Supplementary Fig. 3: Cross-validations of GAM shows that bias-by-longer-term is distribution-specific, whereas bias-by-recent is distribution invariant.
From: Perceptual bias reveals slow-updating in autism and fast-forgetting in dyslexia
Assuming separate b∞(d∞) functions for each distribution (n = 490) significantly improves the performance of the model (W = 1, p = 0.007, two-sided Wilcoxon signed-rank, cross-validation), but adding a distribution-specific b1(d1) function does not (W = 12, p = 0.11, two-sided Wilcoxon signed-rank, cross-validation). We compared 4 models using 10-fold cross-validation scores over the aggregated data collected via M-Turk for 4 distributions (Broad uniform, Narrow uniform, Gaussian and Bimodal). All models, fitted with GAM, included the same term with pre-fitted sensitivities per-participant -αsδt, but had different terms of the recent (b1(d1)) and longer term (b∞(d∞)) bias functions. The models differed in the number of fitted functions, specifically, whether a single function was fitted for all distributions, or 4 distribution-specific functions were fitted: - Recent and longer term components are each shared across distributions – b1(d1) + b∞(d∞) - Recent and longer term components are each fitted separately for each distribution – \(\mathop {\sum}\nolimits_{i = 1}^4 {b_1\left( {d_1} \right)_i} + \mathop {\sum}\nolimits_{i = 1}^4 {b_\infty \left( {d_\infty } \right)_i}\), where i denotes the distribution. - Longer term component shared across distributions, recent component fitted separately – \(\mathop {\sum}\nolimits_{i = 1}^4 {b_1\left( {d_1} \right)_i + b_\infty \left( {d_\infty } \right)}\) - Recent component shared across distributions, longer term component fitted separately – \(b_1\left( {d_1} \right) + \mathop {\sum}\nolimits_{i = 1}^4 {b_\infty \left( {d_\infty } \right)_i}\). The last model (top in the plot) yielded the best predictive performance. The x axis shows the difference in AUC (area under ROC curve, larger for better predictions) between the best model (upper mode) and each of the other 3 models. Red squares and red vertical lines indicate the mean and median values of each group, respectively. Gray lines correspond to each cross-validation instance. Error bars show lower to upper quartile values of the data.
