decrease in control condition
Figure 6A shows the posterior distribution of m-ratio for the 83 participants. There was no difference between conditions (median ∆m-ratio = − 0.049, 95% HDI [− 0.208, 0.109]; Fig. 6B). Moreover, m-ratios across conditions were not correlated (median ρ = 0.224, 95% HDI [− 0.395, 0.812]; Fig. 6C), and there were large individual differences as shown in Fig. 6D. These findings suggest that, even when the task difficulty was equated across the participants, substantial individual differences remained in the metacognitive monitoring of control. In the supplementary analysis, trends similar to main analysis observed for all metrics (See Supplementary material S1.2).
Fig. 6Results of m-ratio after exclusion (N = 83). Panel A shows the posterior distribution of m-ratio at the group-level under each condition, and no substantial difference was observed between the two conditions (Panel B). Panel C shows the posterior distribution of the correlation coefficient between two conditions and no substantial difference was observed. Panel D is forest plot of individual ∆m-ratio and illustrates the individual difference of m-ratio between conditions. These results indicate that even when subjective difficulty is equated across participants using staircase, individual differences in the relative advantages of each process persist
The present study aimed to clarify whether perceiving an increase and a decrease in control relies on different perceptual processes, and whether these processes are monitored differently at metacognitive level. Participants controlled a dot on the screen for 5 s, and they first judged whether they experienced a change in control over the dot during the trial, and then rated their confidence in that response on a 4-point scale. The results of Experiment 1 provided substantial evidence that the perceptual sensitivity (d´) was more sensitive under the decrease condition than under the increase condition, even though the magnitude of change was identical across conditions. Moreover, a moderate correlation in d´ was observed between two conditions, suggesting that the perceptual processes may be linked to some extent to the increase and decrease in control at group-level. In contrast, the m-ratio did not show a clear directional dependence between the conditions at the group-level, suggesting that metacognitive monitoring does not differ as a function of the direction of control change unlike perceptual process. Given the high estimated m-ratio values, both the detection of increases and decreases in the control appear to be highly explicit. Furthermore, Experiment 2 used a staircase to hold detection accuracy as close as possible to 71%. The findings replicated the main results of Experiment the m-ratio again did not show a substantial difference between the conditions. On the other hand, the direction of the difference in Experiment 2 was opposite to that in Experiment 1. This is most likely because range of the changing level of control was fixed in Experiment 1, which caused the d´ estimates for some participants to be small under the increase in control condition. In fact, the result of Experiment 2 showed that a larger magnitude of change was required for the detection in an increase in control compared with a decrease in control through staircase adjustment. Furthermore, when stricter participant exclusion criteria were applied and only a subset of participants meeting those criteria were included in the analysis, the results of Experiment 1 were consistent with those of Experiment 2.
Sense of agency has typically been explained within prediction framework based on internal models. In this framework, the brain is thought to generate predicted sensory feedback from efference copies of motor commands and then compares these predictions with the actual sensory feedback. Prediction errors are continuously monitored, but only those exceeding a certain threshold give rise to explicit awareness that control has been lost. This error-monitoring mechanism may be efficient when a stable mapping between one’s actions and sensory feedback has already been acquired and the belief of control is strong. In this case, even small prediction errors can trigger salient drop in sense of agency (Wen et al. 2024a, b; Wen et al. 2024a, b). Our results are consistent with this view. The detection of a decrease in control was significantly more sensitive than the detection of an increase in control, even when the magnitude of change was identical (Experiment 1). Moreover, participants were able to detect relatively smaller changes in control when control decreased from 90%, compared to when it increased to 90%. Such sensitive detection reflects a reliable error-detection mechanism. Limanowski (2026) highlighted that the salience of such prediction errors depends on how the sensory feedback deviates from the established when a stable visuomotor mapping has been acquired, even relatively small deviations from the predicted feedback generate clear error signals at the comparator. In the present study, the decrease condition likely engages this comparator efficiently, because participant had already acquired a belief in control at 90% control, and the subsequent decrease in control would produce salient prediction errors.
