Fig 1.
Temporal order of cue availability for prospective and retrospective confidence.
Prior to an action prospective cues to confidence are available, such as sensory input, and prior knowledge about motor abilities. After the action has been executed, retrospective cues become available including proprioception and sensory feedback when available. Prospective cues can be attributed to any action, while retrospective cues are specific to a single, specific action. Figure created by the authors using a licensed copy of Adobe Illustrator (https://www.adobe.com/legal/terms.html).
Fig 2.
Participants responded with reaching movements recorded by a Wacom tablet placed on a desk. A mirror was suspended between a frosted glass screen and the tablet surface in the same horizontal plane. The projector above the glass screen projected stimuli downward. Participants viewed the mirror from a fixed head position and could not see the tablet or their hand while performing reaches with a stylus. The virtual image of the display was in the plane of the tablet. Figure created by the authors using a licensed copy of Adobe Illustrator (https://www.adobe.com/legal/terms.html).
Fig 3.
Control motor-awareness task trial sequence.
Participants moved the stylus into the start point annulus to begin the trial. A target (white dot) appeared straight in front of the starting annulus in the same location on every trial. The target then turned green signaling the participant to begin the reach. The participant then made a reach to the target with the unseen hand, after which they returned to the start point annulus and switched to a mouse to report their perceived endpoint location (white dot) in relation to the target location which was still presented in green. Figure created by the authors using a licensed copy of Adobe Illustrator (https://www.adobe.com/legal/terms.html).
Fig 4.
Main experiment trial sequence.
Participants moved the stylus to a start location annulus at the bottom of the tablet to start the trial. A target (green dot) appeared for 1 s. When it disappeared, participants were required to initiate a reach within 800 ms. After lifting the stylus off of the trackpad and away from the start location annulus, they had 1200 ms to complete the reach (illustrated by dashed line, presented for graphical purposes only as no feedback was given during reach). After reach completion, they returned to the start location annulus and were either shown endpoint feedback (yellow dot) or asked to report their confidence without endpoint feedback (by varying the size of the yellow annulus). The trial was skipped and shuffled back into the remaining possible target locations if the participant left the start location too early, did not start or finish the reach within the allotted time, or did not lift the stylus off the tablet while making the reach. Figure created by the authors using a licensed copy of Adobe Illustrator (https://www.adobe.com/legal/terms.html).
Fig 5.
Confidence was reported by expanding a circle centered on the target location. Points were determined by the radius, with smaller circles awarding more points (maximum of 10, decreasing linearly with increasing circle size). In a confidence-judgement trial the endpoint circle (shown here in white) was not displayed but is included in this figure for reference purposes. If the confidence circle did not intersect or enclose the endpoint circle, no points were earned on that trial. If the confidence-circle radius was 70 mm or larger, the reward was zero as well. Participants knew the points possible for a given circle size but not the amount of points they had earned thus far. Figure created by the authors using a licensed copy of Adobe Illustrator (https://www.adobe.com/legal/terms.html).
Table 1.
Parameters and equations for the motor-awareness model from the observer’s perspective.
This task design forced the observer to use proprioception so this parameter may be isolated during the model fits.
Fig 6.
Cartoon of control motor-awareness task model.
The observer knows the target location and aims for it, resulting in a reach endpoint (red dot) that is perturbed by motor noise (red Gaussian), knowledge of which is a prospective cue along with the target location. The sensed location (blue dot) is where the observer’s hand is felt to be located based on proprioception, which has associated variability (blue Gaussian), knowledge of which is a retrospective cue along with the sensed location. Observers combine these two cues to get a noisy estimate of the endpoint (green Gaussian) and indicate the most likely endpoint location (green dot).
Table 2.
Parameters and equations for the Ideal, Retrospective and Prospective models.
Note that the free parameters listed here are those that impact the fit of the data from the confidence-judgment task. Because we simultaneously fit the data from the control task, all models require all three parameters.
Fig 7.
