Together, food choices, preferences, and choice-preference functions can be used to elucidate the mechanisms underlying the PHS effects. If choices and preferences for healthy food items are increased in the PHS-activated compared to the PHS-deactivated condition, but if the choice-preference function is unaffected, one can conclude that the PHS modulates choices by affecting explicit preferences. In contrast, if choices of healthy food items are increased but preferences are not, then a decrease in the choice-preference function's slopes or a positive choice bias may indicate that the PHS affects implicit food preferences that are not explicitly accessible. Finally, the increase in preferences without any modulation of choices but accompanied by increased slopes of the choice-preference function or induction of negative bias for healthy items indicates that the PHS can only affect explicit preferences that are insufficient for affecting choices.

Concerning unhealthy food items, if preferences and choices are decreased, a stable choice-preference function indicates that the PHS modulates choices by affecting explicit food preferences. In contrast, if choices of unhealthy food items are reduced but not preferences, an increase in slopes of the choice-preference function and/or a negative choice bias should be expected. This can be interpreted as related to an increased contribution of top-down cognitive control in food choices. Notably, for unhealthy food items, we expect any decrease in preferences to be accompanied by a decrease in choices.

Furthermore, we expected the PHS effects on food choice and food preferences to be stable across sessions. Finally, participants' hypnotizability should be correlated with the observed behavioral effects.

Of the respondents to our advertisements, 55 (43 female, mean Age = 26.9 [19 − 39] years±6.03) were recruited in the study, of which 50 (38 female, mean Age = 26.6 [19 − 39] years±5.70) completed all three sessions. The minimum sample size of 40 participants had been based on a priori power analysis with α<0.05, 1-β>0.95, ηp2>0.08. The critical values were determined based on the suggestion of Cohen (2016), and the effect size was based on previous results (e.g., Zahedi et al., 2020a). Notably, Zahedi et al. (2020a) found a medium effect size of ηp2 = 0.22. However, since only medium- and high-hypnotizable participants were included in that sample, we adjusted the expected effect size for the current study from medium, i.e., ηp2 = 0.22, to small, i.e., , ηp2 = 0.08. This adjustment ascertained that in the current study, where participants were included regardless of their hypnotizability scores, we have the statistical power to detect possible effects. Notably, the a priori power analysis, in tandem with the Bayesian statistics used, gives us the necessary tools to interpret possible null results appropriately, as well.

The exclusion criteria were being either underweight (BMI <18) or obese (BMI > 30), or having a history of psychological or neurological problems. The criteria for healthy body weight were selected based on the recommendation of WHO (2022). However, all volunteers met the inclusion criteria, and therefore, no one had to be excluded (mean BMI was 22.0 [18.0 − 27.1]±2.40). The study was approved by the ethics committee of the Department of Psychology of the Humboldt-Universität zu Berlin (approval number 2021-36). Prior to the experiment, informed consent was obtained according to the declaration of Helsinki, and participation was compensated with 10 Euro/hour (N = 25) or course credits (N = 30). The study was conducted fully online.

The hypnotizability of participants was measured by the German version (Bongartz, 1985) of the Harvard group scale of hypnotic susceptibility—form A (HGSHS: A; Shor and Orne, 1962). In HGSHS: A, 12 different suggestions are delivered to participants, and their responsiveness is determined based on the number of items to which they could respond (based on self-reports). According to the scoring procedure suggested by Kihlstrom and Register (1984), scores between 0 and 12 can be achieved.

Other questionnaires to be completed were the Edinburgh Handedness Questionnaire (EHQ; Oldfield, 1971), the German Nutrition Knowledge Questionnaire (NKQ; De Souza et al., 2015), and the Self-Regulation of Eating Behavior Questionnaire (SREBQ; Kliemann et al., 2016). EHQ consists of 20 questions, evaluating which hand is usually used for administrating specific tasks, such as writing or throwing. The NKQ consists of 22 questions about the knowledge of healthy food choices and the sources of nutrients in food. The SREBQ consists of four questions aiming to evaluate an individual's capacity for regulating their eating behavior.