In contrast, when control increases from a lower level to a higher level, people must explore the regularity between their actions and the sensory feedback. In this case, prediction errors are less informative because the mapping between actions and outcome is uncertain. The process of detecting regularities between actions and outcomes is likely to be more dominant than the error-detection process in perceiving an increase in control. A previous study reported that the detection of an increase in control shows much larger individual differences than the detection of a decrease in control (Wen et al. 2021). However, it was unclear whether the large individual differences arose from the criterion used to determine whether they had gained sufficient control, or from the sensitivity in perceiving such a change. Our results show a similar trend of larger individual differences in the detection of an increase than the detection of a decrease in control, indicating that a large portion of the individual differences lies in sensitivity. This is likely because regularity detection is linked to motor learning (Nobusako et al. 2022; Wen et al. 2021), and different strategies and skills can be developed during such learning. For example, it has been suggested that while areas of the posterior temporal cortex are activated during the early stages of the process of acquiring new visuomotor mappings, the extent of this activation varies individually (Limanowski 2026).
This asymmetry in sensitivity mirrors findings from motor learning and speech studies, in which the brain shows higher sensitivity to errors that deviate from a learned stable state compared to those that move toward it (Tang et al. 2025; Todorov et al. 2025). The selection between error-detection processes and regularity-detection processes is thought to depend on the belief in control (Wen et al. 2024a, b; Wen et al. 2024a, b). When the belief in control is strong, an exploitation mode is activated and the error detection process dominates in the sense of agency; when the belief in control is weak, a exploration mode is activated, and the process of regularity detection dominates in the sense of agency (Wen et al. 2024a, b). Because the range of control levels (i.e., 60%-90%) largely falls in the category of being in control (Wen et al. 2020), exploitation mode likely prevailed, which may explain the higher sensitivity to decrease than to increases in control. The mode may switch depending on the belief in control, and the asymmetry may become comparable or even reverse in different circumstances. Nevertheless, our results show that the two types of processes underlying the sense of agency play very different roles in the detection of a change in control depending on the direction of the change.
Despite this asymmetry in perceptual sensitivity, the present study also highlighted the symmetry of metacognitive monitoring in the processes involved in detecting an increase and a decrease in control. Regarding the perceptual sensitivity, a clear directional dependence (asymmetry) was observed between the two conditions. A decrease in control could be detected with smaller change (difference in difficulty; Fig. 4B), and discrimination was also higher (difference in d´; Fig. 4C and E). Furthermore, condition differences were observed in criteria, with a more liberal criterion adopted during increased control (∆c = -0.287, 95% HDI [-0.390, -0.188], pd = 1.000; Supplementary Figure S2). In the increase condition, the convergence of the staircase resulted in a larger magnitude of change compared to the decrease condition (increase around 30%, decrease around 21%). This suggests that exposure to larger changes may have strengthened the tendency to judge “there is change” in the increase condition. However, even with the adoption of this liberal criterion and the large magnitude of change, detecting the increase in control remained difficult.
On the other hand, no difference was observed in the m-ratio results between the two conditions, suggesting that metacognitive monitoring was of a similar degree between the two processes. Since there was no correlation between the criterion and the m-ratio within each condition, nor between difficulty and the m-ratio, it is unlikely that this symmetry is due to confounding by these factors. The m-ratio was high in both conditions, indicating that the detection of changes in the sense of agency was highly explicit. However, the group-level correlation of the m-ratio had a wide HDI (median ρ = 0.231, 95% HDI [-0.369, 0.828]; Fig. 6C), making it impossible to clearly determine the presence or absence of a correlation. As shown in Fig. 6D, the individual-level ∆m-ratio was widely distributed around zero. For example, while one participant demonstrated high metacognitive efficiency in both conditions, another participant demonstrated high metacognitive efficiency in one condition but low metacognitive efficiency in the other. The symmetry observed at the group-level is a consequence of these individual differences not being systematically biased in either direction. The complexity of these individual differences is also reflected in the wide range of the 95% HDI for the correlation coefficient (ρ) between conditions. This suggests that while metacognitive efficiency was equivalent at the group-level, the underlying processes of metacognitive monitoring may differ between conditions. However, it remains unclear where the individual differences in metacognitive monitoring come from and how they shape the sense of agency. One possibility is that each individual may use the error detection process and the regularity-detection process differently in the sense of agency, and that metacognitive efficiency may be driven by the relative weightings of these processes. The present study was not designed to directly test this possibility, and it is worth further examination in future research.
