Extended Data Fig. 2: Model S–R–8, the S–R equivalent of winning model S–S–R–8, replicates some of the results concerning participants’ (n = 44) group-level behavior (panels a and b) but not the result that requires state inference (panel c).
This figure is equivalent to Fig. 4 but for model S–R–8 rather than model S–S–R–8. a, Average (±s.e.m.) Go probability, P(Go), for each season type: rewarding (R), neutral (N) and punishing (P). We analyzed the model fits using the approach described in the caption of Fig. 4a. Like for participants (see caption of Fig. 4a), P(Go) for the fits of model S–R–8 was largest for rewarding, intermediate for neutral and smallest for punishing seasons (main effect of season type: \({\chi }_{2}^{2}=971.71\), P < 10−16; repeated contrasts: rewarding versus neutral, b = 0.68, z = 8.79, two-sided P < 10−16, 95% CI (0.53, 0.83), OR = 1.97; neutral versus punishing, b = 1.39, z = 23.41, two-sided P < 10−16, 95% CI (1.27, 1.50), OR = 4.00). b, Average (±s.e.m.) P(Go) as a function of the shell phase, for each shell. The fits from model S–R–8 tracked the changes in participants’ choices as the seasons changed. c, Average (±s.e.m.) probability of a correct response, P(Correct), in the phases following the first and second identical state transitions: phases 2 and 4, respectively. As in Fig. 4c, P(Correct) was calculated using only R and P seasons, as there was no correct response for N seasons. We analyzed P(Correct) using a rmANOVA with independent variables phase (2 versus 4) and data type (participants versus fits of the S–R–8 model). As expected, the interaction was significant (F1,43 = 11.19, P = 0.002, \({\eta }_{p}^{2}=0.21\)). Planned contrasts confirmed that P(Correct) was significantly greater in phase 4 than in phase 2 for participants (mean difference = 0.05, t43 = 2.61, two-sided P = 0.012, 95% CI (0.01, 0.10), Cohen’s d = 0.39), like in Fig. 4c, but not for fits of the S–R–8 model (mean difference = 0.00, t43 = 0.01, two-sided P = 0.994, 95% CI (–0.02, 0.02), Cohen’s d = 0.00). Thus, unlike participants and model S–S–R–8 (Fig. 4c), model S–R–8 did not show better performance in phase 4 than in phase 2. NS: not significant; *P < 0.05; ***P < 0.001.