The online supermarket (Figure 1) was based on eight food categories, including 170 products in total. The organization and items were inspired by existing online shops and aimed to simulate real-life online food shopping behavior. For instance, a diverse array of options was presented for each product (i.e., full-fat and low-fat milk) to enable participants to choose their preferred items. The eight categories of food items in the supermarket are as follows:

After choosing a food category, between 16 and 26 images per category were shown with the name underneath. Further, the nutrition facts for each item could be inspected by clicking a corresponding button on the screen (“Nährwertangaben”). Each item could be placed in the shopping basket by pressing a corresponding button on the screen (“in den Warenkorb legen”). The package sizes per item were relatively small, equal to approximately one serving; for example, participants could choose to buy a single egg or a single potato. However, there was no limit to the number of a given item that could be placed in the shopping basket. Also, participants could directly select a specific number (i.e., 1 ≤ n ≤ 20) of each item. The shopping basket could be inspected to correct the number of items in the basket before placing the final order.

The online supermarket was introduced with the instructions that participants should imagine that they have to quarantine for 1 week. All food they wanted to consume during this period had to be ordered from the online supermarket. They had no budget limit and could choose as many products as desired. The only restriction was the time limit of 15 min for the supermarket task. The shopping task is publicly available for non-commercial use; please see Supplementary material for further information.

In the food preference rating task, participants were shown all the food items offered in the supermarket task in randomized order. Participants were to rate each item for how much they liked it in principle, independently of whether they wanted it at the moment. Ratings were performed on a Likert scale from 1 (Don't like it at all) to 7 (Like it very much). There was a response window of 20 s for each item, after which the trial was considered a miss. The food preference rating task required about 10 min.

The experiment was conducted online via the Zoom platform and involved three sessions. All questionnaires were implemented through the SoSci Survey platform (Version 3.0. 01, www.soscisurvey.de), and the individualized links were sent to participants in real time during each session. In Session 1, written informed consent was obtained, and demographic information (i.e., age, sex, height, weight, educational background), NKQ, and SREBQ were collected. Afterward, the German version of HGSHS: A was administered to determine the hypnotic susceptibility of participants. We did not exclude any participants based on the screening results. Instead, susceptibility scores were used as a regressor in subsequent analyses. Session 1 took about 2 h and was conducted as an online group session with up to five participants. About 1 week (mean = 8.51 ± 1.26 days) after Session 1, Session 2 was conducted, lasting about 2 h, followed by Session 3 after 3–10 days (mean = 6.24 ± 2.28 days), which took about 1 h. In Sessions 2 and 3, participants were tested individually. Session 2 started with hypnosis that included a PHS aiming to induce a strong desire for healthy food. The hypnosis procedure and the employed PHS (for details, see Appendix A) were the same as in Zahedi et al. (2020a). Next, the food preference rating and the online supermarket were administrated twice, once with the PHS activated and once deactivated. The order of conditions (i.e., PHS activated and deactivated) was counterbalanced across participants. Session 3 was identical in its procedure to Session 2, except that no hypnosis was applied. The order of PHS activation and deactivation for each participant was the same as in Session 2.

Based on our previous results (Zahedi et al., 2020a), we expected that posthypnotic suggestions would increase subjective preferences for healthy food items and decrease the subjective preferences for unhealthy food without affecting the choice-preference function. That means participants choose what they want based on the same principles as before, and therefore, the choice-preference function is unaltered. Thus, if preferences for healthy food items are increased, participants will choose more healthy food while the choice-preference function remains the same. Alternatively, choices may change, although preferences have not. In this case, the choice-preference function will also be affected, indicating that other mechanisms, such as increased suppression of temptation, must be considered as the driver of the changes. Finally, if preferences or choices of neutral food items (i.e., control items) were modulated, it reveals the opportunistic strategy used in response to experimental manipulation.

Independently from food categories, online supermarket items were categorized regarding their healthiness. Following Clark et al. (2019), we categorized the following items as healthy: (1) vegetables, (2) fruits, (3) legumes, and (4) some fish and marine products. Unhealthy food items were: (1) red meat, (2) processed and ultra-processed food, and (3) sugary and salty snacks. The choice set also contained items neither belonging to the healthy nor unhealthy food category and represented neutral items, used as our control items in subsequent analyses. The complete list of food items and their healthiness category can be found in the Supplementary material.

