Supplementary Fig. 5: Cross-validation shows that GAM performs better than GLM for all four distributions administered in M-Turk.

Inertia bias has less explanatory power than contraction bias. (a–d) We compared the following models for: (a) Broad uniform (n = 125), (b), Narrow uniform (n = 94) (c), Gaussian (n = 163) (d) Bimodal performed (n = 108) in M-Turk: Inertia and feedback effects^29,39—\(\alpha ^s\delta ^t + w_rx_r^t + w_fx_f^t\). Stimulus independent effects of the previous trial. These terms were added to explain the impact of feedback³⁰ and inertia. Negative feedback in the previous trial can promote a switching response, while a positive one might enhance perseverance; response inertia—the tendency to choose the same response as in the previous trial. To account for them we added the response in the previous trial \(x_r^t = y^{t - 1}\) and its feedback \(x_f^t = y^{t - 1}e^{t - 1}\) (where e^t−1 is the 0/1 feedback in the previous trial). Values of both variables’ (w_r,w_f) were {-1,1}. Both covariates (x_r,x_f) were centered. Linear contraction bias (recent and longer term) – \(\alpha ^s\delta ^t + w_1d_1^t + w_\infty d_\infty ^t\)has linear terms for both bias by recent and bias by longer term history. Both are assumed to increase linearly with respective distances. Nonlinear (GAM) non-additive contraction bias – \(\alpha ^s\delta ^t + b\left( {d_1^t,d_\infty ^t} \right)\). A single interaction term, which accounts for recent and longer term bias, allows nonlinear interaction. Nonlinear (GAM) additive contraction bias – \(\alpha ^s\delta ^t + b_1\left( {d_1^t} \right) + b_\infty \left( {d_\infty ^t} \right)\). Additive sum of recent and longer term functions with no interactions assumed. The x axis shows the difference in AUC (area under ROC curve, larger for better predictions) between the additive GAM model with inertia (upper-most model) and the other models for each cross-validation instance (gray lines). The model that contained the response repetition covariates (x_f,x_r) was much less predictive of behavior than a two-term sensory bias GLM. Both nonlinear GAM models always outperformed the linear model. The model that contained the combined bias term \(b\left( {d_1^t,d_\infty ^t} \right)\) did not do better than the model with fitted additive terms \(b_1\left( {d_1^t} \right) + b_\infty \left( {d_\infty ^t} \right)\). Red squares and red vertical lines indicate the mean and median values of each group, respectively. Error bars show lower to upper quartile values of the data.