Introduction

Happiness is a central component of human experience, providing a “measure of right and wrong” and guiding actions undertaken to maximize well-being^1,2. Yet, humans often fail to do so as evidenced by the high prevalence of mood disorders such as depression and anxiety. It is therefore crucial to know what causes mood fluctuations to identify what promote happiness and what triggers mood disorders, and how.

Mood dynamics are strongly influenced by reward prediction error (RPE) — the discrepancy between expected and actual outcomes^3–9. The modulatory role of RPE is particularly prominent in uncertain environments, such as gambling scenarios, where it significantly impacts mood fluctuations^8,10–13. Despite the critical role of RPE-induced mood fluctuations in adaptive behavior^4,7,14,15, atypical mood dynamics are considered risk factors for the development of affective disorders^4,16–18. Specifically, depression, often associated with blunted emotional response^19,20, may suppress mood fluctuations^21–25. In contrast, anxiety, characterized by exaggerated responses to uncertainty²⁶, might intensify them^27,28. However, distinguishing the unique effects of depression and anxiety on mood dynamics presents a significant challenge, owing to their overlapping symptoms and entangled nature^29,30.

Recent advances have been made to understand the unique qualities and differential influences on decision-making based on the bifactor validation of a tripartite model of depression and anxiety^31,32, which segregates symptom variance into common, depression-specific, and anxiety-specific components^30,33,34. For example, Gagne et.al., (2022) has utilized bifactor analysis to demonstrate that depression negatively influences prior belief, while anxiety positively contributes to negative bias for belief updating³¹. Intriguingly, mood sensitivity to RPE seems intact in both patients with major depressive disorder (MDD) and individuals scoring high in depression questionnaires^12,25,35, contrary to the hypothesized decrease in mood patterns in depression²⁵. Individuals with anxiety not only show heightened vigilance before an outcome is known²⁶ but also assign greater precision to the information that resolves that uncertainty^36,37. This precision-weighting amplifies the affective influence of RPE, leading to larger mood shifts when outcomes deviate from expectations^38,39. Given the opposite impacts of depression and anxiety on mood fluctuations^23,24,27,28, an open possibility for the observed intact mood fluctuations²⁵ is their opposite roles in mood sensitivity to RPE, which may counteract each other. To test this hypothesis, we turn to the bifactor model to disentangle these interrelated influences.

This study utilizes a computational model of momentary mood in a gambling task involving five experiments and 2,043 participants who also completed a series of questionnaires, permitting bifactor analysis to disassociate influences from anxiety and depression-specific traits on mood fluctuations. We measured momentary mood by asking participants “How happy are you at the moment?”. This measurement has also been referred to as happiness or momentary subjective well-being^8,14,15,40. Although mood is thought to persist for hours, days, or even weeks^4,5,7,41, momentary mood, measured over the timescale in the laboratory setting, represents the accumulation of the impact of multiple events^{4,7,8,11–13,25,35,42} at the scale of minutes. Momentary well-being external validity is demonstrated e.g., through its association with depression symptoms^12,25. We first validate the tripartite model of depression and anxiety before exploring their specific roles in mood fluctuations (n = 901). Next, we measured mood sensitivity to RPE in a gambling task, and investigated its relation to anxiety vs. depression-specific traits based on the tripartite model in laboratory test (n = 44) and another two online experiment settings (n = 747/235). In the final experiment (n = 116), we confirmed these results in the clinical setting (i.e., patients with affective disorders), revealing dissociable roles of RPE in the contrasting mood dynamics of depression and anxiety.

Results

Experimental Protocol

After completing a battery of questionnaires³² (see Methods), participants performed a gambling task with momentary mood ratings^8,10,13. Within this task, subjects were asked to make decisions between certain vs. gamble options (2 possible outcomes, 50% probability for each). Participants were instructed to assess and rate their mood every 2-3 trials (Figure 1). Detailed participant demographics are outlined in Table 1. The choice (e.g., gambling rates) and mood data (e.g., the initial mood, mean mood, and mood variation) showed similar patterns with previous studies on measurements of momentary moods during the gambling task (Figure S2 & S3)^10,43. We also replicated classic mood-relevant effects^12,40: better mood after gain than loss and mood drifted over time (ps <0.001; Figure S4).

