Altered Perception of Environmental Volatility During Social Learning in Emerging Psychosis

Paranoid delusions or unfounded beliefs that others intend to deliberately cause harm are a frequent and burdensome symptom in early psychosis, but their emergence and consolidation still remains opaque. Recent theories suggest that overly precise prediction errors lead to an unstable model of the world providing a breeding ground for delusions. Here, we employ a Bayesian approach to test for such an unstable model of the world and investigate the computational mechanisms underlying emerging paranoia. We modelled behaviour of 18 first-episode psychosis patients (FEP), 19 individuals at clinical high risk for psychosis (CHR-P), and 19 healthy controls (HC) during an advice-taking task designed to probe learning about others’ changing intentions. We formulated competing hypotheses comparing the standard Hierarchical Gaussian Filter (HGF), a Bayesian belief updating scheme, with a mean-reverting HGF to model an altered perception of volatility. There was a significant group-by-volatility interaction on advice-taking suggesting that CHR-P and FEP displayed reduced adaptability to environmental volatility. Model comparison favored the standard HGF in HC, but the mean-reverting HGF in CHR-P and FEP in line with perceiving increased volatility, although model attributions in CHR-P were heterogeneous. We observed correlations between perceiving increased volatility and positive symptoms generally as well as with frequency of paranoid delusions specifically. Our results suggest that FEP are characterised by a different computational mechanism – perceiving the environment as increasingly volatile – in line with Bayesian accounts of psychosis. This approach may prove useful to investigate heterogeneity in CHR-P and identify vulnerability for transition to psychosis.


Simulations
Supplementary Figures S1 and S2 highlight the different impact that changes in the drift equilibrium point m 3 and changes in the prior expectation about environmental volatility µ (0) 3 have on belief trajectories at different levels of the inferential hierarchy and on simulated behavior.For completeness, we also included simulations illustrating the effects of changing the coupling between hierarchical levels κ 2 (Supplementary Figure S3) and changing the evolution rate ω 2 (Supplementary Figure S4).

Simulating changes in the equilibrium point
Figure S1: Simulations showing the effect of changing the equilibrium point m 3 .Shown are trajectories of beliefs about the volatility the adviser's intentions µ 3 (upper panel), beliefs about the adviser's fidelity µ 2 (middle panel) and about the advice accuracy s(µ 2 ).Black dots indicate inputs (1: helpful advice, 0: misleading advice) and colored dots simulated responses (1: going with the advice, 0: going against the advice).Increasing m 3 (colder colours) results in larger precision-weighted prediction errors leading to stronger belief updates across all levels of the hierarchy that increase over the course of the session.The effect on behavior depends on the input structure.When agents are exposed to volatile changes between very helpful and very misleading advice (trials 68-119), higher m 3 leads agents to detect changes more rapidly (see black arrows labelled A).However, high values of m 3 also increase susceptibility to noisy inputs (e.g., trials 120-136; see black arrow labelled B).For the simulations, all other parameter values were fixed to the values of an ideal observer given the input.

Behaviour between groups across experimental blocks
To provide a more detailed description of how the behaviour differed across groups we analysed behaviour across experimental blocks (each containing 17 trials with different advice accuracy; Figure 1B, main manuscript).We identified a significant group-by-task-block interaction on the frequency of advice-taking (F = 3.419, p < 0.001).To unpack this effect we repeated the analysis with three two-group models.We found significant group-by-task-block interactions when comparing HC vs FEP (F = 5.416, p uncorr < 0.001, p < 0.001, Bonferroni-corrected for the number of comparisons, i.e. n = 3) and FEP vs CHR-P (F = 2.616, p uncorr = 0.013, p = 0.038), but the comparison between HC vs CHR-P did not survive Bonferroni correction (F = 2.241, p uncorr = 0.032, p = 0.095).Post hoc marginal contrasts revealed group differences in blocks 2 (HC vs FEP: p uncorr = 0.039, p = 0.925), block 6 (HC vs FEP: p uncorr < 0.001, p = 0.004; CHR-P vs FEP: p uncorr = 0.039, p = 0.929) and block 8 (HC vs CHR-P, p uncorr = 0.042, p = 1.000).However, only the effect of HC vs FEP in block 6 survived Bonferroni correction for 3 (#groups) x 8 (#blocks) = 24 comparisons, suggesting that FEP were adhering more to the advice, specifically in a block in which the adviser is truly misleading.However, note that FEP were not showing differences in helpful blocks (e.g., blocks 5 and 7), which suggests that this behaviour may not simply reflect giving up in volatile environments.Interestingly, similar findings have been reported in individuals with borderline personality disorder (Henco et al., 2020).None of the covariates significantly impacted advice taking.