Cartoon of Ideal performance model from the observer’s perspective.
This model assumes that the participant incorporates both prospective (target location and motor noise—red) and retrospective (sensed endpoint location—blue) cues when estimating the endpoint location (green). Figure created by the authors using a licensed copy of Adobe Illustrator (https://www.adobe.com/legal/terms.html).
Fig 8.
Cartoon of Retrospective performance model.
This model assumes the decision is only dependent on proprioceptive noise and setting noise, and that motor noise is assumed to be infinite. Consequently, the endpoint estimate is at the sensed location. Figure created by the authors using a licensed copy of Adobe Illustrator (https://www.adobe.com/legal/terms.html).
Fig 9.
Cartoon of Prospective performance model.
The participant sets the circle size based only on the known motor noise and does not take any retrospective cues into account as proprioceptive noise is assumed to be infinite. As a result, the intended circle-size setting is constant over trials. Figure created by the authors using a licensed copy of Adobe Illustrator (https://www.adobe.com/legal/terms.html).
Fig 10.
Scatter plot of reach endpoints relative to the target.
Shown for two sample participants (4 and 10, who will be used throughout the paper) shown in the physical dimensions of the input tablet. The red circle overlay shows the average confidence circle size ± SD for each participant. Participant 4 had a significant correlation between confidence circle size and error, thus reported a wider range of confidence circles which fluctuated with their perceived error across trials. In contrast, participant 10 used a more narrow selection of circle sizes that did not correlate with changes in error across trials.
Fig 11.
Scatter plots comparing uncertainty, error and confidence.
(A) Best-fit motor and proprioceptive noise for each participant. Participants best fit by the Ideal model displayed proprioceptive noise close to their motor noise, while those fit best by the Prospective model generally had substantially higher proprioceptive noise. (B) Confidence circle size vs. reach error on each trial for two sample participants in the main confidence-judgment task. P4 was best fit by the Ideal model while P10 was best fit by the Prospective model. The green shaded area reflects judgments where the participant was able to earn points for enclosing their endpoint, and the red shaded area reflects judgments where the confidence circle was smaller than the distance from the endpoint to the target resulting in no points being awarded. Four of five participants best fit by the Ideal model had a significant correlation between confidence and reach error, while only four of the 11 participants best fit by the Prospective model had a significant correlation. (See S7 Fig for other participants.)
Table 3.
The number in each cell is the BIC score for each model relative to the winning model for that participant. All three models required the same number of parameters. Participants 1–5 were best fit by the ideal model, participant 6 was best fit by the retrospective model and participants 7–16 were best fit by the prospective model. Participants are numbered to group them by the winning model (white background).
Fig 12.
Data compared to model simulations.
Histograms of selected confidence-circle size (yellow) for two example participants. We simulated behavior for each model with the corresponding set of best-fit parameters for each participant. Curves: resulting distributions of confidence-circle sizes (green: ideal model; blue: retrospective model; red: prospective model). Plots for all participants are provided in S9 Fig. (A) Sample participant that was best fit by the ideal model. (B) Sample participant that was best fit by the prospective model.
Fig 13.
Capturing behavior with models.
We simulated a total of 9,600 data sets using each participants’ best fit parameters, target locations, and endpoints for a given model (200 per participant per model) and compared the model’s performance to different behavioral dynamics of the data collected from the participants. In all three plots above there are results from the three simulated models compared to the value measured from each participant, the Ideal Model (green), the Retrospective Model (blue) and the Prospective Model (red). The model that best fit the participant’s data in our analysis is denoted with a filled-in circle. (A) The percent of trials in which the confidence circle successfully intersected the true endpoint, thus earning points on that trial. Error bars reflect standard deviation across simulated data sets. (B) The total amount of points earned during the experiment. Higher points are earned for smaller confidence circles, but only if the true endpoint is intersected. Error bars: standard deviation across simulated data sets. (C) Mean confidence across all trials in the experiment. Error bars are +/- SEM across simulated data sets and individual trials.