At last, the present study manipulated the level of control by mixing others’ movements with participants’ own movements at different ratios. This manipulation ensured a consistent overall level of prediction error within each trial (Wen et al. 2020). However, due to the unpredictability of the other’s motion, frame-to-frame prediction errors could vary. There may be moments in which prediction errors increase or decrease abruptly within a short time window when the pre-recorded movements diverge from or become similar to participants’ ongoing movements in certain frames, even when the overall level of control remains constant. Sensitivity to, and weighting of, such local changes in prediction error may vary across individuals and between conditions involving increases versus decreases in control. Furthermore, the present study matched the speeds of the actual and displayed movements to ensure that participants relied primarily on spatial relationships when making agency judgments. This prevented the use of overly simple strategies, such as abruptly changing movement speed. However, temporal errors may be processed differently from spatial errors in the brain (Limanowski 2026). Therefore, further research is needed to determine whether the findings of the present study can be generalized from the spatial domain to the temporal domain.
This study has several limitations. First, all experiments were conducted online. While current web browsers allow us to obtain participants’ screen resolution and refresh rate, they cannot capture the physical display size or the control-display ratio. Consequently, the physical parameters of the experimental stimuli could not be strictly controlled across participants. To mitigate the potential noise introduced by these variations, we recruited twice the number of participants required by the power analysis for each experiment. After exclusions, data from 99 participants in Experiment 1 and 83 in Experiment 2 were retained for the final analysis. However, the number of trials per block in each experiment was relatively limited. In the present study, Experiment 1 included 60 trials per block, and Experiment 2 included 110 trials per block. Rahnev (2025) suggests that at least 100 trials are typically required to accurately estimate metacognitive indices. To address the issue of limited trial counts, we employed hierarchical Bayesian modeling (Fleming 2017), which allows for accurate parameter estimation even with fewer trials, in addition to standard estimation methods. The results from both approaches were consistent, supporting the robustness of our findings. Future research should nevertheless aim to increase the number of trials per condition to further enhance estimation accuracy.
We included all random effect in the model for the estimation in the main analysis. Consequently, the 95% HDI of the between-condition correlation coefficients for m-ratio was notably wide, suggesting substantial uncertainty in the estimated values. This is likely due in part to the complexity of the model, which simultaneously estimated a large number of parameters, including individual-level d´, criteria, and confidence criteria. Because m-ratio (meta-d´) is derived from how participants distribute their confidence ratings, their individual-level estimates are inherently less precise than those of d´, and this uncertainty propagates into the correlation estimates. Furthermore, if there are strong differences in the participants’ d´ across conditions, this can also distort the posterior distribution of the correlation. In fact, when the difficulty level was adjusted for each participant using a staircase and the exclusion criteria were tightened, the 95% HDI of the correlation did not become excessively wide. At the same time, the wide intervals may also reflect genuine individual differences in metacognitive process across participants. Disentangling modeling uncertainty from true variability would require larger samples and more trials per condition.
In the present experimental design, changes in the level of control were fixed to occur at the 2.5-second mark. Consequently, participants may have anticipated the timing of the change, which could have improved their accuracy. Although this effect was mitigated to some extent by the random interleaving of trials in which the level of control did not change, it will be important for future studies to examine how varying the timing of the change influences performance accuracy.
The present study shows that the contribution of the error detection process and the regularity detection process to the sense of agency are not simply two expressions of a single mechanism but instead rely on different perceptual processes. The metacognitive efficiency of these processes is comparable at the group-level, though substantial individual difference suggests that the relative contribution of each process to metacognitive monitoring may differ across individuals. Our findings refine current models of sense of agency by highlighting the importance of considering different perceptual processes across different modes of sense of agency and shed light on the large individual differences in both perceptual sensitivity and metacognitive monitoring in the sense of agency.
Below is the link to the electronic supplementary material.
Supplementary Material 1
Supplementary Material 2