Model comparison with simpler models
To test whether simpler models were sufficient to explain participants' behaviour in this social learning task, we conducted a supplementary analysis in which we added two simpler models to the model space, a Rescorla-Wagner model and a non-hierarchical two-level HGF.The priors for these models are reported in Table SS1.Model comparison favoured the models reported in the main manuscript (Figure SS6) in line with previous model comparisons (Cole et al., 2020;Diaconescu et al., 2014Diaconescu et al., , 2017Diaconescu et al., , 2020))).

Fixing non-recoverable parameters to test for knock-on effects
To assess whether non-recoverable parameters led to knock-on effects on other parameters, we repeated the analyses presented in the main manuscript, while fixing parameters that could not be recovered in the main manuscript to their priors (i.e., µ 3 = 1, and κ 2 = 0.5).We found that the main result (Bayesian model selection) was comparable when fixing nonrecoverable parameters (Figure SS7).
When repeating the secondary analysis investigating parameter group effects on m 3 to assess whether psychosis was associated with perceiving the environment as increasingly volatile or stable, we again found an effect on m 3 (η 2 = 0.111, p uncorr = 0.048; Figure SS8).As in the main manuscript, this effect did not survive Bonferroni correction for the number of free parameters (p = 0.191).Pairwise comparison revealed higher m 3 in CHR vs HC (p uncorr = 0.021) and a trend-effect of higher m 3 FEP vs HC (p uncorr = 0.060).Both did not survive Bonferroni correction for n = 3 groups (p = 0.063 and p = 0179).
Lastly, we found trend correlations between m 3 and PANSS positive symptoms (τ = 0.185, p uncorr = 0.058 and p = 0.175, adjusted for n = 3 PANSS scales; Figure SS8) and between m 3 and PCL frequency scores (τ = 0.163, p uncorr = 0.084 and p = 0.253, adjusted for n = 3 PCL scales).As stated in the main manuscript, although these correlations were in the expected direction, they should be assessed in a larger sample as our current results are inconclusive.A Protected exceedance probabilities for within-group random-effects Bayesian model selection (Stephan et al., 2009;Rigoux et al., 2014) to arbitrate between Hypothesis I (HI; standard 3-level HGF) and Hypothesis II (HII; mean-reverting HGF with drift at 3 rd level in line with an altered perception of volatility).Two corresponding control models were included (CI and CII), for which the perceptual model parameters were fixed.Model selection was performed separately in healthy controls (HC), individuals at clinical high risk for psychosis (CHR-P), or first-episode psychosis patients (FEP).The dashed line indicates 95% exceedance probability.B Model attributions for each participant.

Reproducibility
To ensure reproducibility of our results, we report the results excluding one participant who did not consent to make their data available for reuse and was excluded from the public repository.Our entire analysis pipeline with instructions can be found here: https://github.com/daniel-hauke/compi_ioio_phase.The data can be downloaded here: https://osf.io/6rdjc/.

