Statistical inference
INSULIN SENSITIVITY
All behavioural, blood and anthropomorphic data were analysed using RStudio (version 1.4.1717) and R (version 4.0.0). First, we performed normality testing using ‘Q-Q plots’ in R. If residuals were normally distributed, analysis of variance (ANOVA) tests based on mixed effect models (test statistic Considering the above-discussed computational states of learning behaviour (that is, sensory prediction error, adaptive learning rate and adaptive prediction error), we first tested whether impaired insulin sensitivity in participants impacts learning behaviour. Here, we applied independent To scrutinize for the effect of liraglutide intervention, we first assessed the effects of group and intervention on sensory prediction error as a basic component of learning. To account for other task-dependent features that changed from trial to trial, we additionally included correctness (incorrect or correct participant response) and predictability (the true probability for the visual outcome dependent on the current cue–outcome association strength varying between 0.9, 0.7, 0.5, 0.3 and 0.1; see task description above). To simplify the analysis, we followed a summary statistics approach and computed a mean sensory prediction error separately for each participant and separately for all possible factor combinations (five predictability levels × two correctness levels). As introduced above, we used absolute sensory prediction errors in our behavioural model. This resulted in the following model:We tested whether liraglutide (relative to placebo) affected the choice prediction error differently in the ISThereafter, we tested the effect of intervention and group on the adaptive learning rate, which reflects the relative impact of sensory prediction error on behavioural updating. The adaptive learning rate is always positive and depends on the variance of the cue predictability (three instead of five levels) rather than on correctness and the predictability itself; thus, we used the following model (Supplementary Table Finally, we scrutinized the effect of group and intervention on the size of the adaptive prediction error, the result from the modulation of the sensory prediction error by the adaptive learning rate and the ultimate readout reflecting the size of the actual behavioural update. Note that here we also ignored the sign of the prediction error (see above); hence, in congruence with MAll post hoc analyses and comparisons were calculated using the Tukey’s procedure ‘lsmeans’ R package (version 2.30-0) for the group × intervention contrasts. Effect size measures (Cohen’s 