Fig. 1

Data, model fit, and parameter estimates for the best learning model. A DOSE data: Example of data, model fit, and parameter estimates for eight participants arranged by doses of training. B EXCITE data: Example for eight participants arranged by the timing of training (immediate vs. delayed). Upper panel: MAL data and fit for the best model for each participant. The fit was overall excellent, with RMSE = 0.28 for all 40 participants (individual RMSE 0.26 \(\pm\)0.19). These examples also illustrate the large variability between participants. Variability in response to training is due to a low (e.g., D27) or high learning rate (e.g., D23). A combination of small learning and self-learning rates is highly detrimental for long-term performance (e.g., D27, D37), but the opposite yields improved long-term outcomes (e.g., D17). Dot: data. Lines: mean model fit. Shaded area: 95% CI. Lower panel: Posterior parameter distributions of the three main parameters (self-training rate \({\gamma }_{i}\), learning rate \({\beta }_{i }\), and retention rate \({\alpha }_{i})\). The thick bars show the 95% parameter CI and the thin bars the 99% CI. C Hyper-parameters: Posterior distributions for the corresponding hyper-parameters. Note that \(\text{T}\left({{\theta }}_{{\alpha }}\right)\) is the transformed \({{\theta }}_{{\alpha }}\) parameter (via the sigmoid function), which corresponds to the median of the logit-normal prior distribution for individual retention rates (\({{\alpha }}_{\text{i}}\))