Behavioural results without one participant
Excluding the participant who did not consent to reusing their data, we still identified a significant group-by-task-phase interaction on the frequency of advice-taking (F = 4.857, p = 0.012).To unpack this effect we repeated the analysis with three two-group models.We found significant group-bytask-phase interactions when comparing HC vs FEP (F = 7.128, p uncorr = 0.012, p = 0.035 Bonferroni-corrected for the number of comparisons, i.e. n = 3) and HC vs CHR-P (F = 7.745, p uncorr = 0.009, p = 0.026), but not when comparing CHR-P vs FEP (F = 0.001, p uncorr = 0.977, p = 1.000), suggesting that both CHR-P and FEP showed reduced flexibility to take environmental volatility into account as the difference between stable and volatile phase was reduced compared to HC.None of the covariates significantly impacted advice taking.

Bayesian model selection without one participant
We also repeated the Bayesian model selection including participants from all groups first.The results were again inconclusive (ϕ = 59.92%, f = 51.22% in favour of Hypothesis II) possibly suggesting that different groups were best explained by different models (i.e., different computational mechanisms).To assess this possibility, we repeated the model selection for each group separately.In HC, the winning model was the standard 3-level HGF (Hypothesis I; ϕ = 96.63%,f = 95.93%).Conversely, in FEP the mean-reverting HGF that included a drift at the third level was selected (Hypothesis II; ϕ = 99.89%,f = 95.69%).For CHR-P, we observed a more heterogeneous results: While the mean-reverting model was favoured (Hypothesis II; ϕ = 84.50%,f = 60.24%),there was also evidence for the standard HGF, albeit to a much lesser extent (Hypothesis I; ϕ = 14.41%, f = 37.19%).Further inspection of the model attributions for all individual participants revealed an interesting pattern.All HC were attributed to the standard HGF with over 97% probability, whereas FEP were attributed to the mean-reverting model with over 99%.Interestingly, model attributions for CHR-P were more heterogeneous ranging from 0 to 100% probability, suggesting that some individuals were better explained by the standard HGF, but others by the mean-reverting model.

Parameter group effects without one participant
In the reduced sample, the drift equilibrium point m 3 significantly differed across the groups (η 2 = 0.130, p uncorr = 0.030).Post hoc tests revealed that m 3 was increased in FEP compared to HC suggesting that FEP perceived the intentions of the adviser as increasingly more volatile over time (η 2 = 0.191, p = 0.029, Bonferroni-corrected for the number of comparisons across groups, i.e., n = 3).We also performed an exploratory analysis including all other free model parameters.This analysis revealed an additional effect on coupling strength κ 2 (η 2 = 0.157, p uncorr = 0.014), which was driven by reduced coupling strength between the second and third level of the perceptual hierarchy in FEP compared to HC (η 2 = 0.245, p = 0.010, Bonferroni-corrected for the number of comparisons across groups, i.e., n = 3).However, neither the effect on m 3 nor κ 2 survived Bonferroni correction for the number of parameters, i.e. n = 7 (p = 0.207 and p = 0.100, respectively), possibly due to a lack of power.
Similarly, there was only a trend correlation when excluding this subject between m 3 and the PCL frequency subscale (τ = 0.170, p uncorr = 0.079, p = 0.475 Bonferroni-adjusted for 2 (#parameters) x 3 (#PCL subscales) = 6 comparisons).Note, that the participant that did not consent to reuse of their data scored high on positive symptoms which likely contributes to the changes in the correlations compared to the full sample.However, as we pointed out in the main manuscript these correlation results should be taken as preliminary due to the small sample size of this study.

Figure S2 :
Figure S2: Simulations showing the effect of changing the prior expectation about environmental volatility µ (0) 3 .Shown are trajectories of beliefs about the volatility the adviser's intentions µ 3 (upper panel), beliefs about the adviser's fidelity µ 2 (middle panel) and about the advice accuracy s(µ 2 ).Black dots indicate inputs (1: helpful advice, 0: misleading advice) and colored dots simulated responses (1: going with the advice, 0: going against the advice).Increasing µ (0) 3 (colder colours) results in changes primarily in the first trials of the session and changes do not propagate strongly to lower levels.