By conducting Bayesian generalized linear modeling, we investigate whether the PHS condition and its interaction with health categories and time (i.e., Session 2 or Session 3) affected the targeted outcome. Two main outcomes were the focus of our analyses: subjective food preferences, as measured by the food rating task, and food choices, as measured by the online shopping task. Depending on the outcome in focus, the models are either denoted as a Preference Model or Choice Model. In each model, the PHS condition (PHS-activated vs. PHS-deactivated), Session (Session 2 vs. Session 3), Healthiness of food items (healthy, neutral, and unhealthy), and the interaction between these factors were included as fixed effects. The intercept for all models was the healthy category, PHS-deactivated, Session 2. Further, three random effects were assumed: (1) a random intercept for the participants, (2) a random intercept for food items, and (3) a random slope for participants' hypnotizability on the PHS and Healthiness interaction (Model 1; Equation 1).

Three additional models were compared to the full model (Model 1) to gauge whether adding each factor improved the model's predictive capability: a model with only random intercepts (Model 4; Equation 4), a model with random intercepts and the fixed effect of Healthiness (Model 3; Equation 3), and a model with random intercepts and slope and the fixed effects of PHS and Healthiness (Model 2; Equation 2).

Further, when a significant behavioral result was observed, we tested the Bayesian equivalent of the robust correlation between the observed effects and the hypnotizability scores.

The results of the food rating and the online supermarket tasks were used to calculate logistic regression models (McKerchar et al., 2009; Scherbaum et al., 2012). For calculating these choice-preference functions, choices were entered into the model as binary input (i.e., yes = 1, no = 0) and subjective ratings as continuous predictors. The output of the model represents the probability of choosing an item, given the subjective rating for that item:

where x designates subjective rating, Y choice, j participant number, i session, k food category, and β₀ and β_l are model parameters. The choice-preference functions were analyzed with the same approach used for assessing subjective ratings and food choices. The only difference is that subjective food ratings will always be used as a regressor in the models (from the baseline model to the full model). Further, the outcome will be a binary choice variable for each item, condition, and participant rather than the number of chosen items, which was used in Choice Models (Equation 6).

All statistical analyses were conducted using the R programming language (http://www.R-project.org/). For calculating Bayesian hierarchical generalized linear models, brms (Bürkner, 2017) and RSTan (https://mc-stan.org/) were employed. The robust Bayesian correlations were calculated using RStan (https://mc-stan.org/). As all the models were multilevel, uninformative priors were preferred (Bürkner, 2017). Hence, we used N(0, 2.5) as uninformative priors in the models for β coefficients, student−t(3, 0, 2.5) for standard deviations, and gamma(0.01, 0.01) for shape when necessary. Subjective food ratings, food choices, and choice-preference functions were modeled using cumulative, negative binomial, and logistic families, respectively. All models were calculated with ten chains, each having 5,000 iterations with 1,000 warmups. If any variable showed a Rhat (i.e., the potential scale reduction factor on split chains) above 1.05, the model was recalculated with increased iterations and reported accordingly. For the model comparison, we used the Pareto smoothed importance sampling (PSIS) estimation of leave-one-out cross-validation (loo) implemented in the loo package (Vehtari et al., 2016; Magnusson et al., 2020).

All hypotheses were tested using the hypothesis package from brms (Bürkner, 2017). Based on the suggestion of van Doorn et al. (2021), Bayes factors(BF)>3 were considered as significant evidence for the tested hypothesis. One-sided hypotheses (BF₊₀ and BF₀₊) were the comparison of the posterior probability of hypotheses against their alternative; two sided-tests (BF₁₀ and BF₀₁) were the comparison between hypotheses and their alternative computed via the Savage-Dickey density ratio method.

