Figure 1
Social learning task and volatility schedule. A Social learning task. B Volatility schedule.
Table 1
Model parameter overview. Prior parameter values were chosen based on the references indicated next to prior means and variances. aCole et al. (2020). bDiaconescu et al. (2014). cHauke et al. (2018).
| HYPOTHESIS I: HGF AND HYPOTHESIS II: MEAN-REVERTING HGF | |||||||
|---|---|---|---|---|---|---|---|
| PARAMETER | MODEL COMPONENT | PRIOR MEAN | PRIOR VARIANCE | TRANSFORMATION | BOUNDS | FIXED? | BASED ON |
| κ2 | Perceptual Model | 0.5a,b,c | 1a,b,c | logit | [0, 1] | – | |
| ω2 | Perceptual Model | –2b,c | 4c | – | (–∞, +∞) | – | |
| θ | Perceptual Model | 0.5a,b,c | 0c | logit | [0, 1] | Yes | c |
| Perceptual Model | 0a,b,c | 1a,b,c | – | (–∞, +∞) | – | ||
| Perceptual Model | 1a,b,c | 0a,c | log | [0, +∞) | Yes | a,c | |
| Perceptual Model | 1a,b,c | 1b,c | – | (–∞, +∞) | – | ||
| Perceptual Model | 1b,c | 0c | log | [0, +∞) | Yes | c | |
| ζ | Response Model | 0.5b,c | 1b,c | logit | [0, 1] | – | |
| ν | Response Model | 48a,b,c | 1a,b,c | log | [0, +∞) | – | |
| HYPOTHESIS II: MEAN-REVERTING HGF | |||||||
| PARAMETER | MODEL COMPONENT | PRIOR MEAN | PRIOR VARIANCE | TRANSFORMATION | BOUNDS | FIXED? | BASED ON |
| m3 | Perceptual Model | 1a,c | 1a,c | – | (–∞, +∞) | – | |
| ϕ3 | Perceptual Model | 0.1a,c | 0a,c | logit | [0, 1] | Yes | a,c |
Figure 2
Simulating an altered perception of environmental volatility. Simulations showing the effect of changing the equilibrium point m3. Increasing m3 (colder colours) corresponds to perceiving the environment as increasingly volatile and results in larger precision-weighted prediction errors leading to stronger belief updates across all levels of the hierarchy. Note, that high values of m3 also increase susceptibility to noisy inputs (e.g., trials 120–136). We hypothesised that this would be the case in early stages of psychosis. Reducing m3 (warmer colours) on the other hand corresponds to perceiving the environment as increasingly stable and leads to reduced learning rates rendering an agent insensitive to true changes in the environment. We hypothesised that this could correspond to explaining away overly precise prediction errors and would be associated with delusional conviction. For the simulations, all other parameter values were fixed to the values of an ideal observer given the input.
Figure 3
Model space. Left: Standard 3-level Hierarchical Gaussian Filter (HGF). (Mathys et al., 2011, 2014) Right: Mean-reverting HGF with a drift at the third level, which captures learning about the volatility of the adviser’s intentions. This model expresses the notion that early psychosis may be characterised by an altered perception of environmental volatility.
Table 2
Demographic and clinical characteristics. All p-values are uncorrected. HC: Healthy controls. CHR-P: Individuals at clinical high risk for psychosis. FEP: First-episode psychosis patients. APS: Attenuated psychotic symptoms. BLIP: Brief and limited intermittent psychotic symptoms. GRD: Genetic risk and deterioration syndrome. COGDIS: Cognitive disturbances. COPER: Cognitive-perceptive basic symptoms. Cpz100mg/day: Antipsychotic equivalent dose for 100mg chlorpromazine per day. Flu40mg/day: Antidepressant equivalent dose for 40mg fluoxetine per day. PANSS: Positive and Negative Syndrome Scale.(Kay et al., 1987) PCL: Paranoia Checklist (Freeman et al., 2005). Bold print highlights p-values significant at: p < 0.05, uncorrected. a Assessed with the digit span backwards task from the Wechsler Adult Intelligence Scale–Revised (Wechsler, 1981). bHigh risk types are not mutually exclusive.