Figure 1.

Table 1.

To confirm model-based findings, we used the classic mood model assuming that momentary moods are contributed by the recency-weighted average of the chosen certain reward (CR), expected value of the chosen gamble (EV), and reward prediction error (RPE; Equation 1; Figure 1H)^8,13. RPE was defined as the difference between the obtained and expected value. We also incorporated a drift parameter to account for the gradual change in happiness over time ^40,42.

This model explained momentary moods well for all datasets (r²: mean ± SD = 0.67 ± 0.20 for the laboratory dataset, 0.69 ± 0.17 for the online dataset 1, and 0.64 ± 0.19 for the online dataset 2, and 0.47 ± 0.21 for the clinical dataset; see Supplementary Materials Note 2 and Note 5 for our model space; see Table S2 & Table S4 for model comparisons), with good performance for parameter recovery (Figure S5). For all datasets with the gambling task, we replicated previous mood model-based findings^8,13: 1) the RPE weight was significantly higher than the EV weight (ts > 3.84, ps < 0.001; Figure 1I), suggesting that moods are more sensitive to the prediction error of experiential outcome than the expectation of value; 2) the baseline mood parameter β₀ was positively correlated with the initial mood before the experiment (rs > 0.25, ps < 0.006), further validating this mood model. We also replicated previous depression-related findings²⁵: depression symptom measured by Beck Depression Inventory (BDI) was negatively correlated with the baseline mood parameter β₀ (r = -0.173, p < 0.001; Figure S6). In sum, these confirmatory results suggest 1) engagements of questionnaires and tasks for all included participants, 2) the important contribution of RPE to momentary mood fluctuations, and 3) robust relationships between depression measured by BDI and mood baseline.

Depression links to blunt mood fluctuations through hypo-sensitivity to RPE

We first examined how depression influences mood fluctuations and the underlying computational mechanism. It has been shown that depression and anxiety often co-occur at the symptom level^29,34,44,45, e.g., high correlation between depression measured by BDI and anxiety measured by the subscale of anxiety in the Trait Anxiety Inventory (r = 0.75, p < 0.001). To differentiate unique influence of anxiety and depression-specific factor, we applied the validated bifactor structure from the psychometric dataset (Figure 1C) to decompose depression/anxiety symptoms into three orthogonal components: the common factor, the anxiety-specific factor, and the depression-specific factor (-0.001 < rs < 0.001, ps = 1.000; see Supplementary Materials Note 1 for psychometric properties of the tripartite model of depression and anxiety in our sample; n = 901). To test the contribution of depression-specific loading on mood fluctuations, we performed correlation analyses between the depression-specific factor and mood variation (i.e., standard deviation of happiness ratings). We found convergent results across the laboratory dataset, the online dataset 1 and online dataset 2. Specifically, results showed significantly negative correlations of the depression-specific score with mood variation (rs < -0.13, ps < 0.041; Figure 2ABC). Model-based correlational analyses further showed significantly negative correlations between the depression-specific factor and mood sensitivity to RPE (β_RPE; rs < -0.14, ps <0.019; Figure 2EFG), which remained significant after controlling for gender, age, earning, and mood drift (ps < 0.035). These results hold with bootstrap validation, indicating reduced mood fluctuations and decreased impact of RPE on mood with depression loading. Given the high correlation between β_RPE and mood variation (rs > 0.67, ps < 0.001), we further conducted mediation analysis among the depression loading, β_RPE, and mood variation, with the assumption of the mediating effect of mood parameter of RPE on the association between depression and mood variation. Result supported our hypothesis (ps < 0.015; Figure 2I), suggesting that higher depression loading flats momentary mood variation by reducing sensitivity to RPE. See Table S7 for statistical values for each dataset. Note that this mediation analysis is in line with previous literature in computational psychiatry⁴⁶. Although both mood fluctuations and mood sensitivity to RPE are indeed derived from the same happiness data during the gambling task, these two measures quantify conceptually distinct aspects of mood dynamics: mood fluctuation captures the overall variability in mood ratings across trials, whereas mood sensitivity to RPE specifically quantifies mood sensitivity to prediction errors on a trial-by-trial basis. To further test whether the impact of depression on mood fluctuations was specific to RPE-based mood sensitivity, we conducted a linear regression against depression-specific factor with mood sensitivity to CR, EV, and RPE as regressors for the combined dataset (N = 1026). We observed deficient RPE-specific mood sensitivity with depression loading (CR: t = 0.274, p = 0.784; EV: t = -1.069, p = 0.285; RPE: t = -3.282, p = 0.001; Figure 2K).