First, to investigate the effectiveness of our PHS, we analyzed participants' subjective preferences (Figure 2A). The full Preference Model (Equation 1) tested the effect of PHS, Session, and Healthiness on subjective food ratings. The full Preference Model (Equation 1) had no divergent transition, all Rhat = 1.00, and all variables had bulk- and tail-effective sample sizes >2,000 and >5,000. Posterior checks showed that the cumulative count model simulations reasonably captured the features of the observed data, including distributions (Figure 2B), means of different conditions (Figure 2C), and dispersion (Figure 2D).

After confirming the validity of the Preference Model, the posteriors drawn from it were used to test our hypotheses (Figure 3). The results showed that activating PHS (PHS+) increased preferences for healthy food items (H₊:ConditionPHS>0; mean = 0.39[0.28, 0.49], sd = 0.07, p.p.>0.99, BF₊₀>9999). Further, activating PHS did not affect the preferences for neutral items (H₀:ConditionPHS+ FoodItemHealthN:ConditionPHS = 0; mean = 0.06[−0.8, 0.19], sd = 0.08, p.p. = 0.97, BF₀₁ = 33.65). Further, activating PHS probably decreased preferences for unhealthy items (H₊:ConditionPHS+ FoodItemHealthU:ConditionPHS < 0; mean = −0.06[−0.16, 0.04], sd = 0.06, p.p. = 0.84, BF₊₀ = 5.19). Notably, although the results indicate that preferences for healthy food items were increased by PHS+, the evidence supporting a concomitant decrease in preferences for unhealthy food items is not strong. Given that zero is within the 95% confidence interval of alterations in unhealthy food preferences due to PHS, one should interpret this result with caution. Hence, although our results indicate that unhealthy food items' preferences were more likely (p.p. = 0.83) to be decreased rather than increased (p.p. = 0.17) due to PHS, one cannot rule out the possibility of no alterations.

Factor Session affected subjective food preference ratings neither as a main effect (H₀:SessionS3 = 0;mean = −0.06[−0.17, 0.05], sd = 0.05, p.p. = 0.96, BF₀₁ = 25.12), nor in interaction with PHS (H₀:SessionS3:ConditionPHS = 0;mean = −0.12[−0.27, 0.03], sd = 0.08, p.p. = 0.91, BF₀₁ = 10.06), food category (H₀:SessionS3:FoodItemHealthN+SessionS3:FoodItemHealthU = 0; mean = 0.04[−0.21, 0.29], sd = 0.13, p.p. = 0.96, BF₀₁ = 25.61), or in interaction with both PHS and food category (H₀:SessionS3:ConditionPHS:FoodItemHealthN+SessionS3:ConditionPHS:FoodItemHealthU = 0; mean = 0.23[−0.13, 0.59], sd = 0.18, p.p. = 0.90, BF₀₁ = 8.83).

Finally, healthy food items were preferred more than neutral items (H₊:FoodItemHealthN < 0; mean = −0.94[−1.41, −0.47], sd = 0.29, p.p.>0.99, BF₊₀ = 644.16), and more than unhealthy items (H₊:FoodItemHealthU < 0; mean = −1.22[−1.71, −0.73], sd = 0.30, p.p.>0.99, BF₊₀ = 3332.33). Also, neutral food items were probably preferred more than unhealthy items (H₊:FoodItemHealthU−FoodItemHealthN < 0; mean = −0.28[−0.78, 0.24], sd = 0.31, p.p. = 0.82, BF₊₀ = 4.66).

In addition, we assessed which fixed effect would enhance the predictive capability of the suggested model using PSIS-loo estimations. To check whether PSIS-loo estimations of the compared models are reliable, the full Preference Model Pareto k^ values were calculated (Figure 2E). All values were below the suggested (Vehtari et al., 2016; Magnusson et al., 2020) threshold of Pareto k^<0.7, ascertaining that the comparison can be trusted. PSIS-loo criteria showed that the addition of PHS and Healthiness would enhance model performance. Although adding Session enhanced PSIS-loo (Table 1), the improvement was below the standard error. Therefore, Preference Model 2 was preferred over the others. This outcome corroborates the results obtained from the full Preference Model, demonstrating that Session and its interactions with Healthiness or PHS did not affect food preferences.