| HC n = 19 | CHR-P n = 19 | FEP n = 18 | TEST STATISTIC | POST HOC CONTRASTS | |
|---|---|---|---|---|---|
| Age mean [SD] | 21.37 [2.52] | 21.05 [3.52] | 33.44 [11.70] | F = 18.182 p < 0.001 | FEP > HC FEP > CHR-P |
| IQ mean [SD] | 108.11 [9.85] | 105.95 [12.28] | 112.29 [16.25] | F = 1.015 p = 0.370 | |
| Working memorya mean [SD] | 6.42 [1.71] | 6.74 [2.16] | 5.83 [1.98] | F = 1.011 p = 0.371 | |
| Sex [f/m] | 11/8 | 11/8 | 7/11 | χ2 = 1.767 p = 0.413 | |
| Cannabis [y/n] | 7/12 | 8/11 | 5/13 | χ2 = 0.842 p = 0.656 | |
| High risk typeb | |||||
| APS | 15 | ||||
| BLIP | 1 | ||||
| GRD | 0 | ||||
| COGDIS | 4 | ||||
| COOPER | 2 | ||||
| Psychotic disorder diagnosis | |||||
| F20 Schizophrenia | 3 | ||||
| F22 Delusional disorder | 6 | ||||
| F23 Brief psychotic disorder | 9 | ||||
| Antipsychotics [y/n] | 0/19 | 2/17 | 14/4 | χ2 = 31.987 p < 0.001 | FEP > CHR-P FEP > HC |
| Aripiprazole | 4 | ||||
| Brexpiprazole | 1 | ||||
| Lurasidone | 1 | ||||
| Olanzapine | 5 | ||||
| Paliperidone | 1 | ||||
| Quetiapine | 2 | ||||
| Risperidone | 1 | ||||
| Haloperidol & Aripiprazol | 1 | ||||
| Antidepressants [y/n] | 0/19 | 9/10 | 1/17 | χ2 = 17.268 p < 0.001 | CHR-P > FEP CHR-P > HC |
| Buproprion | 1 | ||||
| Citalopram | 1 | ||||
| Escitalopram | 1 | ||||
| Fluoxetine | 1 | ||||
| Sertraline | 1 | ||||
| Vortioxetin | 2 | ||||
| Trazodon & Citalopram | 1 | ||||
| Trazodon & Sertralin | 1 | ||||
| Unknown | 1 | ||||
| Cpz100mg/day median [25th, 75th] | 0n= 19 [0, 0] | 0n= 18 [0, 0] | 83n= 18 [33, 188] | η2 = 0.592 p < 0.001 | FEP > CHR-P FEP > HC |
| Flu40mg/day median [25th, 75th] | 0n= 19 [0, 0] | 0n= 17 [0, 30] | 0n= 18 [0, 0] | η2 = 0.246 p = 0.001 | CHR-P > HC |
| PANSS Positive median [25th, 75th] | 8n= 19 [7, 8] | 11n= 19 [10, 14] | 16n= 16 [11, 23] | η2 = 0.514 p < 0.001 | FEP > CHR-P > HC |
| PANSS Negative median [25th, 75th] | 7n= 19 [7, 8] | 9n= 19 [8, 10] | 12n= 16 [9, 15] | η2 = 0.364 p < 0.001 | FEP > CHR-P > HC |
| PANSS General median [25th, 75th] | 18n= 19 [16, 19] | 29n= 19 [22, 32] | 34n= 16 [32, 40] | η2 = 0.674 p < 0.001 | FEP > CHR-P > HC |
| PCL Frequency median [25th, 75th] | 23n= 19 [19, 25] | 30n= 19 [24, 33] | 36n= 17 [23, 44] | η2 = 0.202 p = 0.004 | FEP > HC CHR-P > HC |
| PCL Conviction median [25th, 75th] | 26n= 19 [22, 31] | 33n= 19 [28, 39] | 30n= 17 [22, 55] | η2 = 0.086 p = 0.099 | |
| PCL Distress median [25th, 75th] | 26n= 19 [20, 37] | 29n= 19 [23, 38] | 30n= 17 [21, 46] | η2 = 0.008 p = 0.799 |
Figure 4
Behavioural results and parameter group effects. A Behavioural results (ground truth). Black dashed lines indicate the average accuracy of advice for each of the two phases. B Model prediction. C Parameter effect for drift equilibrium point m3. D Parameter effect for coupling strength κ2. E 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. Note, that one outlier (κ2 = 0.006) was removed for displaying the effect on κ2 in D and E. This outlier was outside of 7 × the interquartile range. Excluding this participant did not affect the significance of the results. P: Positive symptoms. N: Negative symptoms. G: General symptoms. F- and p-values indicate results of ANCOVAs corrected for working memory performance, antipsychotic medication, antidepressant medication, and age. Boxes span the 25th to 75th quartiles and whiskers extend from hinges to the largest and smallest value that lies within 1.5 × interquartile range. Asterisks indicate significance of non-parametric Kruskal-Wallis tests at: * p < 0.05, using Bonferroni correction.
Figure 5
Bayesian model selection results. 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 3rd 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% protected exceedance probability. B Model attributions for each participant.
Figure 6
Model diagnostics. A–G Parameter recovery result for one random seed for the mean-reverting HGF with drift at the 3rd level (Hypothesis II; Figure 3). H Parameter correlations computed across subjects for the mean-reverting HGF with a drift at the 3rd level (Hypothesis II; Figure 3). I Model recovery analysis. The grey scale indicates protected exceedance probability averaged across all 20 random seeds.