Figure S3 :
Figure S3: Simulations showing the effect of changing the coupling strength κ 2 .Shown are trajectories of beliefs about the volatility the adviser's intentions µ 3 (upper panel), beliefs about the adviser's fidelity µ 2 (middle panel) and about the advice accuracy s(µ 2 ).Black dots indicate inputs (1: helpful advice, 0: misleading advice) and colored dots simulated responses (1: going with the advice, 0: going against the advice).

Figure S4 :
Figure S4: Simulations showing the effect of changing the evolution rate ω 2 .Shown are trajectories of beliefs about the volatility the adviser's intentions µ 3 (upper panel), beliefs about the adviser's fidelity µ 2 (middle panel) and about the advice accuracy s(µ 2 ).Black dots indicate inputs (1: helpful advice, 0: misleading advice) and colored dots simulated responses (1: going with the advice, 0: going against the advice).

Figure S5 :
Figure S5: Behaviour between groups and across experimental block.The black line indicates the average advice accuracy of each block.Horizontal lines and squares in box plots represent median and mean, respectively.Boxes span the 25 th to 75 th quartiles and whiskers extend from hinges to the largest and smallest value that lies within 1.5× interquartile range.Asterisks indicate significance of marginal tests at: ** p < 0.01, using Bonferroni correction, adjusted for 3 (#groups) x 8 (#blocks) = 24 comparisons, or at + p < 0.05 uncorrected.
Model parameter overview for simpler models.Prior parameter values were chosen based on the references indicated next to prior means and variances.a Cole et al. (2020).a Cole et al. (2020).b Diaconescu et al. (2014).c Hauke et al. (2018).

Figure S6 :
Figure S6: Bayesian model selection results with simpler models.A Protected exceedance probabilities for within-group random-effects Bayesian model selection(Stephan et al., 2009;Rigoux et al., 2014) to arbitrate between Hypothesis I (HI; standard 3-level HGF) and Hypothesis II (HII; mean-reverting HGF with drift at 3 rd level in line with an altered perception of volatility).Two corresponding control models were included (CI and CII), for which the perceptual model parameters were fixed.Additionally, two simpler models, a Rescorla-Wagner model (RW) and a 2-level HGF (2lHGF), were included in this extended comparison.Model selection was performed separately in healthy controls (HC), individuals at clinical high risk for psychosis (CHR-P), or first-episode psychosis patients (FEP).The dashed line indicates 95% exceedance probability.B Model attributions for each participant.

Figure S7 :
Figure S7: Bayesian model selection results with fixed non-recoverable parameters.A Protected exceedance probabilities for within-group random-effects Bayesian model selection(Stephan et al., 2009;Rigoux et al., 2014) to arbitrate between Hypothesis I (HI; standard 3-level HGF) and Hypothesis II (HII; mean-reverting HGF with drift at 3 rd level in line with an altered perception of volatility).Two corresponding control models were included (CI and CII), for which the perceptual model parameters were fixed.Model selection was performed separately in healthy controls (HC), individuals at clinical high risk for psychosis (CHR-P), or first-episode psychosis patients (FEP).The dashed line indicates 95% exceedance probability.B Model attributions for each participant.

Figure S8 :
Figure S8: Parameter group effects with fixed non-recoverable parameter.A Parameter effect for drift equilibrium point m 3 .B Correlation between model parameters and either Positive and Negative Syndrome Scale (Kay et al., 1987) (PANSS) or Paranoia Checklist (Freeman et al., 2005) (PCL).Note, that raw scores are displayed for illustration purposes only.Statistical analyses were conducted using nonparametric Kendall rank correlations.Displayed regression lines were computed using a linear model based on the raw scores.P: Positive symptoms.Boxes span the 25 th to 75 th quartiles and whiskers extend from hinges to the largest and smallest value that lies within 1.5× interquartile range.