To understand the effects of PHS, Session, and Healthiness on food choices in a realistic shopping simulation, we analyzed the results of the online supermarket task (Figure 4A) by applying the models specified in the Section 2.4. Data analysis. Notably, in the choice models, the number of chosen items per food item (i.e., a discrete-continuous variable) was used as the outcome. The full Choice Model (Equation 1) showed no divergent transition, all Rhat = 1.00, and all variables had bulk- and tail-effective sample sizes >2,000 and >5,000. Posterior checks showed that the negative binomial model simulations reasonably capture the features of the observed data, including distributions (Figure 4B), means of conditions (Figure 4C), and dispersion (Figure 4D).

After confirming the validity of the full Choice Model, the posteriors drawn from it were used to test our hypotheses (Figure 5). The results show that PHS increased choices of healthy food items (H₊:ConditionPHS>0; mean = 0.11[0.02, 0.19], sd = 0.05, p.p. = 0.98, BF₊₀ = 49.70). In contrast, PHS did not affect the choices of neutral items (H₀:ConditionPHS+ FoodItemHealthN:ConditionPHS = 0; mean = −0.05[−0.19, 0.08], sd = 0.07, p.p. = 0.98, BF₀₁ = 39.57). Finally, PHS probably decreased choices of unhealthy food items (H₊:ConditionPHS+ FoodItemHealthU:ConditionPHS < 0; mean = −0.13[−0.35, 0.09], sd = 0.14, p.p. = 0.85, BF₊₀ = 5.56). Similar to preference ratings, even though the results indicated that choices of healthy food items were increased by PHS, the evidence supporting the decrease in choices of unhealthy food items by PHS was not strong. Given that zero is included in the 95% confidence interval of the change in unhealthy food choices due to PHS, one should interpret this result with caution. That is, although this result indicates that choices for unhealthy food items were more likely (p.p. = 0.85) to decrease rather than increase (p.p. = 0.15) due to PHS, one should not rule out the possibility of no modulation.

As for preferences, Session did not affect food choice behavior, neither as a main effect (H₀:SessionS3 = 0;mean = −0.07[−0.16, 0.01], sd = 0.04, p.p. = 0.94, BF₀₁ = 14.42), nor in interaction with PHS (H₀:SessionS3:ConditionPHS = 0; mean = 0.03[−0.09, 0.15], sd = 0.06, p.p. = 0.97, BF₀₁ = 36.02), food category (H₀:SessionS3:FoodItemHealthN+SessionS3:FoodItemHealthU = 0; mean = 0.13[−0.12, 0.37], sd = 0.12, p.p. = 0.94, BF₀₁ = 16.76), or in interaction with both factors (H₀:SessionS3:ConditionPHS:FoodItemHealthN+SessionS3:ConditionPHS:FoodItemHealthU = 0; mean = −0.13[−0.48, 0.22], sd = 0.18, p.p. = 0.94, BF₀₁ = 15.71).

Finally, healthy food items were chosen more often than both neutral items (H₊:FoodItemHealthN < 0; mean = −0.70[−1.10, −0.30], sd = 0.24, p.p.>0.99, BF₊₀ = 299.75), and unhealthy items (H₊:FoodItemHealthU < 0; mean = −1.56[−1.94, −1.19], sd = 0.23, p.p.>0.99, BF₊₀>9999). Also, neutral food items were chosen more often than unhealthy ones (H₊:FoodItemHealthU−FoodItemHealthN < 0; mean = −0.87[−1.20, −0.53], sd = 0.20, p.p.>0.99, BF₊₀> 9999).

Additionally, we assessed which fixed effect would enhance the predictive capability of the suggested model using PSIS-loo estimations. To check whether PSIS-loo estimations of the compared models are reliable, the full Choice Model Pareto k^ values were calculated (Figure 4E). All values were below the suggested (Vehtari et al., 2016; Magnusson et al., 2020) threshold of Pareto k^<0.7, indicating that the comparison can be trusted. PSIS-loo criteria showed that adding PHS and Healthiness enhanced the model performance. However, adding Session deteriorated PSIS-loo (Table 2). Therefore, Choice Model 2 was considered the preferred model. This outcome corroborates the results obtained from the full Choice Model, showing that Session and its interactions did not affect food choices.