Figure 2.

Anxiety relates to intensified mood fluctuations via hyper-sensitivity to RPE

We then examined how anxiety influences mood fluctuations. We observed signs of positive correlations of the anxiety-specific factor with mood variation (the laboratory dataset: r = 0.10, p = 0.531; the online dataset 1: r = 0.08, p = 0.026; the online dataset 2: r = 0.19, p = 0.004), and signs of positive correlations of the anxiety-specific factor with β_RPE (the laboratory dataset: r = 0.04, p = 0.820; the online dataset 1: r = 0.05, p = 0.216; the online dataset 2: r = 0.19, p = 0.004; Figure 2A-C & 2E-G). Note that the phrase “signs of positive correlations” was intended to describe the directionality (i.e., positive r values) of the observed relationships across datasets, regardless of their statistical significance, given inconsistent results at the statistical level. Comparison of correlations showed significant differences both between depression-mood variation and anxiety-mood variation associations (for the laboratory dataset: Z = -1.84, p = 0.033; for the online dataset 1: Z = -5.36, p < 0.001; for the online dataset 2: Z = -3.42, p < 0.001) and between depression-β_RPE and anxiety-β_RPE associations (for the laboratory dataset: Z = -1.77, p = 0.038; for the online dataset 1: Z = -3.67, p < 0.001; for the online dataset 2: Z = -4.00, p < 0.001; Figure 2A-C & 2E-G), suggesting different roles of depression and anxiety in mood fluctuations. Given that recent evidence suggested that reliable individual difference can be tested with large data size⁴⁷ and that anxiety spanned a wide variety of symptoms⁴⁸, we combined data from the laboratory dataset, online dataset 1, and the online dataset 2 (total N = 1026). Linear mixed-effect models against mood variation and β_RPE with all three factors, with dataset as a random factor, showed significant positive association between the anxiety-specific factor and mood variation (t = 3.46, p < 0.001), while significant negative association between the depression-specific factor and mood variation (t = -6.13, p < 0.001). Regarding RPE-based mood sensitivity, we found the anxiety-specific factor was significantly positively correlated with β_RPE (t = 2.60, p = 0.009), while the depression-specific factor was significantly negatively correlated with β_RPE (t = -5.30, p < 0.001). These results remained significant after controlling for gender, age, earning, and mood drift (ps < 0.001). Mediation analyses further showed that hyper-sensitivity of mood to RPE mediated higher mood fluctuations with anxiety loading (a×b = 0.055, 95% CI = [0.013, 0.097], p = 0.010; Figure 2J). Moreover, linear regression against anxiety-specific factor with mood sensitivity to CR, EV, and RPE as regressors showed RPE-specific mood hyper-sensitivity with anxiety loading (CR: t = -0.36, p = 0.718; EV: t = -0.35, p = 0.724; RPE: t = 2.19, p = 0.028; Figure 2L). To rule out potential confounds of subjective calibration of rating scales, for example, individuals with nonlinear utility functions (e.g., risk-seeking participants) could display disproportionately high mood responses for large relative to small wins, we conducted several complementary analyses, including re-analyzing two open datasets using similar risk-based decision-making tasks with repeated happiness ratings: Vanhasbroeck et al. (2021; n = 49) and Rutledge’s smartphone App dataset (n = 46,204). See Supplementary Note 3 for details. Collectively, individual differences in risk preference did not significantly affect the calibration of mood ratings or alter our primary findings regarding distinct mood dynamics in anxiety versus depression. Instead, these results possibly suggest dissociable processes for decision-making (i.e., value perception) and mood dynamics. Together, these results show that depression and anxiety play opposite roles in mood dynamics via RPE-specific mood sensitivity.

