Fig 1.
Reciprocal influences between skill belief and attributions, simulation 1.
A: Skill belief evolution, 100 runs of agent with parameters x0w = 0, x0l = 0, βw = 2, βl = 2, α11 = 0.1, α01 = 0.05, α10 = 0.1, α00 = 0.05. B: Effect of skill belief on attribution at the individual trial level, across all runs plotted in A. C: Effect of attribution on skill belief update at the individual trial level, across all runs plotted in A. D: Time decay of attribution effect. E: Time decay of skill belief effect.
Fig 2.
Removing reciprocal connections in simulation 1.
A: Skill belief evolution, runs with (cyan, same as in Fig 1A) and without (yellow) skill belief effect on attribution. B: S. d. of runs in A.
Fig 3.
Reciprocal influences between skill belief and attributions, simulation 2.
A: Skill belief evolution, 300 agents with parameters x0w = −0.03, x0l = 0, βw = 100, βl = 1, α11 = 0.15, α01 = 0, α10 = 0.15, α00 = 0. B: Effect of skill belief on attribution at the individual trial level, across all runs plotted in A. C: Effect of attribution on skill belief update at the individual trial level, across all runs plotted in A. D: Amplification of attribution effect. E: Time evolution of skill belief effect.
Fig 4.
Latent vulnerability, simulation 3.
A: Skill belief evolution for control (cyan, squares, x0w = 0, x0l = 0, βw = 2, βl = 2, α11 = 0.1, α01 = 0.05, α10 = 0.1, α00 = 0.05) and vulnerable (yellow, stars, βw = 0.5, βl = 5, α11 = 0.12, α10 = 0.15, all other parameters equal to control) agents. B: Effect of skill belief on attribution at the individual trial level. C: Effect of attribution on skill belief update at the individual trial level.
Fig 5.
Task and performance overview.
A: Task structure and example trials: four frames sampled for illustration purposes from two trials are displayed in order on the top and bottom rows. After every two trials, participants are asked to attribute the latest outcome to one of 4 given causes, and then to report how good they believe themselves to be at the task. Dotted arrows indicate the flow of time. B: Evolution of performance across trials, mean ± s.e.m. across participants; top: running average of the proportion of wins, sliding window 20 trials, bottom: per trial proportion of correct key presses, wrong key presses and wrong, but correct for the normal UP orientation.
Fig 6.
Skill estimates and attributions overview.
A: Evolution of skill estimates across trials, mean ± s. e. m. across participants. B: Evolution of skill estimates for individual participants, chosen to illustrate variability. C: Attribution proportions, mean ± s.e.m across participants, overall and conditioned on outcomes. D: Time series of attributions for individual participants, chosen to illustrate variability, not the same as in B.
Fig 7.
Effect of outcome and attribution on skill estimate updates.
A: Model agnostic analyses: faded lines and dots represent individual participants, bold lines represent mean± s.e.m across participants. B:, D: Learning rates, winning model for skill. B: self, D: other. Cyan: learning rates for internal attribution, yellow: learning rates for external attributions. C: Skill estimates model comparison; baseline Rescorla-Wagner model (b), and augmentations with learning rates varying based on session (S), attribution (A), outcome (O) and combinations of these factors. Top: self, bottom: other. Difference in WAIC scores from each model to the preferred one. Smaller WAIC scores indicate better models.
Fig 8.
A: Features of interest (skill estimates, task features, objective performance) and attributions summary self: faded lines represents individual participants, bold lines represent mean ± s.e.m across participants. Orange: losses, teal: wins. B: Attribution model comparison. Top: self, bottom: other. Difference in WAIC scores from each model to the preferred one. Smaller WAIC scores indicate better models. C: Winning attribution model parameters. Effects of path length (left) and proportion of unusual orientations (right). Top: self, bottom: other. D: Effects of key press accuracy (left) and skill estimates (right). Top: self, bottom: other.
Fig 9.
Behavioural measures vs questionnaire scores.