After analyzing the online supermarket and subjective rating tasks separately, we addressed whether the relationship between choice behavior and preferences was modulated by PHS, Session, and Healthiness of the food items. For this purpose, the choice-preference function was calculated (logistic regression hierarchical Bayesian models), where binary choices were modeled by using preferences as a regressor (Figure 6A). The full Choice-Preference Function (Equation 6) showed no divergent transitions, all Rhat = 1.00, and all variables had bulk- and tail-effective sample sizes >3,000 and >6,000. Posterior checks showed that the logistic model simulations reasonably captured the features of the observed data, including distributions (Figure 6C) and means of different conditions (Figure 6D).

After confirming the validity of the full Choice-Preference Function, the posteriors drawn from it were used to test our hypotheses (Figure 7A). Two sets of results are presented; the first set is related to the interaction of the experimental factors with preferences, which are associated with the modulation of slopes of the Choice~Preference relationship (Figure 6B). These results indicate the importance of preferences in choice behavior. The second set is related to the effects of the experimental factors on choices regardless of preferences, which is represented by the intercepts of the Choice~Preference relationship (Figure 6B). These results reveal general biases toward choosing items of a certain category in different conditions, regardless of preferences.

First, we focused on the effects of preferences on choice behavior in the different food categories (Figure 7B). For healthy items, increased preferences positively affected choices (H₊:Preferences>0; mean = 1.01[0.93, 1.09], sd = 0.05, p.p.>0.99, BF₊₀>9999). The relationship between preferences and choices was indistinguishable between the neutral and healthy food categories (H₀:Preferences:FoodItemHealthN = 0; mean = 0.02[−0.11, 0.16], sd = 0.07, p.p. = 0.97, BF₀₁ = 34.35. Interestingly, the importance of preferences in choice behavior was less pronounced for unhealthy compared to healthy food items (H₊:Preferences:FoodItemHealthU < 0; mean = −0.14[−0.24, −0.03], sd = 0.06, p.p. = 0.98, BF₊₀ = 61.31).

Further, participants were more likely to show a negative bias (i.e., diminished choice behavior regardless of preferences) for both neutral (H₊:FoodItemHealthN < 0; mean = −0.51[−1.23, 0.21], sd = 0.44, p.p. = 0.88, BF₊₀ = 7.18) and unhealthy items (H₊:FoodItemHealthU < 0; mean = −0.51[−1.18, 0.16], sd = 0.41, p.p. = 0.88, BF₊₀ = 8.32) as compared to healthy food items. However, there was no difference in choice bias for unhealthy compared to neutral items (H₀:FoodItemHealthU−FoodItemHealthN = 0; mean = 0.0[−0.81, 0.80], sd = 0.42, p.p. = 0.89, BF₀₁ = 8.23).

Second, we addressed whether PHS had altered the relationship between choice behavior and preferences (i.e., slopes) for the different food categories. Notably, PHS did not affect the relationship between choices and preferences for both healthy items (H₀:Preferences:ConditionPHS = 0; mean = −0.10[−0.23, 0.03], sd = 0.07, p.p. = 0.92, BF₀₁ = 11.24) as well as neutral items (H₀:Preferences:ConditionPHS + Preferences:FoodItemHealthN:ConditionPHS = 0; mean = −0.07[−0.21, 0.06], sd = 0.07, p.p. = 0.97, BF₀₁ = 28.43). In contrast, unhealthy items were more likely to be affected by preferences when PHS was activated compared to deactivated (H₊:Preferences:ConditionPHS + Preferences:FoodItemHealthU:ConditionPHS>0; mean = 0.21[0.10, 0.32], sd = 0.07, p.p.>0.99, BF₊₀ = 1110.11).