Clinical utility for deficit RPE-based mood fluctuations with depression

To test whether abnormalities of mood fluctuations driven by RPE can serve as a clinically relevant computational marker for depression and anxiety, we recruited patients with affective disorders (n = 116) to complete the battery of questionnaires and the gambling-momentary mood rating task (Figure 1). For demographic, psychological and clinical information, see Table 1 and Table S8. We observed significantly negative correlations of the depression-specific score with mood variation (r = -0.239, p = 0.009) and RPE-based mood parameter (r = -0.216, p = 0.020), which remained significant after controlling for demographic and clinical characteristics, earning, and mood drift (ps < 0.05). These results hold with bootstrap validation. Mediation analyses further showed that hypo-sensitivity of mood to RPE mediated lower mood fluctuations with depression loading (a×b = -0.141, 95% CI = [-0.261, -0.038], p = 0.021; Figure 3). However, we did not observe any significant correlation with anxiety (mood variation: r = -0.092, p = 0.327; RPE-based mood parameter: r = -0.095, p = 0.311).

Figure 3.

Exploratory analysis of the common factor

Given the theoretical relevance of the common factor—often linked to shared symptoms such as somatic complaints, sleep disturbances, and cognitive impairments³⁴—as well as the potential for non-linear associations with symptom severity, we conducted exploratory analyses to examine its relationship with choice and mood parameters in both healthy and clinical datasets. To ensure robustness and reduce the risk of false positives, we report only findings that were consistent across datasets. Model comparisons using BIC consistently favored linear over non-linear models in capturing associations between the common factor and parameters (Table 2). Specifically, we observed significant negative associations between the common factor and two key variables: the baseline mood parameter and risk attitude for gain (Figure 4). Note these parameters were not consistently related to either the depression-specific or the anxiety-specific factor (depression × baseline mood parameter : r = -0.12, p < 0.001 for the healthy dataset and r = -0.08, p = 0.934 for the clinical dataset; anxiety × baseline mood parameter : r = -0.14, p < 0.001 for the healthy dataset and r = -0.15, p = 0.104 for the clinical dataset; depression × risk attitude for gain : r = -0.02, p = 0.505 for the healthy dataset and r = -0.00, p = 0.961 for the clinical dataset; anxiety × risk attitude for gain : r = 0.01, p = 0.846 for the healthy dataset and r = 0.04, p = 0.688 for the clinical dataset). These findings suggest that higher levels of general internalizing psychopathology are associated with a lower affective setpoint and increased risk aversion, consistent with transdiagnostic features observed across mood and anxiety disorders.

Table 2.

Figure 4.

Discussion

Although atypical mood dynamics are obviously at the core of depression and anxiety^21,23,27,28, little is known about their underlying computational mechanisms. Our study offers computational insights into the differing impacts of depression and anxiety on mood fluctuations. Through the orthogonal decomposition of depression and anxiety, we were able to distinguish their unique effects on mood dynamics. Depression was found to be related with blunt mood fluctuations through a decrease in mood sensitivity to RPE, whereas anxiety was linked to intensified mood fluctuations via a heightened sensitivity to RPE. Of substantial note is our finding that we validated deficit mood sensitivity to RPE with depression in patients with affective disorders, identifying clinical utility for our affective computational markers. Moreover, the shared depression/anxiety component was linked to lower affective baseline and greater risk aversion.

Depression and anxiety, though often coexisting^29,30, have contrasting influences on mood dynamics, aligning with their core characterizers of mood problems^24,27,28. Our computational model not only validates the significant role of RPE in mood dynamics but also highlights the divergent mediating roles of RPE-induced mood sensitivity in the effects of depression and anxiety on mood fluctuations. The opposite impacts of depression and anxiety on mood sensitivity to RPE may complement the previous finding of intact RPE-induced mood fluctuation in depression^12,25,35. This further underscores the necessity of decomposing depression and anxiety for precise measurement in mood studies, which can enhance our understanding of their unique impacts on emotion processing and cognitive flexibility. For example, using bifactor analysis, Gagne et.al., (2020) has shown that the common factor, but not the anxiety-specific factor, contributes to maladaptation to environmental volatility³², which complemented previous findings that trait anxiety influenced inflexible adjustment to volatility⁴⁹.

