### Figure 2-2

Additional model comparisons for trial-by-trial estimates of PM strategy shifts. One concern with fitting models on a by-trial basis is that noise may bias model selection towards the models with fewer parameters. In order to address this concern, we performed a less conservative AIC (without the small sample correction term) model selection analysis and a bootstrap analysis where polynomial fits were calculated for a random subsample of trials. For the AIC analysis, we performed the same regression analysis steps as detailed for the AICc analysis, but simply used the AIC estimation term instead of the AICc term. After calculating an AIC score for each trial, we then selected the lowest score between the 1^{st}, 2^{nd}, and 3^{rd} order polynomial as the best for the trial. We then calculated the relative Akaike weight for each model on each trial and average that value for each model type for each participant. Across participants the average Akaike weights were similar between 1^{st} and 3^{rd} order polynomial fits (mean difference = 0.006 (SE = .010), t(77) = 0.65, p=.52; **panel a**). Significantly more trials for each participant were best fit by a 1^{st} order than a 3^{rd} order polynomial (mean difference = 20.5% (SE = 1.7%), t(77) = 12.014, p<.001; **panel b**). Another way to mitigate the impact of noise on model selection is to fit the model on more than a single trial at a time. To avoid averaging across all trials and still getting an estimate of model-fit reliability, we performed a bootstrap analysis. In this analysis, we first z-scored PM-cost values within each subject. Next, we combined all trials into one super-subject. On each bootstrap iteration, 50 trials of each of the five trial types (increasing starting easy, increasing starting middle, fixed, decreasing starting hard, decreasing starting easy) were randomly selected from the super-subject pool. Then, 1^{st}, 2^{nd}, and 3^{rd} order polynomial models were fit to each trial type sample and the lowest AIC value was selected as the best-fit model type. We repeated this process 1000 times and found that a linear (1^{st} order) polynomial fit a significantly greater number of these samples (57.7% of all trials), followed by a quadratic fit (2^{nd} order, 29.1% of all trials), followed by a cubic fit (3^{rd} order, 13.4% of all trials). This is a significantly greater number of trials selected to be best fit by a linear relationship than would be predicted by chance (χ^{2} (1, n=1000) = 364.06, p <.001). Download Figure 2-2, DOCX file.