Also, when considering choice biases (i.e., intercepts), PHS+ compared to PHS- did not affect choice bias for healthy (H₀:ConditionPHS = 0; mean = 0.51[−0.29, 1.31], sd = 0.41, p.p. = 0.92, BF₀₁ = 11.24) or neutral items (H₀:ConditionPHS + FoodItemHealthN:ConditionPHS = 0; mean = −0.07[−0.21, 0.06], sd = 0.07, p.p. = 0.97, BF₀₁ = 28.43). In contrast, PHS+ induced a negative bias for unhealthy items compared to PHS- (H₊:ConditionPHS + FoodItemHealthU:ConditionPHS < 0; mean = −1.37[−2.10, −0.65], sd = 0.44, p.p.>0.99, BF₊₀ = 753.72).

Together, the results indicate that PHS affected the relationship between preferences and choices only for unhealthy food items (Figure 7B). These effects, however, are two-fold. PHS caused participants to reject unhealthy items more frequently regardless of preferences (i.e., a negative choice bias). Simultaneously, PHS made preferences more critical in participants' unhealthy choices (Figure 7B).

Finally, we checked which fixed effect would enhance the predictive capability of the suggested model using PSIS-loo estimations. To check whether PSIS-loo estimations of the compared models are reliable, the full Choice-Preference Function Pareto k^ values were calculated. All values were below the suggested (Vehtari et al., 2016; Magnusson et al., 2020) threshold (i.e., Pareto k^<0.7), ascertaining that the comparison can be trusted. PSIS-loo criteria showed that the addition of PHS and Healthiness enhanced model performance. However, adding Session deteriorated PSIS-loo (Table 3). Therefore, the Choice-Preference Function 2 was considered the preferred model, suggesting that Session and its interactions did not affect choice-preference relationships.

Two approaches were used to address whether hypnotizability scores predict changes in subjective ratings and choice behavior. First, the full models (Equation 1) were compared with models that did not contain random slopes but were otherwise identical to the full model. Second, a robust Bayesian correlation test was conducted to understand whether the changes in healthy, neutral, or unhealthy categories due to PHS were correlated with hypnotizability scores.

Regarding subjective preferences, the model without random slope was significantly worse than the full model (elpd^diff= -237.4, se(elpd^diff) = 24.1, BF₁₀>999), showing that hypnotizability scores are crucial for predicting participants' preferences. Further, the robust correlation test corroborated this result (Figures 8A–C), revealing that changes in preferences for healthy (ρ_mean = 0.232 [ 0.030, 0.423], sd = 0.100, p.p_ρ>0 = 0.98) and unhealthy items (ρ_mean = −0.202 [ −0.400, −0.010], sd = 0.100, p.p_{ρ < 0} = 0.97) were correlated with hypnotizability scores positively and negatively, respectively. However, the changes in preferences for the neutral food category were not significantly correlated with hypnotizability (ρ_mean = +0.148 [ −0.058, 0.347], sd = 0.104, p.p_ρ>0 = 0.88).

Also, regarding choice behavior in the shopping task, the model without random slope was significantly worse than the full model (elpd^diff= -66.4, se(elpd^diff) = 12.8, BF₁₀>999), showing that hypnotizability is crucial for predicting participants' choices. Additionally, the robust correlation test corroborated this result (Figures 8D–F), revealing that changes in choosing healthy (ρ_mean = 0.520 [0.358, 0.677], sd = 0.081, p.p_ρ>0>0.99) and unhealthy items (ρ_mean = −0.444 [−0.620, −0.272], sd = 0.090, p. p_{ρ < 0} = 0.99) were correlated positively and negatively with hypnotizability, respectively. However, the changes in neutral food category choices were not significantly correlated with hypnotizability (ρ_mean = 0.033 [ −0.182, 0.243], sd = 0.109, p.p_ρ>0 = 0.62).

Finally, for the choice-preference function, we compared the full models (Equation 6) with models without random slopes but otherwise identical to the full model. The model without random slope was significantly worse than the full model (elpd^diff= -23.9, se(elpd^diff) = 7.1, BF₁₀>999), revealing that hypnotizability scores are crucial for predicting the choice-preference function. Notably, as slopes and choice biases derived from the choice-preference function were the prediction of the Bayesian logistic model, using them for modeling the robust Bayesian correlation might have been misleading; therefore, we refrained from using this approach.