This study bridges multiple fields of research on depression. Depression, or anhedonia, describes disability to feel pleasure⁵⁰. From the perspective of affective science, researchers used experience sampling technique across several weeks or months^5,7,27,51, showing flattened mood fluctuations in depression^23,24. Instead, in the field of decision making and learning, most studies adopted laboratory-based learning or gambling tasks^52,53, revealing alterations in reward function in individuals suffering from depression^52,53. However, how their reward processing transfers into aberrant hedonic experience remains largely unknown. Our study employed a gambling task with momentary mood ratings, allowing us to examine reward-induced mood dynamics. In line with previous literature from different fields^20,24, this study provides evidence for mood hypo-sensitivity to reward prediction error with depressive symptoms.

In addition to confirming the putative role of anxiety in intensified mood fluctuations^26–28, we provided its underlying computational account: heightened mood sensitivity to RPE. Our study provides a computational account of this phenomenon, showing that anxiety is associated with heightened mood sensitivity to RPE, but not to value expectation. Anxiety is marked by exaggerated anticipatory responses to uncertainty and excessive affective reactivity²⁶. Since RPE signals the resolution of uncertainty, our findings suggest a mechanistic pathway through which anxiety influences uncertain-resolved mood—by amplifying affective responses to unexpected outcomes. In this way, individuals with higher anxiety may exhibit a stronger need to resolve uncertainty⁴⁹, leading to increased mood reactivity to RPE. Moreover, our results were different to Browning et al. (2015)⁴⁹, who reported impaired learning from uncertainty in anxiety. However, the two findings may reflect different stages or aspects of processing: while Browning et al. focused on learning rate adaptation in response to environmental volatility, our study targets affective responsiveness to outcome-level surprises. Thus, it is possible that anxious individuals exhibit reduced cognitive flexibility in belief updating, yet simultaneously increased emotional reactivity to prediction errors—highlighting a dissociation between cognitive and affective systems. Notably, the pattern of heightened RPE sensitivity observed in the healthy population was not replicated in the clinical sample. This discontinuity may reflect non-linear or stage-dependent features of anxiety and depression, or potential floor effects in affective reactivity among patients with severe symptoms. Alternatively, it may suggest that dimensional models derived from healthy populations do not always generalize straightforwardly to clinical settings. Another possibility is the disruption of mood homeostasis in clinical population (a sign for negative correlation with anxiety)^39,54. In healthy individuals, opposing influences of depression and anxiety on mood variation may work in tandem to maintain emotional equilibrium. In contrast, individuals with affective disorders may lack the regulatory balance required to stabilize mood in the face of competing emotional signals.

The common factor—reflecting general internalizing psychopathology—was robustly and consistently associated with both a lower baseline mood (i.e., affective setpoint) and increased risk aversion for potential gains. Regarding the former, previous large-scale studies have established a reliable association between lower affective setpoint and elevated depressive symptoms, including individuals scoring high on the BDI and patients diagnosed with major depressive disorder (MDD)²⁵. Expanding on this, our bifactor approach decomposed depression and anxiety into three orthogonal components and revealed that only the common factor, not the depression- or anxiety-specific components, was significantly associated with a lower mood baseline. This finding suggests that it is general emotional distress—rather than core features such as anhedonia or pathological worry—that exerts a broader influence on individuals’ affective setpoints⁴. With respect to decision-making, prior literature has linked pathological anxiety with enhanced risk aversion⁵⁵. In line with this, our results again point to the common factor as the driving force, rather than anxiety-specific variance per se. This suggests that heightened risk aversion is a transdiagnostic feature of internalizing psychopathology, rather than uniquely attributable to anxiety. Notably, model comparison favored linear over non-linear associations, indicating that even subclinical levels of general internalizing symptoms can exert measurable influences on mood and decision processes. Taken together, these findings underscore the importance of incorporating general psychopathology dimensions into computational models of affect and choice.

