Figure 3. Hierarchical structure of the model space and model selection results.

(a) The learning and arbitration models considered in this study have a 3 × 3 factorial structure and can be displayed as a tree. The nodes at the top level represent the perceptual model families (three-level HGF, normative HGF, two-level non-volatility HGF). The leaves at the bottom represent response models which integrate and arbitrate between social and individual sources of information (‘Arbitrated’) or exclusively consider social (‘Advice’) or individual (‘Card’) information. (b) Random effects Bayesian model selection revealed one winning model, the Arbitrated three-level HGF. Posterior model probabilities or $p\left(m\right|y)$ indicated that this model best explained participants’ behavior in the majority of the cases.