Table 4.

Models of increasing complexity used for Bayesian linear mixed models analyses

Study #	Model #	Model
1–2
	1	y ∼ 1 + (1|subject)
	2	y ∼ 1 + group + (1|subject)
	3	y ∼ 1 + group + x + (1|subject)
	4	y ∼ 1 + group * x + (1|subject)
	5	y ∼ 1 + group * x + (1 + x|subject)
	6	y ∼ 1 + group * x + (1 + x|subject) + (1|trial)
3
	1	y ∼ 1 + (1|subject)
	2	y ∼ 1 + x + (1|subject)
	3	y ∼ 1 + x + (1 + x|subject)
	4	y ∼ 1 + x + (1 + x|subject) + (1|trial)

Models of increasing complexity used in Studies 1 and 2 (top) and Study 3 (bottom). In Studies 1 and 2, y corresponds to the motor performance (log_mIKI or log_RT); x is the unsigned centered value of the prediction about the tendency of the action-reward contingency (|${\widehat{\mu }}_2$|_c). This parameter represents the strength of the predictions. In model 1, y is explained by a fixed effect of the intercept and a random effect of intercept by subject (the latter accounts for repeated measurements); model 2 adds a fixed effect of group; model 3 includes the fixed effect of x, which allows to assess the sensitivity (slope) of performance tempo or RT to |${\widehat{\mu }}_2$|_c in the reference group; model 4 incorporates the interaction term between group and x, which allows to investigate the between-group differences in the sensitivity (slope) of performance tempo or RT to |${\widehat{\mu }}_2$|_c; model 5 includes the random effect of |${\widehat{\mu }}_2$|_c by subject; last, model 6 includes a random effect of intercept by trial. In Study 3, y corresponds to the motor performance (log_mIKI or log_RT); x is the confidence rating. In model 1, y is explained by a fixed effect of the intercept and a random effect of intercept by subject (the latter accounts for repeated measurements); model 2 adds a fixed effect of x, which allows to assess the sensitivity (slope) of performance tempo or RT to confidence ratings; model 3 includes the random effect of confidence ratings by subject; last, model 4 includes a random effect of intercept by trial.