Several limitations of the present study should be noted. First, although the r-to-z transformed correlation comparisons appeared more consistent than individual zero-order correlations for anxiety-related results, this pattern may suggest potential confounding due to scale-related variability—that is, differences in how participants use mood rating scales. While our additional analyses, including those conducted on two publicly available datasets with similar paradigms (Vanhasbroeck et al., 2021¹³, n = 49; Rutledge et al., n = 46,204), did not support this explanation (see Supplementary Note 3), future studies would benefit from task designs that better control for scale sensitivity and enhance mood responsiveness to risk, possibly by incorporating more emotionally salient or high-stakes decision contexts. Second, adolescence represents a critical developmental period for the emergence of emotional problems, and the transition from anxiety to depression is a well-documented trajectory during this stage. However, how affective computational parameters such as mood sensitivity to RPE evolve during this transition remains unclear. Specifically, questions such as whether mood homeostasis becomes more vulnerable in adolescence, or whether the mechanisms underlying mood regulation shift qualitatively during this period, are of high relevance. Addressing these developmental questions could inform preventive strategies and improve early interventions aimed at reducing maladaptive emotional reactivity—particularly in adolescents who are at heightened risk for internalizing psychopathology.

In conclusion, our findings emphasize the distinct effects of depression and anxiety on mood fluctuations, underlining the essential role of symptom variance partition in affective science. The specific association we identified between depression and RPE-induced mood sensitivity has significant implications for the development of computational mechanism-based treatments for affective disorders, providing a promising direction for future research and clinical treatment.

Methods

A total of 2634 participants via online platforms (questionnaires from https://www.wjx.cn and tasks from https://www.naodao.com) took part in four experiments, including a psychometric experiment, a laboratory experiment, an online replication experiment, and an online intervention experiment. The study was approved by the Ethics Committee of Beijing Normal University. Written informed consent was obtained from all participants before each experiment. Finally, participants were paid for the basic participation fee and a bonus based on their task performance, which was instructed before the experiment.

Participants

Data from 1145 participants was collected in the psychometric experiment. Participants were excluded if 1) they failed any of the attentional checks (4 items); 2) they made the same choices for all items; 3) they responded with extreme inconsistency in two similar questionnaires (difference in z-scores out of ±2). The final sample for the psychometric dataset consisted of 901 participants. We recruited 59, 1087, and 343 participants for the laboratory experiment, the online replication experiment, and the online intervention experiment, respectively. Participants were excluded if 1) they failed any of the attentional checks in questionnaires (4 items) 2) they failed any of the catch trials (4 trials) and 3) they responded too fast (reaction time for decision < 200 ms) in more than 10% of the 90 trials. The final sample for the laboratory dataset, the online dataset 1, and the online dataset 2 included 44, 747, and 235 participants, separately. See Table 1 for demographic information.

Measurements of anxiety and depression

In line with previous literature orthogonally decomposing anxiety and depression^31,32, participants completed a set of Chinese version questionnaires of anxiety and depression. These measurements included the Mood and Anxiety Symptoms Questionnaire (MASQ; 62 items)⁵⁶, the Trait subscale of the State-Trait Anxiety Inventory (TAI; 20 items)⁵⁷, the Beck Depression Inventory (BDI; 21 items)⁵⁸, the Penn State Worry Questionnaire (PSWQ; 16 items)⁵⁹, the Center for Epidemiologic Studies Depression Scale (CESD; 20 items)⁶⁰, and the Big Five Inventory-2 (BFI; 60 items)⁶¹. Each item in the TAI, BDI, and CESD was rated on a four-point Likert scale, while five-point Likert rating scale was used for the MASQ, PSWQ, and BFI. There were four items for attentional checks, which required the participants to make a specific choice and were embedded in the entire measurements, e.g., “please select the second option for this item”.

Patients with affective disorders

We also recruited 121 patients with affective disorder, including major depressive disorder, anxiety disorder, and bipolar disorder. After excluding participants without mood variance, the final sample included 116 patients. See Table 1 and Table S8 for details.

