Accuracy for outcome prediction: Difficulty only vs difficulty and skill models.

Colours correspond to different wd values in the skill and difficulty models; note that wd = 0 (purple) is equivalent to a model with skill only; black is used for the model with difficulty only. Top: overall accuracy; each dot represents one subject. Bottom: accuracy per difficulty level; mean ± s.e.m across subjects; difficulty was z-scored for each subject and discretised in 10-quantiles. (TIF)</p

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.</p

Behavioural measures vs questionnaire scores.

Behavioural measures vs questionnaire scores.</p

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.</p

Model parameters, winning attribution model: Effects of reported skill on external attributions.

(DOCX)</p

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.</p

Staircase procedure.

(DOCX)</p

Model parameters, winning attribution model: Effects of path length on internal attributions and attributions to Maze.

(DOCX)</p

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.</p

SAO skill model parameters: Attribution response shuffling.

(DOCX)</p