Experimental Procedure

Participants were asked to make a choice between a certain option and a gamble (50% probability for each outcome) and to rate their momentary moods. Before the task protocol, participants were asked to rate their current happiness that we consider as their initial mood. At the beginning of the task, participants were endowed with 500 points. Each trial started with two options (a gamble option and a certain option) that presented randomly on each side (Figure 1F). Upon response, the chosen option would be highlighted in yellow for 0.5 s. Then the corresponding outcome at the screen center was presented for 1 s, followed by a fixation cross with a random duration (0.6~1.4 s). If the gamble was chosen, participants had equal probability to obtain each outcome. The obtained outcome would be accumulated to their total score, which was presenting at the top-right concern. Every 2~3 trials, participants rated “how happy are you at this moment” from 0 (very unhappy) to 100 (very happy) by moving a slider anchoring at midpoint (i.e., 50). Upon identifying their current mood, a fixation cross was presented with a random duration (0.6~1.4 s). Please note that the slider in the laboratory experiment was anchoring at the midpoint, i.e., 50. To exclude the potential anchoring effect, we did not set an anchor in the online replication experiment to check the robustness of our findings. This task consisted of 90 randomly presented trials, including 30 mixed trials, 30 gain trials, and 30 loss trials. In mixed trials, participants made a choice between a certain amount 0 and a gamble with a gain amount {40, 45, or 75} and a loss amount determined by a multiplier {0.2, 0.34, 0.5, 0.64, 0.77, 0.89, 1, 1.1, 1.35, or 2} on the gain amount. In gain trials, there was a certain gain amount {35, 45, or 55} and a gamble with 0 and a gain amount determined by a multiplier {1.68, 1.82, 2, 2.22, 2.48, 2.8, 3.16, 3.6, 4.2, or 5} on the certain gain amount. In loss trials, there were a certain loss amount {-35, -45, or -55} and a gamble with 0 and a loss amount determined by a multiplier {1.68, 1.82, 2, 2.22, 2.48, 2.8, 3.16, 3.6, 4.2, or 5} on the certain loss amount. Many amounts and multipliers were used to accommodate a wide range of risk and loss sensitivity, as in previous literature^8,10. We also set 4 trials embedded in the entire task for attentional checks. For example, participants were asked to make a choice between a certain gain 20 and a gamble 35/55, where the correct response for this trial was the gamble choice. All experimental procedures were programmed using Psychopy3 (2021.2.3) builder and hosted on https://www.naodao.com.

Model fitting

We fit model parameters by using the method of maximum likelihood estimation (MLE) with fmincon function of MATLAB (version R2015a) at the individual level. To avoid local minimum, we ran this optimization function with random starting locations 50 times. Bayesian information criteria (BIC) were used to compare model fits.

Mediation model

The mediation model was conducted using a sequence of regression steps. First, a regression of the independent variable depression on the dependent variable mood variation was performed; Second, a regression of the independent variable depression on the mediator variable β_RPE was performed; Next, a regression of the independent variable depression and the mediator variable on the dependent variable mood variation β_RPE was performed; Finally, the indirect and total effects were estimated.

Statistical analysis

We performed correlations among depression/anxiety factor scores, behavioral indices, and parameters using Matlab R2015a. To further validate our main correlational results, the percentile bootstrap CIs were estimated using the R package ‘boot’ and 5000 bootstrap resamples. We used an online calculator (https://www.psychometrica.de/correlation.html) to examine differences between two correlation coefficients. All reported tests are two-tailed. We set the significance level at p = 0.05.

Data availability

The data and code that support the findings of this study are available from https://github.com/ZhihaoWangpsyer/depression_anxiety_mood.

Acknowledgements

This study was funded by the National Natural Science Foundation of China (32371104, 31920103009 and 32271093), the Major Project of National Social Science Foundation (20&ZD153), the National Science and Technology Innovation 2030 Major Program (2022ZD0205500), Beijing Natural Science Foundation (Z230010), Shenzhen-Hong Kong Institute of Brain Science – Shenzhen Fundamental Research Institutions (2023SHIBS0003).

Additional files

Supplementary material

Additional information

Funding

MOST | National Natural Science Foundation of China (NSFC) (32371104)

• Yuejia Luo